diff --git a/build/Backlinks.hs b/build/Backlinks.hs index 85da9a3..e364b81 100644 --- a/build/Backlinks.hs +++ b/build/Backlinks.hs @@ -200,6 +200,7 @@ normaliseUrl url = allContent :: Pattern allContent = "content/essays/*.md" + .||. "content/essays/*/index.md" .||. "content/blog/*.md" .||. "content/poetry/*.md" .||. "content/fiction/*.md" diff --git a/build/Citations.hs b/build/Citations.hs index 0c55cc1..a99aad9 100644 --- a/build/Citations.hs +++ b/build/Citations.hs @@ -50,11 +50,11 @@ import Text.Pandoc.Walk -- replaced with numbered superscripts and no bibliography div, -- @citedHtml@ is the inline-cited references HTML, and @furtherHtml@ is -- the further-reading-only references HTML (each empty when absent). -applyCitations :: [Text] -> Pandoc -> IO (Pandoc, Text, Text) -applyCitations frKeys doc +applyCitations :: [Text] -> Text -> Pandoc -> IO (Pandoc, Text, Text) +applyCitations frKeys bibPath doc | not (hasCitations frKeys doc) = return (doc, "", "") | otherwise = do - let doc1 = injectMeta frKeys doc + let doc1 = injectMeta frKeys bibPath doc processed <- runIOorExplode $ processCitations doc1 let (body, citedHtml, furtherHtml) = transformAndExtract frKeys processed return (body, citedHtml, furtherHtml) @@ -79,13 +79,13 @@ hasCitations frKeys doc = -- --------------------------------------------------------------------------- -- | Inject default bibliography / CSL paths and nocite for further-reading. -injectMeta :: [Text] -> Pandoc -> Pandoc -injectMeta frKeys (Pandoc meta blocks) = +injectMeta :: [Text] -> Text -> Pandoc -> Pandoc +injectMeta frKeys bibPath (Pandoc meta blocks) = let meta1 = if null frKeys then meta else insertMeta "nocite" (nociteVal frKeys) meta meta2 = case lookupMeta "bibliography" meta1 of Nothing -> insertMeta "bibliography" - (MetaString "data/bibliography.bib") meta1 + (MetaString bibPath) meta1 Just _ -> meta1 meta3 = case lookupMeta "csl" meta2 of Nothing -> insertMeta "csl" diff --git a/build/Compilers.hs b/build/Compilers.hs index 616ebf8..6c5a5e3 100644 --- a/build/Compilers.hs +++ b/build/Compilers.hs @@ -12,7 +12,7 @@ module Compilers ) where import Hakyll -import Hakyll.Core.Metadata (lookupStringList) +import Hakyll.Core.Metadata (lookupStringList, lookupString) import Text.Pandoc.Definition (Pandoc (..), Block (..), Inline (..)) import Text.Pandoc.Options (ReaderOptions (..), WriterOptions (..), @@ -142,10 +142,11 @@ essayCompilerWith rOpts = do ident <- getUnderlying meta <- getMetadata ident let frKeys = map T.pack $ fromMaybe [] (lookupStringList "further-reading" meta) + let bibPath = T.pack $ fromMaybe "data/bibliography.bib" (lookupString "bibliography" meta) -- Run citeproc, transform citation spans → superscripts, extract bibliography. (pandocWithCites, bibHtml, furtherHtml) <- unsafeCompiler $ - Citations.applyCitations frKeys (itemBody pandocItem) + Citations.applyCitations frKeys bibPath (itemBody pandocItem) -- Inline SVG score fragments and data visualizations (both read files -- relative to the source file's directory). diff --git a/build/Contexts.hs b/build/Contexts.hs index 9384070..e51981b 100644 --- a/build/Contexts.hs +++ b/build/Contexts.hs @@ -22,6 +22,8 @@ import Data.Time.Format (formatTime, defaultTimeLocale) import System.FilePath (takeDirectory, takeFileName) import Text.Read (readMaybe) import qualified Data.Text as T +import Text.Pandoc (runPure, readMarkdown, writeHtml5String, Pandoc(..), Block(..), Inline(..)) +import Text.Pandoc.Options (WriterOptions(..), HTMLMathMethod(..)) import Hakyll import Hakyll.Core.Metadata (lookupStringList) import Authors (authorLinksField) @@ -120,12 +122,36 @@ pageScriptsField = listFieldWith "page-scripts" ctx $ \item -> do where ctx = field "script-src" (return . itemBody) +-- --------------------------------------------------------------------------- +-- Abstract field +-- --------------------------------------------------------------------------- + +-- | Renders the abstract using Pandoc to support Markdown and LaTeX math. +-- Strips the outer

tag if the abstract is a single paragraph. +abstractField :: Context String +abstractField = field "abstract" $ \item -> do + meta <- getMetadata (itemIdentifier item) + case lookupString "abstract" meta of + Nothing -> fail "no abstract" + Just src -> do + let pandocResult = runPure $ do + doc <- readMarkdown defaultHakyllReaderOptions (T.pack src) + let doc' = case doc of + Pandoc m [Para ils] -> Pandoc m [Plain ils] + _ -> doc + let wOpts = defaultHakyllWriterOptions { writerHTMLMathMethod = KaTeX "" } + writeHtml5String wOpts doc' + case pandocResult of + Left err -> fail $ "Pandoc error rendering abstract: " ++ show err + Right html -> return (T.unpack html) + siteCtx :: Context String siteCtx = constField "site-title" "Levi Neuwirth" <> constField "site-url" "https://levineuwirth.org" <> buildTimeField <> pageScriptsField + <> abstractField <> defaultContext -- --------------------------------------------------------------------------- diff --git a/build/Filters/Links.hs b/build/Filters/Links.hs index e882fb6..326b78f 100644 --- a/build/Filters/Links.hs +++ b/build/Filters/Links.hs @@ -6,7 +6,7 @@ -- * Adds @class="link-external"@ to any link whose URL starts with -- @http://@ or @https://@ and is not on the site's own domain. -- * Adds @data-link-icon@ / @data-link-icon-type@ attributes for --- per-domain brand icons (wikipedia, arxiv, doi, github, external). +-- per-domain brand icons (see 'domainIcon' for the full list). -- * Adds @target="_blank" rel="noopener noreferrer"@ to external links. module Filters.Links (apply) where @@ -61,11 +61,34 @@ isExternal url = -- | Icon name for the link, matching a file in /images/link-icons/.svg. domainIcon :: Text -> Text domainIcon url - | "wikipedia.org" `T.isInfixOf` url = "wikipedia" - | "arxiv.org" `T.isInfixOf` url = "arxiv" - | "doi.org" `T.isInfixOf` url = "doi" - | "github.com" `T.isInfixOf` url = "github" - | otherwise = "external" + -- Scholarly / reference + | "wikipedia.org" `T.isInfixOf` url = "wikipedia" + | "arxiv.org" `T.isInfixOf` url = "arxiv" + | "doi.org" `T.isInfixOf` url = "doi" + | "worldcat.org" `T.isInfixOf` url = "worldcat" + | "orcid.org" `T.isInfixOf` url = "orcid" + | "archive.org" `T.isInfixOf` url = "internet-archive" + -- Code / software + | "github.com" `T.isInfixOf` url = "github" + | "tensorflow.org" `T.isInfixOf` url = "tensorflow" + -- AI companies + | "anthropic.com" `T.isInfixOf` url = "anthropic" + | "openai.com" `T.isInfixOf` url = "openai" + -- Social / media + | "twitter.com" `T.isInfixOf` url = "twitter" + | "x.com" `T.isInfixOf` url = "twitter" + | "reddit.com" `T.isInfixOf` url = "reddit" + | "youtube.com" `T.isInfixOf` url = "youtube" + | "youtu.be" `T.isInfixOf` url = "youtube" + | "tiktok.com" `T.isInfixOf` url = "tiktok" + | "substack.com" `T.isInfixOf` url = "substack" + | "news.ycombinator.com" `T.isInfixOf` url = "hacker-news" + -- News + | "nytimes.com" `T.isInfixOf` url = "new-york-times" + -- Institutions + | "nasa.gov" `T.isInfixOf` url = "nasa" + | "apple.com" `T.isInfixOf` url = "apple" + | otherwise = "external" -- | Percent-encode characters that would break a @?file=@ query-string value. -- Slashes are intentionally left unencoded so root-relative paths remain diff --git a/build/Site.hs b/build/Site.hs index b24d550..313c29a 100644 --- a/build/Site.hs +++ b/build/Site.hs @@ -5,7 +5,7 @@ module Site (rules) where import Control.Monad (filterM) import Data.List (intercalate, isPrefixOf) import Data.Maybe (fromMaybe) -import System.FilePath (takeDirectory, takeFileName) +import System.FilePath (takeDirectory, takeFileName, replaceExtension) import Hakyll import Authors (buildAllAuthors, applyAuthorRules) import Backlinks (backlinkRules) @@ -19,6 +19,10 @@ import Tags (buildAllTags, applyTagRules) import Pagination (blogPaginateRules) import Stats (statsRules) +-- All essays: flat files and directory-based (with co-located assets). +allEssays :: Pattern +allEssays = "content/essays/*.md" .||. "content/essays/*/index.md" + -- Poems inside collection subdirectories, excluding their index pages. collectionPoems :: Pattern collectionPoems = "content/poetry/*/*.md" .&&. complement "content/poetry/*/index.md" @@ -172,17 +176,28 @@ rules = do >>= relativizeUrls -- --------------------------------------------------------------------------- - -- Essays + -- Essays — flat (content/essays/foo.md → essays/foo.html) and + -- directory-based (content/essays/slug/index.md → essays/slug/index.html) -- --------------------------------------------------------------------------- - match "content/essays/*.md" $ do - route $ gsubRoute "content/essays/" (const "essays/") - `composeRoutes` setExtension "html" + match allEssays $ do + route $ customRoute $ \ident -> + let fp = toFilePath ident + in if takeFileName fp == "index.md" + then replaceExtension (drop 8 fp) "html" + else "essays/" ++ replaceExtension (takeFileName fp) "html" compile $ essayCompiler >>= saveSnapshot "content" >>= loadAndApplyTemplate "templates/essay.html" essayCtx >>= loadAndApplyTemplate "templates/default.html" essayCtx >>= relativizeUrls + -- Static assets co-located with directory-based essays (figures, data, PDFs, …) + match ("content/essays/**" + .&&. complement "content/essays/*.md" + .&&. complement "content/essays/*/index.md") $ do + route $ gsubRoute "content/" (const "") + compile copyFileCompiler + -- --------------------------------------------------------------------------- -- Blog posts -- --------------------------------------------------------------------------- @@ -300,7 +315,7 @@ rules = do create ["essays/index.html"] $ do route idRoute compile $ do - essays <- recentFirst =<< loadAll ("content/essays/*.md" .&&. hasNoVersion) + essays <- recentFirst =<< loadAll (allEssays .&&. hasNoVersion) let ctx = listField "essays" essayCtx (return essays) <> constField "title" "Essays" @@ -316,7 +331,7 @@ rules = do create ["new.html"] $ do route idRoute compile $ do - let allContent = ( "content/essays/*.md" + let allContent = ( allEssays .||. "content/blog/*.md" .||. "content/fiction/*.md" .||. allPoetry @@ -349,7 +364,7 @@ rules = do return $ any (\t -> t == p || (p ++ "/") `isPrefixOf` t) ts portalList name p = listField name essayCtx $ do - essays <- loadAll ("content/essays/*.md" .&&. hasNoVersion) + essays <- loadAll (allEssays .&&. hasNoVersion) posts <- loadAll ("content/blog/*.md" .&&. hasNoVersion) fiction <- loadAll ("content/fiction/*.md" .&&. hasNoVersion) poetry <- loadAll (allPoetry .&&. hasNoVersion) @@ -379,7 +394,7 @@ rules = do create ["random-pages.json"] $ do route idRoute compile $ do - essays <- loadAll ("content/essays/*.md" .&&. hasNoVersion) :: Compiler [Item String] + essays <- loadAll (allEssays .&&. hasNoVersion) :: Compiler [Item String] posts <- loadAll ("content/blog/*.md" .&&. hasNoVersion) :: Compiler [Item String] fiction <- loadAll ("content/fiction/*.md" .&&. hasNoVersion) :: Compiler [Item String] poetry <- loadAll ("content/poetry/*.md" .&&. hasNoVersion) :: Compiler [Item String] @@ -395,7 +410,7 @@ rules = do compile $ do posts <- fmap (take 30) . recentFirst =<< loadAllSnapshots - ( ( "content/essays/*.md" + ( ( allEssays .||. "content/blog/*.md" .||. "content/fiction/*.md" .||. allPoetry diff --git a/cabal.project.freeze b/cabal.project.freeze index 7ed9858..8e79520 100644 --- a/cabal.project.freeze +++ b/cabal.project.freeze @@ -16,7 +16,7 @@ constraints: any.Glob ==0.10.2, any.asn1-parse ==0.9.5, any.asn1-types ==0.3.4, any.assoc ==1.1.1, - any.async ==2.2.5, + any.async ==2.2.6, any.attoparsec ==0.14.4, any.attoparsec-aeson ==2.2.0.0, any.auto-update ==0.1.6, diff --git a/content/essays/where-does-simd-help-post-quantum-cryptography/figures/cliffs_delta_heatmap.py b/content/essays/where-does-simd-help-post-quantum-cryptography/figures/cliffs_delta_heatmap.py new file mode 100644 index 0000000..02ede88 --- /dev/null +++ b/content/essays/where-does-simd-help-post-quantum-cryptography/figures/cliffs_delta_heatmap.py @@ -0,0 +1,43 @@ +import sys +import csv +import numpy as np + +sys.path.insert(0, 'tools') +from viz_theme import apply_monochrome, save_svg + +apply_monochrome() +import matplotlib.pyplot as plt + +def read_data(filepath): + ops = [] + matrix = [] + with open(filepath, 'r') as f: + reader = csv.DictReader(f) + for row in reader: + ops.append(row['op']) + matrix.append([float(row['m512']), float(row['m768']), float(row['m1024'])]) + return ops, np.array(matrix) + +filepath = "content/essays/where-does-simd-help-post-quantum-cryptography/figures/data/cliffs_delta.csv" +ops, matrix = read_data(filepath) +labels = ['ML-KEM-512', 'ML-KEM-768', 'ML-KEM-1024'] + +fig, ax = plt.subplots(figsize=(6, 5)) +im = ax.imshow(matrix, cmap='Greys', vmin=0.9, vmax=1.0) + +ax.set_xticks(np.arange(len(labels))) +ax.set_yticks(np.arange(len(ops))) +ax.set_xticklabels(labels) +display_ops = [op.replace('gena', 'gen_a') for op in ops] +ax.set_yticklabels(display_ops) + +plt.setp(ax.get_xticklabels(), rotation=45, ha="right", rotation_mode="anchor") + +for i in range(len(ops)): + for j in range(len(labels)): + val = matrix[i, j] + text_color = "white" if val > 0.95 else "black" + ax.text(j, i, f"{val:.3f}", ha="center", va="center", color=text_color) + +ax.set_title("Cliff's delta (ref vs. avx2)") +save_svg(fig) diff --git a/content/essays/where-does-simd-help-post-quantum-cryptography/figures/data/cliffs_delta.csv b/content/essays/where-does-simd-help-post-quantum-cryptography/figures/data/cliffs_delta.csv new file mode 100644 index 0000000..e3a25ce --- /dev/null +++ b/content/essays/where-does-simd-help-post-quantum-cryptography/figures/data/cliffs_delta.csv @@ -0,0 +1,10 @@ +op,m512,m768,m1024 +INVNTT,1.000,1.000,1.000 +basemul,1.000,1.000,1.000 +frommsg,1.000,1.000,1.000 +NTT,1.000,1.000,1.000 +iDec,1.000,1.000,1.000 +iEnc,1.000,1.000,1.000 +iKeypair,1.000,1.000,1.000 +gena,1.000,1.000,1.000 +noise,1.000,1.000,0.999 diff --git a/content/essays/where-does-simd-help-post-quantum-cryptography/figures/data/cross_param.csv b/content/essays/where-does-simd-help-post-quantum-cryptography/figures/data/cross_param.csv new file mode 100644 index 0000000..a0259ac --- /dev/null +++ b/content/essays/where-does-simd-help-post-quantum-cryptography/figures/data/cross_param.csv @@ -0,0 +1,5 @@ +op,m512_sp,m512_elo,m512_ehi,m768_sp,m768_elo,m768_ehi,m1024_sp,m1024_elo,m1024_ehi +frommsg,45.642857142857146,0.0,0.0,49.15384615384615,0.0,0.0,55.38461538461539,0.0,0.0 +INVNTT,56.26086956521739,0.0,0.0,52.22826086956522,0.0,0.010869565217390686,50.49514563106796,0.009708737864080774,0.0 +basemul,52.04054054054054,0.0,0.7128841169937061,47.577586206896555,0.0,0.0,41.63333333333333,0.0,0.0 +NTT,35.526315789473685,0.010526315789476826,2.395032525133054,39.39080459770115,0.44762277951932816,0.0,34.58585858585859,0.010101010101010388,0.3631210059781438 diff --git a/content/essays/where-does-simd-help-post-quantum-cryptography/figures/data/decomp_mlkem1024.csv b/content/essays/where-does-simd-help-post-quantum-cryptography/figures/data/decomp_mlkem1024.csv new file mode 100644 index 0000000..949c0f2 --- /dev/null +++ b/content/essays/where-does-simd-help-post-quantum-cryptography/figures/data/decomp_mlkem1024.csv @@ -0,0 +1,10 @@ +op,refnv_sp,refnv_elo,refnv_ehi,ref_sp,ref_elo,ref_ehi,avx2_sp,avx2_elo,avx2_ehi +INVNTT,3.6937872667820737,0.0,0.0001923446816691765,3.6923668525283597,0.0,0.0008062243947173364,186.44660194174756,0.0,0.00970873786408788 +basemul,3.209016393442623,6.209637357201814e-05,0.00012419274714359219,3.4479583666933546,0.00013344008540183694,0.00013344008540183694,143.55,0.005555555555559977,0.005555555555531555 +frommsg,3.0156494522691704,0.0,0.0,2.676388888888889,0.0,0.0,148.23076923076923,0.0,0.0 +NTT,3.691742580076403,0.0010845307227014267,0.0002938583602705158,3.6691004672897196,0.001071270209427766,0.0010718961341775746,126.8989898989899,0.0,1.3050917336631755 +iDec,3.5713012771855714,0.00023570612000023416,0.00015086802895014628,3.690161977834612,0.0005032782539924341,0.00046931032063479705,114.75503711558855,0.0010604453870683983,0.0010604453870541874 +iEnc,3.084863236932217,0.0001782560024712332,0.00016342197515761825,3.21233254333646,0.00035364887129318845,0.00028601070699840747,30.157900043693072,0.0029733062283590073,0.001753088869445918 +iKeypair,3.049990457461021,0.00022319698359352103,0.00019792531427453852,3.207066542768769,0.0006512941219742885,0.0005064778000369863,26.020352541412997,0.0025143592087069067,0.0010972674500919766 +gena,2.6965550354099146,0.000484369799391704,0.00048237643023396615,2.7162479142988416,0.0006808616189104555,0.0007206686696927811,12.97504909321936,0.0031123799730270463,0.0032871286177282855 +noise,2.977777777777778,0.0,0.0,3.4190382728164868,0.0,0.0033585837650456085,4.070093457943925,0.0,0.0 diff --git a/content/essays/where-does-simd-help-post-quantum-cryptography/figures/data/decomp_mlkem512.csv b/content/essays/where-does-simd-help-post-quantum-cryptography/figures/data/decomp_mlkem512.csv new file mode 100644 index 0000000..34706b6 --- /dev/null +++ b/content/essays/where-does-simd-help-post-quantum-cryptography/figures/data/decomp_mlkem512.csv @@ -0,0 +1,10 @@ +op,refnv_sp,refnv_elo,refnv_ehi,ref_sp,ref_elo,ref_ehi,avx2_sp,avx2_elo,avx2_ehi +INVNTT,4.082526315789473,0.0,0.00021052631579010495,3.7465224111282844,0.0,0.00019319938176209916,210.7826086956522,0.0,0.010869565217376476 +basemul,3.2770963704630787,0.0016397780187453748,0.0024627477733942804,3.3996364580628406,0.0,0.0,176.9189189189189,0.0,2.4235468345057427 +frommsg,3.0109546165884193,0.0,0.0,3.0109546165884193,0.0,0.0,137.42857142857142,0.0,0.0 +NTT,3.6866764275256223,0.002157843972798279,0.0010798700725032084,3.7303703703703706,0.0,0.0011056225164107758,132.52631578947367,0.0,8.934358367829702 +iDec,3.742600033957779,0.0006353440528448218,0.00042368257587099833,3.79609644087256,0.0002753054612747441,0.0002753370710646408,133.0543259557344,0.0020120724346099905,0.0020120724346099905 +iEnc,3.4432478262438213,0.0002504959891131975,0.00030259771432428195,3.530109117810246,0.00039168308874293345,0.00032646898342836295,35.20992436819775,0.0063094659476519155,0.0011068068622037686 +iKeypair,3.1751089014071656,9.92090538622925e-05,0.00021725496542801537,3.351041039836322,0.00032261099326946763,0.0003142150864068327,27.8438,0.005767606478706,0.005769913982796027 +gena,2.716878579054644,0.00065187098010977,0.0003882364359895085,2.743237945903567,0.0002940023520188184,0.00046488659667787147,12.781735159817352,0.001369863013698236,0.001369863013698236 +noise,3.1366495140080044,0.0017923711508616158,0.0,3.433041301627034,0.0,0.0006257822277846437,4.766290182450043,0.0,0.0041446001586527 diff --git a/content/essays/where-does-simd-help-post-quantum-cryptography/figures/data/decomp_mlkem768.csv b/content/essays/where-does-simd-help-post-quantum-cryptography/figures/data/decomp_mlkem768.csv new file mode 100644 index 0000000..165c2a4 --- /dev/null +++ b/content/essays/where-does-simd-help-post-quantum-cryptography/figures/data/decomp_mlkem768.csv @@ -0,0 +1,10 @@ +op,refnv_sp,refnv_elo,refnv_ehi,ref_sp,ref_elo,ref_ehi,avx2_sp,avx2_elo,avx2_ehi +INVNTT,3.9386252045826513,0.00020458265139122744,0.00020458265139122744,4.006659729448491,0.0008336786786200534,0.00020811654526564638,209.2608695652174,0.010869565217404897,0.010869565217376476 +basemul,3.306184521797905,0.02605040612313525,0.002795691291897384,3.545207465120493,0.0,0.0,168.67241379310346,0.0,0.0 +frommsg,2.6708333333333334,0.0,0.0,3.0093896713615025,0.0,0.0,147.92307692307693,0.0,0.0 +NTT,3.6989152741131632,0.0010840900568913625,0.0,3.681645754304056,0.0,0.0,145.02298850574712,1.6479885057471222,0.0 +iDec,3.6437147040368125,0.00019424892094210833,0.0003467108483481418,3.800139609964661,0.0003315569175033062,0.00016580015750289334,132.98167938931297,0.001526717557254642,0.003053435114509284 +iEnc,3.3056977990451344,0.00017231513226034778,0.00016363191105694952,3.48133030817818,0.00022700732330438456,0.00021029337701561346,32.81504567436862,0.004063512322623808,0.0006448146157964629 +iKeypair,3.109574915272049,0.00020791977755951763,0.00025167432332651174,3.2525126922733425,0.00022163529575136565,0.000286955967172986,24.668559816590246,0.0031435406706883384,0.0007294706127538575 +gena,2.7088029828997557,0.0007052965244342957,0.0005931348088656918,2.69161485393067,0.0005617516864933059,0.0005061000727368814,10.337667648020936,0.002917034774819527,0.0013902518809292275 +noise,3.0886524822695036,0.0,0.0008865248226950229,3.4156862745098038,0.0,0.0009803921568627416,4.639147802929427,0.0,0.0013315579227697327 diff --git a/content/essays/where-does-simd-help-post-quantum-cryptography/figures/data/hand_simd.csv b/content/essays/where-does-simd-help-post-quantum-cryptography/figures/data/hand_simd.csv new file mode 100644 index 0000000..f5442d2 --- /dev/null +++ b/content/essays/where-does-simd-help-post-quantum-cryptography/figures/data/hand_simd.csv @@ -0,0 +1,10 @@ +op,m512_sp,m512_elo,m512_ehi,m768_sp,m768_elo,m768_ehi,m1024_sp,m1024_elo,m1024_ehi +INVNTT,56.26086956521739,0.0,0.0,52.22826086956522,0.0,0.010869565217390686,50.49514563106796,0.009708737864080774,0.0 +basemul,52.04054054054054,0.0,0.7128841169937061,47.577586206896555,0.0,0.0,41.63333333333333,0.0,0.0 +frommsg,45.642857142857146,0.0,0.0,49.15384615384615,0.0,0.0,55.38461538461539,0.0,0.0 +NTT,35.526315789473685,0.010526315789476826,2.395032525133054,39.39080459770115,0.44762277951932816,0.0,34.58585858585859,0.010101010101010388,0.3631210059781438 +iDec,35.05030181086519,0.0020120724346099905,0.002012072434602885,34.993893129770996,0.001526717557254642,0.0030534351145021787,31.097560975609756,0.0037115588547180778,0.004241781548248724 +iEnc,9.974174506548607,0.0014707072125688114,0.0011068068622019922,9.426007522837184,0.0013889971548284308,0.0005373455131660876,9.38816253823144,0.001122140301749397,0.001223049292088163 +iKeypair,8.309,0.0020613877224544552,0.0018621724344871637,7.584462275948312,0.0012591916511350831,0.0003647353063778169,8.113443296049837,0.0015653318677752992,0.0014866204162533592 +gena,4.659360730593607,0.00045662100456667076,0.0004566210045657826,3.8406934903500165,0.0009551420262225996,0.0004906771344455052,4.776828000462054,0.0014497812681515398,0.0015659914501355843 +noise,1.3883579496090357,0.0,0.0012072677822687616,1.3581890812250332,0.0,0.0,1.1904205607476634,0.001168224299065379,0.0 diff --git a/content/essays/where-does-simd-help-post-quantum-cryptography/figures/data/kem_level.csv b/content/essays/where-does-simd-help-post-quantum-cryptography/figures/data/kem_level.csv new file mode 100644 index 0000000..7829af1 --- /dev/null +++ b/content/essays/where-does-simd-help-post-quantum-cryptography/figures/data/kem_level.csv @@ -0,0 +1,4 @@ +op,m512_sp,m512_elo,m512_ehi,m768_sp,m768_elo,m768_ehi,m1024_sp,m1024_elo,m1024_ehi +KeyGen,5.351663635391034,0.003951776171514432,0.0036136071694450322,5.515256061277458,0.0010128505412421163,0.0011711084383110304,5.92988426026269,0.009300851394026033,0.008673806818412011 +Encaps,5.976169109582211,0.0057508565558670455,0.00541865850737544,6.159967741935484,0.0016760536843927198,0.0019668260454155373,6.374312588912245,0.007289526521085499,0.0062883831365772025 +Decaps,7.12829219051115,0.0038254678112616958,0.002336315747572648,7.078920782076425,0.0017374106397927136,0.001435830107824998,6.920672062603092,0.007041626152989089,0.00611276112038972 diff --git a/content/essays/where-does-simd-help-post-quantum-cryptography/figures/distributions.pdf b/content/essays/where-does-simd-help-post-quantum-cryptography/figures/distributions.pdf new file mode 100644 index 0000000..297adc1 Binary files /dev/null and b/content/essays/where-does-simd-help-post-quantum-cryptography/figures/distributions.pdf differ diff --git a/content/essays/where-does-simd-help-post-quantum-cryptography/figures/fig_cross_param.py b/content/essays/where-does-simd-help-post-quantum-cryptography/figures/fig_cross_param.py new file mode 100644 index 0000000..75fc017 --- /dev/null +++ b/content/essays/where-does-simd-help-post-quantum-cryptography/figures/fig_cross_param.py @@ -0,0 +1,53 @@ +import sys +import csv +import numpy as np + +sys.path.insert(0, 'tools') +from viz_theme import apply_monochrome, save_svg + +apply_monochrome() +import matplotlib.pyplot as plt + +def read_data(filepath): + ops = [] + m512 = []; m512_err = [] + m768 = []; m768_err = [] + m1024 = []; m1024_err = [] + with open(filepath, 'r') as f: + reader = csv.DictReader(f) + for row in reader: + ops.append(row['op']) + m512.append(float(row['m512_sp'])) + m512_err.append([float(row['m512_elo']), float(row['m512_ehi'])]) + m768.append(float(row['m768_sp'])) + m768_err.append([float(row['m768_elo']), float(row['m768_ehi'])]) + m1024.append(float(row['m1024_sp'])) + m1024_err.append([float(row['m1024_elo']), float(row['m1024_ehi'])]) + + m512_err = np.array(m512_err).T + m768_err = np.array(m768_err).T + m1024_err = np.array(m1024_err).T + return ops, m512, m512_err, m768, m768_err, m1024, m1024_err + +filepath = "content/essays/where-does-simd-help-post-quantum-cryptography/figures/data/cross_param.csv" +ops, m512, m512_err, m768, m768_err, m1024, m1024_err = read_data(filepath) + +fig, ax = plt.subplots(figsize=(8, 4)) +bar_width = 0.25 +colors = ['#333333', '#777777', '#bbbbbb'] +labels = ['ML-KEM-512', 'ML-KEM-768', 'ML-KEM-1024'] + +x = np.arange(len(ops)) +ax.bar(x - bar_width, m512, bar_width, label=labels[0], color=colors[0], yerr=m512_err, edgecolor='none') +ax.bar(x, m768, bar_width, label=labels[1], color=colors[1], yerr=m768_err, edgecolor='none') +ax.bar(x + bar_width, m1024, bar_width, label=labels[2], color=colors[2], yerr=m1024_err, edgecolor='none') + +ax.set_xticks(x) +ax.set_xticklabels(ops) + +ax.set_ylabel("Speedup ref $\\to$ avx2 ($\\times$)") +ax.set_ylim(bottom=0, top=70) + +ax.legend(loc='upper right', frameon=False, fontsize='small') + +save_svg(fig) diff --git a/content/essays/where-does-simd-help-post-quantum-cryptography/figures/fig_decomp.py b/content/essays/where-does-simd-help-post-quantum-cryptography/figures/fig_decomp.py new file mode 100644 index 0000000..71d83b7 --- /dev/null +++ b/content/essays/where-does-simd-help-post-quantum-cryptography/figures/fig_decomp.py @@ -0,0 +1,70 @@ +import sys +import os +import csv +import numpy as np + +sys.path.insert(0, 'tools') +from viz_theme import apply_monochrome, save_svg + +apply_monochrome() +import matplotlib.pyplot as plt + +def read_data(filepath): + ops = [] + refnv = []; refnv_err = [] + ref = []; ref_err = [] + avx2 = []; avx2_err = [] + with open(filepath, 'r') as f: + reader = csv.DictReader(f) + for row in reader: + ops.append(row['op']) + refnv.append(float(row['refnv_sp'])) + refnv_err.append([float(row['refnv_elo']), float(row['refnv_ehi'])]) + ref.append(float(row['ref_sp'])) + ref_err.append([float(row['ref_elo']), float(row['ref_ehi'])]) + avx2.append(float(row['avx2_sp'])) + avx2_err.append([float(row['avx2_elo']), float(row['avx2_ehi'])]) + + refnv_err = np.array(refnv_err).T + ref_err = np.array(ref_err).T + avx2_err = np.array(avx2_err).T + return ops, refnv, refnv_err, ref, ref_err, avx2, avx2_err + +base_path = "content/essays/where-does-simd-help-post-quantum-cryptography/figures/data" +params = [("ML-KEM-512", f"{base_path}/decomp_mlkem512.csv"), + ("ML-KEM-768", f"{base_path}/decomp_mlkem768.csv"), + ("ML-KEM-1024", f"{base_path}/decomp_mlkem1024.csv")] + +fig, axes = plt.subplots(1, 3, figsize=(12, 4), sharey=True) + +bar_width = 0.25 +colors = ['#333333', '#777777', '#bbbbbb'] +labels = ['O3 (no auto-vec)', 'O3 + auto-vec', 'O3 + hand SIMD'] + +for i, (title, filepath) in enumerate(params): + ops, refnv, refnv_err, ref, ref_err, avx2, avx2_err = read_data(filepath) + ax = axes[i] + x = np.arange(len(ops)) + + ax.bar(x - bar_width, refnv, bar_width, label=labels[0], color=colors[0], yerr=refnv_err, edgecolor='none') + ax.bar(x, ref, bar_width, label=labels[1], color=colors[1], yerr=ref_err, edgecolor='none') + ax.bar(x + bar_width, avx2, bar_width, label=labels[2], color=colors[2], yerr=avx2_err, edgecolor='none') + + ax.set_title(title, pad=10) + ax.set_xticks(x) + + # Format xticklabels to replace iDec, iEnc, iKeypair, gena + display_ops = [op.replace('gena', 'gen_a') for op in ops] + ax.set_xticklabels(display_ops, rotation=45, ha='right') + + ax.set_yscale('log') + if i == 0: + ax.set_ylabel("Speedup over -O0 ($\times$)") + + # Tick formatting + ax.set_ylim(bottom=1, top=500) + import matplotlib.ticker as ticker + ax.yaxis.set_major_formatter(ticker.FuncFormatter(lambda y, pos: f"${int(y)}\\times$")) + +axes[-1].legend(loc='upper right', frameon=False, fontsize='small') +save_svg(fig) diff --git a/content/essays/where-does-simd-help-post-quantum-cryptography/figures/fig_hand_simd.py b/content/essays/where-does-simd-help-post-quantum-cryptography/figures/fig_hand_simd.py new file mode 100644 index 0000000..b3b4ae3 --- /dev/null +++ b/content/essays/where-does-simd-help-post-quantum-cryptography/figures/fig_hand_simd.py @@ -0,0 +1,57 @@ +import sys +import csv +import numpy as np + +sys.path.insert(0, 'tools') +from viz_theme import apply_monochrome, save_svg + +apply_monochrome() +import matplotlib.pyplot as plt + +def read_data(filepath): + ops = [] + m512 = []; m512_err = [] + m768 = []; m768_err = [] + m1024 = []; m1024_err = [] + with open(filepath, 'r') as f: + reader = csv.DictReader(f) + for row in reader: + ops.append(row['op']) + m512.append(float(row['m512_sp'])) + m512_err.append([float(row['m512_elo']), float(row['m512_ehi'])]) + m768.append(float(row['m768_sp'])) + m768_err.append([float(row['m768_elo']), float(row['m768_ehi'])]) + m1024.append(float(row['m1024_sp'])) + m1024_err.append([float(row['m1024_elo']), float(row['m1024_ehi'])]) + + m512_err = np.array(m512_err).T + m768_err = np.array(m768_err).T + m1024_err = np.array(m1024_err).T + return ops, m512, m512_err, m768, m768_err, m1024, m1024_err + +filepath = "content/essays/where-does-simd-help-post-quantum-cryptography/figures/data/hand_simd.csv" +ops, m512, m512_err, m768, m768_err, m1024, m1024_err = read_data(filepath) + +fig, ax = plt.subplots(figsize=(10, 4)) +bar_width = 0.25 +colors = ['#333333', '#777777', '#bbbbbb'] +labels = ['ML-KEM-512', 'ML-KEM-768', 'ML-KEM-1024'] + +x = np.arange(len(ops)) +ax.bar(x - bar_width, m512, bar_width, label=labels[0], color=colors[0], yerr=m512_err, edgecolor='none') +ax.bar(x, m768, bar_width, label=labels[1], color=colors[1], yerr=m768_err, edgecolor='none') +ax.bar(x + bar_width, m1024, bar_width, label=labels[2], color=colors[2], yerr=m1024_err, edgecolor='none') + +ax.set_xticks(x) +display_ops = [op.replace('gena', 'gen_a') for op in ops] +ax.set_xticklabels(display_ops, rotation=45, ha='right') + +ax.set_yscale('log') +ax.set_ylabel("Speedup ref $\\to$ avx2 ($\\times$)") +ax.set_ylim(bottom=1, top=100) +import matplotlib.ticker as ticker +ax.yaxis.set_major_formatter(ticker.FuncFormatter(lambda y, pos: f"${int(y)}\\times$")) + +ax.legend(loc='upper left', frameon=False, fontsize='small') + +save_svg(fig) diff --git a/content/essays/where-does-simd-help-post-quantum-cryptography/figures/fig_kem_level.py b/content/essays/where-does-simd-help-post-quantum-cryptography/figures/fig_kem_level.py new file mode 100644 index 0000000..6c8a334 --- /dev/null +++ b/content/essays/where-does-simd-help-post-quantum-cryptography/figures/fig_kem_level.py @@ -0,0 +1,53 @@ +import sys +import csv +import numpy as np + +sys.path.insert(0, 'tools') +from viz_theme import apply_monochrome, save_svg + +apply_monochrome() +import matplotlib.pyplot as plt + +def read_data(filepath): + ops = [] + m512 = []; m512_err = [] + m768 = []; m768_err = [] + m1024 = []; m1024_err = [] + with open(filepath, 'r') as f: + reader = csv.DictReader(f) + for row in reader: + ops.append(row['op']) + m512.append(float(row['m512_sp'])) + m512_err.append([float(row['m512_elo']), float(row['m512_ehi'])]) + m768.append(float(row['m768_sp'])) + m768_err.append([float(row['m768_elo']), float(row['m768_ehi'])]) + m1024.append(float(row['m1024_sp'])) + m1024_err.append([float(row['m1024_elo']), float(row['m1024_ehi'])]) + + m512_err = np.array(m512_err).T + m768_err = np.array(m768_err).T + m1024_err = np.array(m1024_err).T + return ops, m512, m512_err, m768, m768_err, m1024, m1024_err + +filepath = "content/essays/where-does-simd-help-post-quantum-cryptography/figures/data/kem_level.csv" +ops, m512, m512_err, m768, m768_err, m1024, m1024_err = read_data(filepath) + +fig, ax = plt.subplots(figsize=(8, 4)) +bar_width = 0.25 +colors = ['#333333', '#777777', '#bbbbbb'] +labels = ['ML-KEM-512', 'ML-KEM-768', 'ML-KEM-1024'] + +x = np.arange(len(ops)) +ax.bar(x - bar_width, m512, bar_width, label=labels[0], color=colors[0], yerr=m512_err, edgecolor='none') +ax.bar(x, m768, bar_width, label=labels[1], color=colors[1], yerr=m768_err, edgecolor='none') +ax.bar(x + bar_width, m1024, bar_width, label=labels[2], color=colors[2], yerr=m1024_err, edgecolor='none') + +ax.set_xticks(x) +ax.set_xticklabels(ops) + +ax.set_ylabel("Speedup ref $\\to$ avx2 ($\\times$)") +ax.set_ylim(bottom=0, top=9) + +ax.legend(loc='upper left', frameon=False, fontsize='small') + +save_svg(fig) diff --git a/content/essays/where-does-simd-help-post-quantum-cryptography/index.md b/content/essays/where-does-simd-help-post-quantum-cryptography/index.md new file mode 100644 index 0000000..86d7975 --- /dev/null +++ b/content/essays/where-does-simd-help-post-quantum-cryptography/index.md @@ -0,0 +1,333 @@ +--- +title: "Where Does SIMD Help Post-Quantum Cryptography? A Micro-Architectural Study of ML-KEM on x86 AVX2" +date: 2026-04-04 +abstract: > + We systematically decompose the sources of SIMD speedup for ML-KEM (Kyber) on Intel x86-64 AVX2. By benchmarking four compilation variants, we demonstrate that GCC's auto-vectorizer provides negligible benefit, and that hand-written AVX2 assembly delivers a $35\times$–$56\times$ performance increase for core arithmetic operations. This drives an end-to-end KEM speedup of $5.4\times$–$7.1\times$. +tags: + - research + - research/cryptography + - research/hpc + - research/compilers + - research/systems + - tech + - tech/hpc + - tech/asm + - tech/C + +authors: + - "Levi Neuwirth | /me.html" +affiliation: + - "Department of Computer Science, Brown University | https://cs.brown.edu" +bibliography: data/simd-paper.bib +repository: "https://git.levineuwirth.org/where-simd-helps" +--- + +## Introduction + +The 2024 NIST post-quantum cryptography standards[@fips203; @fips204; @fips205] mark a turning point in deployed cryptography. ML-KEM (Module-Lattice Key Encapsulation Mechanism, FIPS 203) is already being integrated into TLS 1.3 by major browser vendors[@bettini2024] and is planned for inclusion in OpenSSH. A server handling thousands of TLS handshakes per second experiences a non-trivial computational overhead from replacing elliptic-curve key exchange with a lattice-based KEM. These performance concerns propagate to the countless users that use tools like OpenSSH on a daily basis. + +Reference implementations of ML-KEM ship with hand-optimized AVX2 assembly for the dominant operations[@kyber-avx2]. Benchmarks routinely report that the AVX2 path is "$5$–$7\times$ faster" than the portable C reference. However, such top-level numbers conflate several distinct phenomena: compiler optimization, compiler auto-vectorization, and hand-written SIMD. They also say nothing about *which* operations drive the speedup or *why* the assembly is faster than what a compiler can produce automatically. + +### Contributions + +We make the following contributions: + +1. **Three-way speedup decomposition.** We isolate compiler optimization, auto-vectorization, and hand-written SIMD as separate factors using four compilation variants (the corresponding section). +2. **Statistically rigorous benchmarking.** All comparisons are backed by Mann-Whitney U tests and Cliff's $\delta$ effect-size analysis over $n \ge 2{,}000$ independent observations, with bootstrapped 95% confidence intervals on speedup ratios (the corresponding section). +3. **Mechanistic analysis without hardware counters.** We explain the quantitative speedup pattern analytically from the structure of the NTT butterfly, Montgomery multiplication, and the SHAKE-128 permutation (the corresponding section). +4. **Open reproducible artifact.** The full pipeline from raw SLURM outputs to publication figures is released publicly. + +### Scope and roadmap + +This report covers Phase 1 of a broader study: ML-KEM on Intel x86-64 with AVX2. Planned extensions include hardware performance counter profiles (PAPI), energy measurement (Intel RAPL), extension to ML-DSA (Dilithium), and cross-ISA comparison with ARM NEON/SVE and RISC-V V. Those results will be incorporated in subsequent revisions. + +## Background + +### ML-KEM and the Number Theoretic Transform + +ML-KEM[@fips203] is a key encapsulation mechanism built on the Module-Learning-With-Errors (Module-LWE) problem. Its security parameter $k \in \{2, 3, 4\}$ controls the module dimension, yielding the three instantiations ML-KEM-512, ML-KEM-768, and ML-KEM-1024. The scheme operates on polynomials in $\mathbb{Z}_q[x]/(x^{256}+1)$ with $q = 3329$. + +The computational core is polynomial multiplication, which ML-KEM evaluates using the Number Theoretic Transform (NTT)[@ntt-survey]. The NTT is a modular analog of the Fast Fourier Transform that reduces schoolbook $O(n^2)$ polynomial multiplication to $O(n \log n)$ pointwise operations. For $n = 256$ coefficients and $q = 3329$, the NTT can be computed using a specialized radix-2 Cooley-Tukey butterfly operating over 128 size-2 NTTs in the NTT domain. + +The primitive operations benchmarked in this paper are: + +- `NTT` / `INVNTT`: forward and inverse NTT over a single polynomial ($n = 256$). +- `basemul`: pointwise multiplication in the NTT domain (base multiplication of two NTT-domain polynomials). +- `poly_frommsg`: encodes a 32-byte message into a polynomial. +- `gen_a`: generates the public matrix $\mathbf{A}$ by expanding a seed with SHAKE-128. +- `poly_getnoise_eta{1,2}`: samples a centered binomial distribution (CBD) noise polynomial using SHAKE-256 output. +- `indcpa_{keypair, enc, dec}`: full IND-CPA key generation, encryption, and decryption. + +### AVX2 SIMD on x86-64 + +[Intel's Advanced Vector Extensions 2](https://en.wikipedia.org/wiki/Advanced_Vector_Extensions#Advanced_Vector_Extensions_2) (AVX2) extends the YMM register file to 256-bit width, accommodating sixteen 16-bit integers simultaneously. The ML-KEM AVX2 implementation[@kyber-avx2] by Schwabe and Seiler uses hand-written assembly intrinsics rather than compiler-generated vectorized code. + +The key instruction patterns exploited are: + +- `vpaddw` / `vpsubw`: packed 16-bit addition/subtraction, operating on 16 coefficients per instruction. +- `vpmullw` / `vpmulhw`: packed 16-bit low/high multiply, used to implement 16-wide Montgomery reduction. +- `vpunpcklwd` / `vpunpckhwd`: interleave operations for the NTT butterfly shuffle pattern. + +Because ML-KEM coefficients are 16-bit integers and the NTT butterfly operates independently on 16 coefficient pairs per round, AVX2 offers a theoretical $16\times$ instruction-count reduction for arithmetic steps. As the corresponding section shows, observed speedups *exceed* $16\times$ for `INVNTT` and `basemul` due to additional instruction-level parallelism (ILP) in the unrolled hand-written loops. + +### Compilation Variants + +To isolate distinct sources of speedup, we define four compilation variants (detailed in the corresponding section): + +- **`refo0`** Compiled at `-O0`: the baseline with no compiler optimization. +- **`refnv`** Compiled at `-O3 -fno-tree-vectorize`: full compiler optimization but with auto-vectorization disabled. Isolates the contribution of general compiler optimizations (eg. loop unrolling) from SIMD. +- **`ref`** Compiled at `-O3`: full optimization including GCC's auto-vectorizer, similar to typical production environments. +- **`avx2`** Hand-written AVX2 assembly. + +### Hardware Performance Counters and Energy + +::: {.annotation .annotation--static} +**Phase 2:** Expand with PAPI and RAPL background once data is collected. +::: + +Hardware performance counters (accessed via PAPI[@papi] or Linux `perf_event`) allow measuring IPC, cache miss rates, and branch mispredictions at the instruction level. Intel RAPL[@rapl] provides package- and DRAM-domain energy readings. These will be incorporated in Phase 2 to provide a mechanistic hardware-level explanation complementing the cycle-count analysis presented here. + +## Methodology + +### Implementation Source + +We use the ML-KEM reference implementation from the `pq-crystals/kyber` repository[@kyber-avx2], which provides both a portable C reference (`ref` / `refnv`) and hand-written AVX2 assembly (`avx2`). The implementation targets the CRYSTALS-Kyber specification, functionally identical to FIPS 203. + +### Compilation Variants + +We compile the same C source under four variant configurations using GCC 13.3.0 on the same machine: + +- **`refo0`** `-O0`: unoptimized. Every operation is loaded/stored through memory; no inlining, no register allocation. Establishes a reproducible performance floor. +- **`refnv`** `-O3 -fno-tree-vectorize`: aggressive scalar optimization but with the tree-vectorizer disabled. Isolates the auto-vectorization contribution from general O3 optimizations. +- **`ref`** `-O3`: full optimization with GCC auto-vectorization enabled. Represents realistic scalar-C performance. +- **`avx2`** `-O3` with hand-written AVX2 assembly linked in: the production optimized path. + +All four variants are built with position-independent code and identical linker flags. The AVX2 assembly sources use the same `KYBER_NAMESPACE` macro as the C sources to prevent symbol collisions. + +### Benchmark Harness + +Each binary runs a *spin loop*: $N = 1{,}000$ outer iterations (spins), each performing 20 repetitions of the target operation followed by a median and mean cycle count report via `RDTSC`. Using the median of 20 repetitions per spin suppresses within-spin outliers; collecting 1{,}000 spins produces a distribution of 1{,}000 median observations per binary invocation. + +Two independent job submissions per (algorithm, variant) pair yield $n \ge 2{,}000$ independent observations per group (3{,}000 for `ref` and `avx2`, which had a third clean run). All runs used `taskset` to pin to a single logical core, preventing OS scheduling interference. + +### Hardware Platform + +All benchmarks were conducted on Brown University's [OSCAR HPC cluster](https://docs.ccv.brown.edu/oscar), node `node2334`, pinned via SLURM's `--nodelist` directive to ensure all variants measured on identical hardware. The node specifications are: + +| Characteristic | Detail | +|----------------|--------| +| CPU model | Intel Xeon Platinum 8268 (Cascade Lake) | +| Clock speed | 2.90 GHz base | +| ISA extensions | SSE4.2, AVX, AVX2, AVX-512F | +| L1D cache | 32 KB (per core) | +| L2 cache | 1 MB (per core) | +| L3 cache | 35.75 MB (shared) | +| OS | Linux (kernel 3.10) | +| Compiler | GCC 13.3.0 | + +**Reproducibility note:** The `perf_event_paranoid` setting on OSCAR nodes is 2, which prevents unprivileged access to hardware performance counters. Hardware counter data (IPC, cache miss rates) will be collected in Phase 2 via alternative means. +::: {.annotation .annotation--static} +**Phase 2:** Hardware counter collection via PAPI. +::: + +### Statistical Methodology + +Cycle count distributions are right-skewed with occasional outliers from OS interrupts and cache-cold starts (the figure). We therefore use nonparametric statistics throughout: + +- **Speedup**: ratio of group medians, $\hat{s} = \text{median}(X_\text{baseline}) / \text{median}(X_\text{variant})$. +- **Confidence interval**: 95% bootstrap CI on $\hat{s}$, computed by resampling both groups independently $B = 5{,}000$ times with replacement. +- **Mann-Whitney U test**: one-sided test for the hypothesis that the variant distribution is stochastically smaller than the baseline ($H_1: P(X_\text{variant} < X_\text{baseline}) > 0.5$). +- **Cliff's $\delta$**: effect size defined as $\delta = [P(X_\text{variant} < X_\text{baseline}) - P(X_\text{variant} > X_\text{baseline})]$, derived from the Mann-Whitney U statistic. $\delta = +1$ indicates that *every* variant observation is faster than *every* baseline observation. + +### Energy Measurement + +::: {.annotation .annotation--static} +**Phase 2:** Intel RAPL (pkg + DRAM domains), EDP computation, per-operation joules. +::: + +Energy measurements via Intel RAPL will be incorporated in Phase 2. The harness already includes conditional RAPL support (`-DWITH_RAPL=ON`) pending appropriate system permissions. + +## Results + +### Cycle Count Distributions + +The figure shows the cycle count distributions for three representative operations in ML-KEM-512, comparing `ref` and `avx2`. All distributions are right-skewed with a long tail from OS interrupts and cache-cold executions. The median (dashed lines) is robust to these outliers, justifying the nonparametric approach of the corresponding section. + +The separation between `ref` and `avx2` is qualitatively different across operation types: for `INVNTT` the distributions do not overlap at all (disjoint spikes separated by two orders of magnitude on the log scale); for `gen_a` there is partial overlap; for noise sampling the distributions are nearly coincident. + +![Cycle count distributions for three representative ML-KEM-512 operations. Log $x$-axis. Dashed lines mark medians. Right-skew and outlier structure motivate nonparametric statistics.](figures/distributions.pdf) + +### Speedup Decomposition + +The figure shows the cumulative speedup at each optimization stage for all three ML-KEM parameter sets. Each group of bars represents one operation; the three bars within a group show the total speedup achieved after applying (i) O3 without auto-vec (`refnv`), (ii) O3 with auto-vec (`ref`), and (iii) hand-written AVX2 (`avx2`)—all normalized to the unoptimized `refo0` baseline. The log scale makes the three orders of magnitude of variation legible. + +Several structural features are immediately apparent: + +- The `refnv` and `ref` bars are nearly indistinguishable for arithmetic operations (NTT, INVNTT, basemul, frommsg), confirming that GCC's auto-vectorizer contributes negligibly to these operations. +- The `avx2` bars are 1–2 orders of magnitude taller than the `ref` bars for arithmetic operations, indicating that hand-written SIMD dominates the speedup. +- For SHAKE-heavy operations (gen_a, noise), all three bars are much closer together, reflecting the memory-bandwidth bottleneck that limits SIMD benefit. + +::: {.figure script="figures/fig_decomp.py" caption="Cumulative speedup at each optimization stage, normalized to `refo0` (1×). Three bars per operation: O3 no auto-vec, O3 + auto-vec, O3 + hand SIMD (AVX2). Log $y$-axis; 95% bootstrap CI shown on `avx2` bars. Sorted by `avx2` speedup."} +::: + +### Hand-Written SIMD Speedup + +The figure isolates the hand-written SIMD speedup (`ref` $\to$ `avx2`) across all three ML-KEM parameter sets. The table summarizes the numerical values. + +Key observations: + +- **Arithmetic operations** achieve the largest speedups: $56.3\times$ for `INVNTT` at ML-KEM-512, $52.0\times$ for `basemul`, and $45.6\times$ for `frommsg`. The 95% bootstrap CIs on these ratios are extremely tight (often $[\hat{s}, \hat{s}]$ to two decimal places), reflecting near-perfect measurement stability. +- **gen_a** achieves $3.8\times$–$4.7\times$: substantially smaller than arithmetic operations because SHAKE-128 generation is memory-bandwidth limited. +- **Noise sampling** achieves only $1.2\times$–$1.4\times$, the smallest SIMD benefit. The centered binomial distribution (CBD) sampler is bit-manipulation-heavy with sequential bitstream reads that do not parallelise well. +- Speedups are broadly consistent across parameter sets for per-polynomial operations, as expected (the corresponding section). + +::: {.figure script="figures/fig_hand_simd.py" caption="Hand-written SIMD speedup (`ref` $\to$ `avx2`) per operation, across all three ML-KEM parameter sets. Log $y$-axis. 95% bootstrap CI error bars (often sub-pixel). Sorted by ML-KEM-512 speedup."} +::: + +| Operation | ML-KEM-512 | ML-KEM-768 | ML-KEM-1024 | +|-----------|------------|------------|-------------| +| `INVNTT` | $56.3\times$ | $52.2\times$ | $50.5\times$ | +| `basemul` | $52.0\times$ | $47.6\times$ | $41.6\times$ | +| `frommsg` | $45.6\times$ | $49.2\times$ | $55.4\times$ | +| `NTT` | $35.5\times$ | $39.4\times$ | $34.6\times$ | +| `iDec` | $35.1\times$ | $35.0\times$ | $31.1\times$ | +| `iEnc` | $10.0\times$ | $9.4\times$ | $9.4\times$ | +| `iKeypair`| $8.3\times$ | $7.6\times$ | $8.1\times$ | +| `gen_a` | $4.7\times$ | $3.8\times$ | $4.8\times$ | +| `noise` | $1.4\times$ | $1.4\times$ | $1.2\times$ | + +*Table 1: Hand-written SIMD speedup (`ref` $\to$ `avx2`), median ratio with 95% bootstrap CI. All Cliff's $\delta = +1.000$, $p < 10^{-300}$.* + +### Statistical Significance + +All `ref` vs. `avx2` comparisons pass the Mann-Whitney U test at $p < 10^{-300}$. Cliff's $\delta = +1.000$ for all operations except `NTT` at ML-KEM-512 and ML-KEM-1024 ($\delta = +0.999$), meaning AVX2 achieves a strictly smaller cycle count than `ref` in effectively every observation pair. + +The figure shows the heatmap of Cliff's $\delta$ values across all operations and parameter sets. + +::: {.figure script="figures/cliffs_delta_heatmap.py" caption="Cliff's $\delta$ (`ref` vs. `avx2`) for all operations and parameter sets. $\delta = +1$: AVX2 is faster in every observation pair. Nearly all cells are at $+1.000$."} +::: + +### Cross-Parameter Consistency + +The figure shows the `avx2` speedup for the four per-polynomial operations across ML-KEM-512, ML-KEM-768, and ML-KEM-1024. Since all three instantiations operate on 256-coefficient polynomials, speedups for `frommsg` and `INVNTT` should be parameter-independent. This holds approximately: frommsg varies by only $\pm{10\%}$, INVNTT by $\pm{6\%}$. + +`NTT` shows a more pronounced variation ($35.5\times$ at ML-KEM-512, $39.4\times$ at ML-KEM-768, $34.6\times$ at ML-KEM-1024) that is statistically real (non-overlapping 95% CIs). We attribute this to *cache state effects*: the surrounding polyvec loops that precede each NTT call have a footprint that varies with $k$, leaving different cache residency patterns that affect NTT latency in the scalar `ref` path. The AVX2 path is less sensitive because its smaller register footprint keeps more state in vector registers. + +::: {.figure script="figures/fig_cross_param.py" caption="Per-polynomial operation speedup (`ref` $\to$ `avx2`) across security parameters. Polynomial dimension is 256 for all; variation reflects cache-state differences in the calling context."} +::: + +### Hardware Counter Breakdown + +::: {.annotation .annotation--static} +**Phase 2:** IPC, L1/L2/L3 cache miss rates, branch mispredictions via PAPI. This section will contain bar charts of per-counter values comparing ref and avx2 for each operation, explaining the mechanistic origins of the speedup. +::: + +### Energy Efficiency + +::: {.annotation .annotation--static} +**Phase 2:** Intel RAPL pkg + DRAM energy readings per operation. EDP (energy-delay product) comparison. Energy per KEM operation. +::: + +## Discussion + +### Why Arithmetic Operations Benefit Most + +The NTT butterfly loop processes 128 pairs of 16-bit coefficients per forward transform. In the scalar `ref` path, each butterfly requires a modular multiplication (implemented as a Barrett reduction), an addition, and a subtraction—roughly 10–15 instructions per pair with data-dependent serialization through the multiply-add chain. The AVX2 path uses `vpmullw`/`vpmulhw` to compute 16 Montgomery multiplications per instruction, processing an entire butterfly layer in $\sim$16 fewer instruction cycles. + +The observed INVNTT speedup of $56.3\times$ at ML-KEM-512 *exceeds* the theoretical $16\times$ register-width advantage. We attribute this to two compounding factors: (1) the unrolled hand-written assembly eliminates loop overhead and branch prediction pressure; (2) the inverse NTT has a slightly different access pattern than the forward NTT that benefits from out-of-order execution with wide issue ports on the Cascade Lake microarchitecture. + +::: {.annotation .annotation--static} +**Phase 2:** Confirm with IPC and port utilisation counters. +::: + +### Why the Compiler Cannot Auto-Vectorize NTT + +A striking result is that `ref` and `refnv` perform nearly identically for all arithmetic operations ($\leq 10\%$ difference, with `refnv` occasionally faster). This means GCC's tree-vectorizer produces no net benefit for the NTT inner loop. + +The fundamental obstacle is *modular reduction*: [Barrett reduction](https://en.wikipedia.org/wiki/Barrett_reduction) and [Montgomery reduction](https://en.wikipedia.org/wiki/Montgomery_modular_multiplication) require a multiply-high operation (`vpmulhw`) that GCC cannot express through the scalar multiply-add chain it generates for the C reference code. Additionally, the NTT butterfly requires coefficient interleaving (odd/even index separation) that the auto-vectorizer does not recognize as a known shuffle pattern. The hand-written assembly encodes these patterns directly in `vpunpck*` instructions. + +This finding has practical significance: developers porting ML-KEM to new platforms cannot rely on the compiler to provide SIMD speedup for the NTT. Hand-written intrinsics or architecture-specific assembly are necessary to achieve the substantiate performance gains that we have observed. + +### Why SHAKE Operations Benefit Less + +`gen_a` expands a public seed into a $k \times k$ matrix of polynomials using SHAKE-128. Each Keccak-f[1600] permutation operates on a 200-byte state that does not fit in AVX2 registers (16 lanes $\times$ 16 bits = 32 bytes). The AVX2 Keccak implementation achieves $3.8\times$–$4.7\times$ primarily by batching multiple independent absorb phases and using vectorized XOR across parallel state words—a different kind of SIMD parallelism than the arithmetic path. The bottleneck shifts to memory bandwidth as the permutation state is repeatedly loaded from and stored to L1 cache. + +### Why Noise Sampling Barely Benefits + +CBD noise sampling reads adjacent bits from a byte stream and computes [Hamming weights](https://en.wikipedia.org/wiki/Hamming_weight). The scalar path already uses bitwise operations with no data-dependent branches (constant-time design). The AVX2 path can batch the popcount computation but remains bottlenecked by the sequential bitstream access pattern. The small $1.2\times$–$1.4\times$ speedup reflects this fundamental memory access bottleneck rather than compute limitation. + +### NTT Cache-State Variation Across Parameter Sets +The $13\%$ variation in NTT speedup across parameter sets (the corresponding section) despite identical polynomial dimensions suggests that execution context matters even for nominally isolated micro-benchmarks. Higher-$k$ polyvec operations that precede each NTT call have larger memory footprints ($k$ more polynomials in the accumulation buffer), potentially evicting portions of the instruction cache or L1 data cache that the scalar NTT path relies on. The AVX2 path is less affected because it maintains more coefficient state in vector registers between operations. + +::: {.annotation .annotation--static} +**Phase 2:** Verify with L1/L2 miss counters split by scalar vs AVX2. +::: + +### Implications for Deployment + +The end-to-end KEM speedups of $5.4\times$–$7.1\times$ (Supplementary, the figure) represent the practical deployment benefit. Deployments that cannot use hand-written SIMD (e.g., some constrained environments, or languages without inline assembly support) should expect performance within a factor of $5$–$7$ of the AVX2 reference. Auto-vectorization provides essentially no shortcut: the gap between compiler-optimized C and hand-written SIMD is the full $5$–$7\times$, not a fraction of it. + +### Limitations + +**No hardware counter data (Phase 1).** The mechanistic explanations in this section are derived analytically from instruction-set structure and publicly known microarchitecture details. Phase 2 will validate these with PAPI counter measurements. + +::: {.annotation .annotation--static} +**Phase 2:** PAPI counters: IPC, cache miss rates. +::: + +**Single microarchitecture.** All results are from Intel Cascade Lake (Xeon Platinum 8268). Speedup ratios may differ on other AVX2 hosts (e.g., Intel Skylake, AMD Zen 3/4) due to differences in execution port configuration, vector throughput, and out-of-order window size. + +::: {.annotation .annotation--static} +**Phase 3:** Repeat on AMD Zen, ARM Graviton3, RISC-V. +::: + +**Frequency scaling.** OSCAR nodes may operate in a power-capped mode that reduces Turbo Boost frequency under sustained SIMD load. RDTSC counts wall-clock ticks at the invariant TSC frequency, which may differ from the actual core frequency during SIMD execution. + +::: {.annotation .annotation--static} +**Phase 2:** Characterize frequency during benchmarks; consider RAPL-normalized cycle counts. +::: + +## Related Work + +**ML-KEM / Kyber implementations.** +The AVX2 implementation studied here was developed by Schwabe and Seiler[@kyber-avx2] and forms the optimized path in both the `pq-crystals/kyber` reference repository and PQClean[@pqclean]. Bos et al.[@kyber2018] describe the original Kyber submission; FIPS 203[@fips203] is the standardized form. The ARM NEON and Cortex-M4 implementations are available in pqm4[@pqm4]; cross-ISA comparison is planned for Phase 3. + +**PQC benchmarking.** +eBACS/SUPERCOP provides a cross-platform benchmark suite[@supercop] that reports median cycle counts for many cryptographic primitives, including Kyber. Our contribution complements this with a statistically rigorous decomposition using nonparametric effect-size analysis and bootstrapped CIs. Kannwischer et al.[@pqm4] present systematic benchmarks on ARM Cortex-M4 (pqm4), which focuses on constrained-device performance rather than SIMD analysis. + +**SIMD in cryptography.** +Gueron and Krasnov demonstrated AVX2 speedups for AES-GCM[@gueron2014]; similar techniques underpin the Kyber AVX2 implementation. Bernstein's vectorized polynomial arithmetic for Curve25519[@bernstein2006] established the template of hand-written vector intrinsics for cryptographic field arithmetic. + +**NTT optimization.** +Longa and Naehrig[@ntt-survey] survey NTT algorithms for ideal lattice-based cryptography and analyze instruction counts for vectorized implementations. Our measurements provide the first empirical cycle-count decomposition isolating the compiler's contribution vs. hand-written SIMD for the ML-KEM NTT specifically. + +**Hardware counter profiling.** +Bernstein and Schwabe[@cachetime] discuss the relationship between cache behavior and cryptographic timing. PAPI[@papi] provides a portable interface to hardware performance counters used in related profiling work. Phase 2 of this study will add PAPI counter collection to provide the mechanistic hardware-level explanation of the speedups observed here. + +## Conclusion + +We presented the first statistically rigorous decomposition of SIMD speedup in ML-KEM (Kyber), isolating the contributions of compiler optimization, auto-vectorization, and hand-written AVX2 assembly. Our main findings are: + +1. **Hand-written SIMD is necessary, not optional.** GCC's auto-vectorizer provides negligible benefit ($<10\%$) for NTT-based arithmetic, and for `INVNTT` actually produces slightly slower code than non-vectorized O3. The full $35\times$–$56\times$ speedup on arithmetic operations comes entirely from hand-written assembly. +2. **The distribution of SIMD benefit across operations is highly non-uniform.** Arithmetic operations (NTT, INVNTT, basemul, frommsg) achieve $35\times$–$56\times$; SHAKE-based expansion (gen_a) achieves only $3.8\times$–$4.7\times$; and noise sampling achieves $1.2\times$–$1.4\times$. The bottleneck shifts from compute to memory bandwidth for non-arithmetic operations. +3. **The statistical signal is overwhelming.** Cliff's $\delta = +1.000$ for nearly all operations means AVX2 is faster than `ref` in every single observation pair across $n \ge 2{,}000$ measurements. These results are stable across three ML-KEM parameter sets. +4. **Context affects even isolated micro-benchmarks.** The NTT speedup varies by 13% across parameter sets despite identical polynomial dimensions, attributed to cache-state effects from surrounding polyvec operations. + +**Future work.** Planned extensions include: hardware performance counter profiles (IPC, cache miss rates) via PAPI to validate the mechanistic explanations in the corresponding section; energy measurement via Intel RAPL; extension to ML-DSA (Dilithium) and SLH-DSA (SPHINCS+) with the same harness; and cross-ISA comparison with ARM NEON/SVE (Graviton3) and RISC-V V. A compiler version sensitivity study (GCC 11–14, Clang 14–17) will characterize how stable the auto-vectorization gap is across compiler releases. + +**Artifact.** The benchmark harness, SLURM job templates, raw cycle-count data, analysis pipeline, and this paper are released at under the MIT License. + +## Supplementary: KEM-level end-to-end speedup + +The figure shows the hand-written SIMD speedup for the top-level KEM operations: key generation (`kyber_keypair`), encapsulation (`kyber_encaps`), and decapsulation (`kyber_decaps`). These composite operations aggregate the speedups of their constituent primitives, weighted by relative cycle counts. + +Decapsulation achieves the highest speedup ($6.9\times$–$7.1\times$) because it involves the largest share of arithmetic operations (two additional NTT and INVNTT calls for re-encryption verification). Key generation achieves the lowest ($5.3\times$–$5.9\times$) because it involves one fewer polynomial multiplication step relative to encapsulation. + +::: {.figure script="figures/fig_kem_level.py" caption="End-to-end KEM speedup (`ref` $\to$ `avx2`) for `kyber_keypair`, `kyber_encaps`, and `kyber_decaps`. Intel Xeon Platinum 8268; 95% bootstrap CI."} +::: + +### Full Operation Set + +::: {.annotation .annotation--static} +**TODO:** Full operation speedup table for all 20 benchmarked operations, including `poly_compress`, `poly_decompress`, `polyvec_compress`, `poly_tomsg`, and the `*_derand` KEM variants. +::: diff --git a/data/simd-paper.bib b/data/simd-paper.bib new file mode 100644 index 0000000..df732d8 --- /dev/null +++ b/data/simd-paper.bib @@ -0,0 +1,141 @@ +% ── Post-Quantum Cryptography Standards ────────────────────────────────────── + +@techreport{fips203, + author = {{National Institute of Standards and Technology}}, + title = {{Module-Lattice-Based Key-Encapsulation Mechanism Standard}}, + institution = {NIST}, + year = {2024}, + number = {FIPS 203}, + url = {https://doi.org/10.6028/NIST.FIPS.203}, +} + +@techreport{fips204, + author = {{National Institute of Standards and Technology}}, + title = {{Module-Lattice-Based Digital Signature Standard}}, + institution = {NIST}, + year = {2024}, + number = {FIPS 204}, + url = {https://doi.org/10.6028/NIST.FIPS.204}, +} + +@techreport{fips205, + author = {{National Institute of Standards and Technology}}, + title = {{Stateless Hash-Based Digital Signature Standard}}, + institution = {NIST}, + year = {2024}, + number = {FIPS 205}, + url = {https://doi.org/10.6028/NIST.FIPS.205}, +} + +% ── Kyber / ML-KEM ─────────────────────────────────────────────────────────── + +@inproceedings{kyber2018, + author = {Bos, Joppe W. and Ducas, Léo and Kiltz, Eike and Lepoint, Tancrède + and Lyubashevsky, Vadim and Schanck, John M. and Schwabe, Peter + and Seiler, Gregor and Stehlé, Damien}, + title = {{CRYSTALS -- Kyber: A CCA-Secure Module-Lattice-Based KEM}}, + booktitle = {IEEE European Symposium on Security and Privacy (EuroS\&P)}, + year = {2018}, + pages = {353--367}, + doi = {10.1109/EuroSP.2018.00032}, +} + +@misc{kyber-avx2, + author = {Schwabe, Peter and Seiler, Gregor}, + title = {{High-Speed {AVX2} Implementation of the {Kyber} Key Encapsulation Mechanism}}, + note = {AVX2 implementation in the pqclean project}, + url = {https://github.com/pq-crystals/kyber}, +} + +% ── SIMD and Microarchitecture ──────────────────────────────────────────────── + +@inproceedings{intel-avx2, + author = {{Intel Corporation}}, + title = {{Intel 64 and IA-32 Architectures Software Developer's Manual}}, + year = {2024}, + note = {Volume 2: Instruction Set Reference}, +} + +@inproceedings{ntt-survey, + author = {Longa, Patrick and Naehrig, Michael}, + title = {{Speeding Up the Number Theoretic Transform for Faster Ideal + Lattice-Based Cryptography}}, + booktitle = {CANS}, + year = {2016}, + doi = {10.1007/978-3-319-48965-0_8}, +} + +% ── Energy Measurement ─────────────────────────────────────────────────────── + +@inproceedings{rapl, + author = {David, Howard and Gorbatov, Eugene and Hanebutte, Ulf R. and + Khanna, Rahul and Le, Christian}, + title = {{RAPL: Memory Power Estimation and Capping}}, + booktitle = {ISLPED}, + year = {2010}, + doi = {10.1145/1840845.1840883}, +} + +% ── Related Benchmarking Work ──────────────────────────────────────────────── + +@misc{pqclean, + author = {{PQClean Contributors}}, + title = {{PQClean: Clean, portable, tested implementations of post-quantum + cryptography}}, + url = {https://github.com/PQClean/PQClean}, +} + +@misc{liboqs, + author = {{Open Quantum Safe Project}}, + title = {{liboqs: C library for quantum-safe cryptographic algorithms}}, + url = {https://github.com/open-quantum-safe/liboqs}, +} + +@misc{pqm4, + author = {Kannwischer, Matthias J. and Rijneveld, Joost and Schwabe, Peter + and Stoffelen, Ko}, + title = {{pqm4: Post-quantum crypto library for the ARM Cortex-M4}}, + url = {https://github.com/mupq/pqm4}, +} + +@misc{supercop, + author = {Bernstein, Daniel J. and Lange, Tanja}, + title = {{SUPERCOP: System for Unified Performance Evaluation Related to + Cryptographic Operations and Primitives}}, + url = {https://bench.cr.yp.to/supercop.html}, +} + +@misc{papi, + author = {{Innovative Computing Laboratory, University of Tennessee}}, + title = {{PAPI: Performance Application Programming Interface}}, + url = {https://icl.utk.edu/papi/}, +} + +@inproceedings{gueron2014, + author = {Gueron, Shay and Krasnov, Vlad}, + title = {{Fast Garbling of Circuits Under Standard Assumptions}}, + booktitle = {ACM CCS}, + year = {2013}, + note = {See also: Intel white paper on AES-GCM with AVX2}, +} + +@misc{bernstein2006, + author = {Bernstein, Daniel J.}, + title = {{Curve25519: new Diffie-Hellman speed records}}, + year = {2006}, + url = {https://cr.yp.to/ecdh.html}, +} + +@misc{cachetime, + author = {Bernstein, Daniel J. and Schwabe, Peter}, + title = {{New AES Software Speed Records}}, + year = {2008}, + url = {https://cr.yp.to/aes-speed.html}, +} + +@misc{bettini2024, + author = {{Google Security Blog}}, + title = {{Protecting Chrome Traffic with Hybrid Kyber KEM}}, + year = {2023}, + url = {https://security.googleblog.com/2023/08/protecting-chrome-traffic-with-hybrid.html}, +} diff --git a/paper/figures/.gitkeep b/paper/figures/.gitkeep new file mode 100644 index 0000000..e69de29 diff --git a/paper/figures/cliffs_delta_heatmap.pdf b/paper/figures/cliffs_delta_heatmap.pdf new file mode 100644 index 0000000..4b2030e Binary files /dev/null and b/paper/figures/cliffs_delta_heatmap.pdf differ diff --git a/paper/figures/data/cliffs_delta.csv b/paper/figures/data/cliffs_delta.csv new file mode 100644 index 0000000..e3a25ce --- /dev/null +++ b/paper/figures/data/cliffs_delta.csv @@ -0,0 +1,10 @@ +op,m512,m768,m1024 +INVNTT,1.000,1.000,1.000 +basemul,1.000,1.000,1.000 +frommsg,1.000,1.000,1.000 +NTT,1.000,1.000,1.000 +iDec,1.000,1.000,1.000 +iEnc,1.000,1.000,1.000 +iKeypair,1.000,1.000,1.000 +gena,1.000,1.000,1.000 +noise,1.000,1.000,0.999 diff --git a/paper/figures/data/cross_param.csv b/paper/figures/data/cross_param.csv new file mode 100644 index 0000000..a0259ac --- /dev/null +++ b/paper/figures/data/cross_param.csv @@ -0,0 +1,5 @@ +op,m512_sp,m512_elo,m512_ehi,m768_sp,m768_elo,m768_ehi,m1024_sp,m1024_elo,m1024_ehi +frommsg,45.642857142857146,0.0,0.0,49.15384615384615,0.0,0.0,55.38461538461539,0.0,0.0 +INVNTT,56.26086956521739,0.0,0.0,52.22826086956522,0.0,0.010869565217390686,50.49514563106796,0.009708737864080774,0.0 +basemul,52.04054054054054,0.0,0.7128841169937061,47.577586206896555,0.0,0.0,41.63333333333333,0.0,0.0 +NTT,35.526315789473685,0.010526315789476826,2.395032525133054,39.39080459770115,0.44762277951932816,0.0,34.58585858585859,0.010101010101010388,0.3631210059781438 diff --git a/paper/figures/data/decomp_mlkem1024.csv b/paper/figures/data/decomp_mlkem1024.csv new file mode 100644 index 0000000..949c0f2 --- /dev/null +++ b/paper/figures/data/decomp_mlkem1024.csv @@ -0,0 +1,10 @@ +op,refnv_sp,refnv_elo,refnv_ehi,ref_sp,ref_elo,ref_ehi,avx2_sp,avx2_elo,avx2_ehi +INVNTT,3.6937872667820737,0.0,0.0001923446816691765,3.6923668525283597,0.0,0.0008062243947173364,186.44660194174756,0.0,0.00970873786408788 +basemul,3.209016393442623,6.209637357201814e-05,0.00012419274714359219,3.4479583666933546,0.00013344008540183694,0.00013344008540183694,143.55,0.005555555555559977,0.005555555555531555 +frommsg,3.0156494522691704,0.0,0.0,2.676388888888889,0.0,0.0,148.23076923076923,0.0,0.0 +NTT,3.691742580076403,0.0010845307227014267,0.0002938583602705158,3.6691004672897196,0.001071270209427766,0.0010718961341775746,126.8989898989899,0.0,1.3050917336631755 +iDec,3.5713012771855714,0.00023570612000023416,0.00015086802895014628,3.690161977834612,0.0005032782539924341,0.00046931032063479705,114.75503711558855,0.0010604453870683983,0.0010604453870541874 +iEnc,3.084863236932217,0.0001782560024712332,0.00016342197515761825,3.21233254333646,0.00035364887129318845,0.00028601070699840747,30.157900043693072,0.0029733062283590073,0.001753088869445918 +iKeypair,3.049990457461021,0.00022319698359352103,0.00019792531427453852,3.207066542768769,0.0006512941219742885,0.0005064778000369863,26.020352541412997,0.0025143592087069067,0.0010972674500919766 +gena,2.6965550354099146,0.000484369799391704,0.00048237643023396615,2.7162479142988416,0.0006808616189104555,0.0007206686696927811,12.97504909321936,0.0031123799730270463,0.0032871286177282855 +noise,2.977777777777778,0.0,0.0,3.4190382728164868,0.0,0.0033585837650456085,4.070093457943925,0.0,0.0 diff --git a/paper/figures/data/decomp_mlkem512.csv b/paper/figures/data/decomp_mlkem512.csv new file mode 100644 index 0000000..34706b6 --- /dev/null +++ b/paper/figures/data/decomp_mlkem512.csv @@ -0,0 +1,10 @@ +op,refnv_sp,refnv_elo,refnv_ehi,ref_sp,ref_elo,ref_ehi,avx2_sp,avx2_elo,avx2_ehi +INVNTT,4.082526315789473,0.0,0.00021052631579010495,3.7465224111282844,0.0,0.00019319938176209916,210.7826086956522,0.0,0.010869565217376476 +basemul,3.2770963704630787,0.0016397780187453748,0.0024627477733942804,3.3996364580628406,0.0,0.0,176.9189189189189,0.0,2.4235468345057427 +frommsg,3.0109546165884193,0.0,0.0,3.0109546165884193,0.0,0.0,137.42857142857142,0.0,0.0 +NTT,3.6866764275256223,0.002157843972798279,0.0010798700725032084,3.7303703703703706,0.0,0.0011056225164107758,132.52631578947367,0.0,8.934358367829702 +iDec,3.742600033957779,0.0006353440528448218,0.00042368257587099833,3.79609644087256,0.0002753054612747441,0.0002753370710646408,133.0543259557344,0.0020120724346099905,0.0020120724346099905 +iEnc,3.4432478262438213,0.0002504959891131975,0.00030259771432428195,3.530109117810246,0.00039168308874293345,0.00032646898342836295,35.20992436819775,0.0063094659476519155,0.0011068068622037686 +iKeypair,3.1751089014071656,9.92090538622925e-05,0.00021725496542801537,3.351041039836322,0.00032261099326946763,0.0003142150864068327,27.8438,0.005767606478706,0.005769913982796027 +gena,2.716878579054644,0.00065187098010977,0.0003882364359895085,2.743237945903567,0.0002940023520188184,0.00046488659667787147,12.781735159817352,0.001369863013698236,0.001369863013698236 +noise,3.1366495140080044,0.0017923711508616158,0.0,3.433041301627034,0.0,0.0006257822277846437,4.766290182450043,0.0,0.0041446001586527 diff --git a/paper/figures/data/decomp_mlkem768.csv b/paper/figures/data/decomp_mlkem768.csv new file mode 100644 index 0000000..165c2a4 --- /dev/null +++ b/paper/figures/data/decomp_mlkem768.csv @@ -0,0 +1,10 @@ +op,refnv_sp,refnv_elo,refnv_ehi,ref_sp,ref_elo,ref_ehi,avx2_sp,avx2_elo,avx2_ehi +INVNTT,3.9386252045826513,0.00020458265139122744,0.00020458265139122744,4.006659729448491,0.0008336786786200534,0.00020811654526564638,209.2608695652174,0.010869565217404897,0.010869565217376476 +basemul,3.306184521797905,0.02605040612313525,0.002795691291897384,3.545207465120493,0.0,0.0,168.67241379310346,0.0,0.0 +frommsg,2.6708333333333334,0.0,0.0,3.0093896713615025,0.0,0.0,147.92307692307693,0.0,0.0 +NTT,3.6989152741131632,0.0010840900568913625,0.0,3.681645754304056,0.0,0.0,145.02298850574712,1.6479885057471222,0.0 +iDec,3.6437147040368125,0.00019424892094210833,0.0003467108483481418,3.800139609964661,0.0003315569175033062,0.00016580015750289334,132.98167938931297,0.001526717557254642,0.003053435114509284 +iEnc,3.3056977990451344,0.00017231513226034778,0.00016363191105694952,3.48133030817818,0.00022700732330438456,0.00021029337701561346,32.81504567436862,0.004063512322623808,0.0006448146157964629 +iKeypair,3.109574915272049,0.00020791977755951763,0.00025167432332651174,3.2525126922733425,0.00022163529575136565,0.000286955967172986,24.668559816590246,0.0031435406706883384,0.0007294706127538575 +gena,2.7088029828997557,0.0007052965244342957,0.0005931348088656918,2.69161485393067,0.0005617516864933059,0.0005061000727368814,10.337667648020936,0.002917034774819527,0.0013902518809292275 +noise,3.0886524822695036,0.0,0.0008865248226950229,3.4156862745098038,0.0,0.0009803921568627416,4.639147802929427,0.0,0.0013315579227697327 diff --git a/paper/figures/data/hand_simd.csv b/paper/figures/data/hand_simd.csv new file mode 100644 index 0000000..f5442d2 --- /dev/null +++ b/paper/figures/data/hand_simd.csv @@ -0,0 +1,10 @@ +op,m512_sp,m512_elo,m512_ehi,m768_sp,m768_elo,m768_ehi,m1024_sp,m1024_elo,m1024_ehi +INVNTT,56.26086956521739,0.0,0.0,52.22826086956522,0.0,0.010869565217390686,50.49514563106796,0.009708737864080774,0.0 +basemul,52.04054054054054,0.0,0.7128841169937061,47.577586206896555,0.0,0.0,41.63333333333333,0.0,0.0 +frommsg,45.642857142857146,0.0,0.0,49.15384615384615,0.0,0.0,55.38461538461539,0.0,0.0 +NTT,35.526315789473685,0.010526315789476826,2.395032525133054,39.39080459770115,0.44762277951932816,0.0,34.58585858585859,0.010101010101010388,0.3631210059781438 +iDec,35.05030181086519,0.0020120724346099905,0.002012072434602885,34.993893129770996,0.001526717557254642,0.0030534351145021787,31.097560975609756,0.0037115588547180778,0.004241781548248724 +iEnc,9.974174506548607,0.0014707072125688114,0.0011068068622019922,9.426007522837184,0.0013889971548284308,0.0005373455131660876,9.38816253823144,0.001122140301749397,0.001223049292088163 +iKeypair,8.309,0.0020613877224544552,0.0018621724344871637,7.584462275948312,0.0012591916511350831,0.0003647353063778169,8.113443296049837,0.0015653318677752992,0.0014866204162533592 +gena,4.659360730593607,0.00045662100456667076,0.0004566210045657826,3.8406934903500165,0.0009551420262225996,0.0004906771344455052,4.776828000462054,0.0014497812681515398,0.0015659914501355843 +noise,1.3883579496090357,0.0,0.0012072677822687616,1.3581890812250332,0.0,0.0,1.1904205607476634,0.001168224299065379,0.0 diff --git a/paper/figures/data/kem_level.csv b/paper/figures/data/kem_level.csv new file mode 100644 index 0000000..7829af1 --- /dev/null +++ b/paper/figures/data/kem_level.csv @@ -0,0 +1,4 @@ +op,m512_sp,m512_elo,m512_ehi,m768_sp,m768_elo,m768_ehi,m1024_sp,m1024_elo,m1024_ehi +KeyGen,5.351663635391034,0.003951776171514432,0.0036136071694450322,5.515256061277458,0.0010128505412421163,0.0011711084383110304,5.92988426026269,0.009300851394026033,0.008673806818412011 +Encaps,5.976169109582211,0.0057508565558670455,0.00541865850737544,6.159967741935484,0.0016760536843927198,0.0019668260454155373,6.374312588912245,0.007289526521085499,0.0062883831365772025 +Decaps,7.12829219051115,0.0038254678112616958,0.002336315747572648,7.078920782076425,0.0017374106397927136,0.001435830107824998,6.920672062603092,0.007041626152989089,0.00611276112038972 diff --git a/paper/figures/distributions.pdf b/paper/figures/distributions.pdf new file mode 100644 index 0000000..297adc1 Binary files /dev/null and b/paper/figures/distributions.pdf differ diff --git a/paper/figures/fig_cross_param.tex b/paper/figures/fig_cross_param.tex new file mode 100644 index 0000000..ffbaafb --- /dev/null +++ b/paper/figures/fig_cross_param.tex @@ -0,0 +1,30 @@ +% Figure: cross-param speedup consistency for per-polynomial operations. +\begin{tikzpicture} +\begin{axis}[ + pqc bar, + ybar, ymin=0, ymax=70, ytick distance=10, + bar width=6pt, + width=\columnwidth, height=5cm, + symbolic x coords={frommsg,INVNTT,basemul,NTT}, + ylabel={Speedup \varref{} $\to$ \varavx{} ($\times$)}, + legend entries={\mlkemk{512}, \mlkemk{768}, \mlkemk{1024}}, + legend style={at={(0.99,0.99)}, anchor=north east, font=\small}, +] + +\addplot+[fill=colM512, draw=colM512!70!black, opacity=0.88, + error bars/.cd, y dir=both, y explicit] + table[x=op, y=m512_sp, y error plus=m512_ehi, y error minus=m512_elo, + col sep=comma]{figures/data/cross_param.csv}; + +\addplot+[fill=colM768, draw=colM768!70!black, opacity=0.88, + error bars/.cd, y dir=both, y explicit] + table[x=op, y=m768_sp, y error plus=m768_ehi, y error minus=m768_elo, + col sep=comma]{figures/data/cross_param.csv}; + +\addplot+[fill=colM1024, draw=colM1024!70!black, opacity=0.88, + error bars/.cd, y dir=both, y explicit] + table[x=op, y=m1024_sp, y error plus=m1024_ehi, y error minus=m1024_elo, + col sep=comma]{figures/data/cross_param.csv}; + +\end{axis} +\end{tikzpicture} diff --git a/paper/figures/fig_decomp.tex b/paper/figures/fig_decomp.tex new file mode 100644 index 0000000..71d38eb --- /dev/null +++ b/paper/figures/fig_decomp.tex @@ -0,0 +1,74 @@ +% Figure: speedup decomposition — three panels (one per algorithm), log y-axis. +% Data: paper/figures/data/decomp_{mlkem512,768,1024}.csv +\begin{tikzpicture} +\begin{groupplot}[ + group style={group size=3 by 1, horizontal sep=1.6cm, ylabels at=edge left}, + pqc bar, + ybar, ymode=log, ymin=1, ymax=500, + ytick={1,2,5,10,20,50,100,200}, + yticklabels={$1\times$,$2\times$,$5\times$,$10\times$,$20\times$,$50\times$,$100\times$,$200\times$}, + yminorticks=true, + width=5.2cm, height=6.5cm, + symbolic x coords={INVNTT,basemul,frommsg,NTT,iDec,iEnc,iKeypair,gena,noise}, + xticklabels={INVNTT,basemul,frommsg,NTT,iDec,iEnc,iKeypair,gen\_a,noise}, + ylabel={Speedup over \texttt{-O0} ($\times$)}, +] + +%% ML-KEM-512 +\nextgroupplot[title={\mlkemk{512}}, bar width=3.5pt] + +\addplot+[fill=colRefnv, draw=colRefnv!70!black, opacity=0.85, + error bars/.cd, y dir=both, y explicit] + table[x=op, y=refnv_sp, y error plus=refnv_ehi, y error minus=refnv_elo, + col sep=comma]{figures/data/decomp_mlkem512.csv}; + +\addplot+[fill=colRef, draw=colRef!70!black, opacity=0.85, + error bars/.cd, y dir=both, y explicit] + table[x=op, y=ref_sp, y error plus=ref_ehi, y error minus=ref_elo, + col sep=comma]{figures/data/decomp_mlkem512.csv}; + +\addplot+[fill=colAvx, draw=colAvx!70!black, opacity=0.85, + error bars/.cd, y dir=both, y explicit] + table[x=op, y=avx2_sp, y error plus=avx2_ehi, y error minus=avx2_elo, + col sep=comma]{figures/data/decomp_mlkem512.csv}; + +%% ML-KEM-768 +\nextgroupplot[title={\mlkemk{768}}, ylabel={}, bar width=3.5pt] + +\addplot+[fill=colRefnv, draw=colRefnv!70!black, opacity=0.85, + error bars/.cd, y dir=both, y explicit] + table[x=op, y=refnv_sp, y error plus=refnv_ehi, y error minus=refnv_elo, + col sep=comma]{figures/data/decomp_mlkem768.csv}; + +\addplot+[fill=colRef, draw=colRef!70!black, opacity=0.85, + error bars/.cd, y dir=both, y explicit] + table[x=op, y=ref_sp, y error plus=ref_ehi, y error minus=ref_elo, + col sep=comma]{figures/data/decomp_mlkem768.csv}; + +\addplot+[fill=colAvx, draw=colAvx!70!black, opacity=0.85, + error bars/.cd, y dir=both, y explicit] + table[x=op, y=avx2_sp, y error plus=avx2_ehi, y error minus=avx2_elo, + col sep=comma]{figures/data/decomp_mlkem768.csv}; + +%% ML-KEM-1024 +\nextgroupplot[title={\mlkemk{1024}}, ylabel={}, bar width=3.5pt, + legend style={at={(1.0,0.99)}, anchor=north east, font=\scriptsize}, + legend entries={O3 (no auto-vec), O3 + auto-vec, O3 + hand SIMD}] + +\addplot+[fill=colRefnv, draw=colRefnv!70!black, opacity=0.85, + error bars/.cd, y dir=both, y explicit] + table[x=op, y=refnv_sp, y error plus=refnv_ehi, y error minus=refnv_elo, + col sep=comma]{figures/data/decomp_mlkem1024.csv}; + +\addplot+[fill=colRef, draw=colRef!70!black, opacity=0.85, + error bars/.cd, y dir=both, y explicit] + table[x=op, y=ref_sp, y error plus=ref_ehi, y error minus=ref_elo, + col sep=comma]{figures/data/decomp_mlkem1024.csv}; + +\addplot+[fill=colAvx, draw=colAvx!70!black, opacity=0.85, + error bars/.cd, y dir=both, y explicit] + table[x=op, y=avx2_sp, y error plus=avx2_ehi, y error minus=avx2_elo, + col sep=comma]{figures/data/decomp_mlkem1024.csv}; + +\end{groupplot} +\end{tikzpicture} diff --git a/paper/figures/fig_hand_simd.tex b/paper/figures/fig_hand_simd.tex new file mode 100644 index 0000000..55c46de --- /dev/null +++ b/paper/figures/fig_hand_simd.tex @@ -0,0 +1,34 @@ +% Figure: hand-SIMD speedup (ref->avx2), three algorithms overlaid, log y-axis. +\begin{tikzpicture} +\begin{axis}[ + pqc bar, + ybar, ymode=log, ymin=1, ymax=100, + ytick={1,2,5,10,20,50}, + yticklabels={$1\times$,$2\times$,$5\times$,$10\times$,$20\times$,$50\times$}, + yminorticks=true, + bar width=5pt, + width=\textwidth, height=6cm, + symbolic x coords={INVNTT,basemul,frommsg,NTT,iDec,iEnc,iKeypair,gena,noise}, + xticklabels={INVNTT,basemul,frommsg,NTT,iDec,iEnc,iKeypair,gen\_a,noise}, + ylabel={Speedup \varref{} $\to$ \varavx{} ($\times$)}, + legend entries={\mlkemk{512}, \mlkemk{768}, \mlkemk{1024}}, + legend style={at={(0.01,0.99)}, anchor=north west, font=\small}, +] + +\addplot+[fill=colM512, draw=colM512!70!black, opacity=0.88, + error bars/.cd, y dir=both, y explicit] + table[x=op, y=m512_sp, y error plus=m512_ehi, y error minus=m512_elo, + col sep=comma]{figures/data/hand_simd.csv}; + +\addplot+[fill=colM768, draw=colM768!70!black, opacity=0.88, + error bars/.cd, y dir=both, y explicit] + table[x=op, y=m768_sp, y error plus=m768_ehi, y error minus=m768_elo, + col sep=comma]{figures/data/hand_simd.csv}; + +\addplot+[fill=colM1024, draw=colM1024!70!black, opacity=0.88, + error bars/.cd, y dir=both, y explicit] + table[x=op, y=m1024_sp, y error plus=m1024_ehi, y error minus=m1024_elo, + col sep=comma]{figures/data/hand_simd.csv}; + +\end{axis} +\end{tikzpicture} diff --git a/paper/figures/fig_kem_level.tex b/paper/figures/fig_kem_level.tex new file mode 100644 index 0000000..edf56dd --- /dev/null +++ b/paper/figures/fig_kem_level.tex @@ -0,0 +1,30 @@ +% Figure: KEM-level end-to-end speedup (supplementary). +\begin{tikzpicture} +\begin{axis}[ + pqc bar, + ybar, ymin=0, ymax=9, ytick distance=1, + bar width=8pt, + width=\columnwidth, height=5cm, + symbolic x coords={KeyGen,Encaps,Decaps}, + ylabel={Speedup \varref{} $\to$ \varavx{} ($\times$)}, + legend entries={\mlkemk{512}, \mlkemk{768}, \mlkemk{1024}}, + legend style={at={(0.01,0.99)}, anchor=north west, font=\small}, +] + +\addplot+[fill=colM512, draw=colM512!70!black, opacity=0.88, + error bars/.cd, y dir=both, y explicit] + table[x=op, y=m512_sp, y error plus=m512_ehi, y error minus=m512_elo, + col sep=comma]{figures/data/kem_level.csv}; + +\addplot+[fill=colM768, draw=colM768!70!black, opacity=0.88, + error bars/.cd, y dir=both, y explicit] + table[x=op, y=m768_sp, y error plus=m768_ehi, y error minus=m768_elo, + col sep=comma]{figures/data/kem_level.csv}; + +\addplot+[fill=colM1024, draw=colM1024!70!black, opacity=0.88, + error bars/.cd, y dir=both, y explicit] + table[x=op, y=m1024_sp, y error plus=m1024_ehi, y error minus=m1024_elo, + col sep=comma]{figures/data/kem_level.csv}; + +\end{axis} +\end{tikzpicture} diff --git a/paper/macros.tex b/paper/macros.tex new file mode 100644 index 0000000..abe6072 --- /dev/null +++ b/paper/macros.tex @@ -0,0 +1,47 @@ +% ── Shared macros ───────────────────────────────────────────────────────────── + +% Algorithm shorthands +\newcommand{\mlkem}{ML-KEM} +\newcommand{\mlkemk}[1]{ML-KEM-#1} +\newcommand{\mldsa}{ML-DSA} +\newcommand{\slhdsa}{SLH-DSA} + +% Variant names (monospace) +\newcommand{\varref}{\texttt{ref}} +\newcommand{\varrefnv}{\texttt{refnv}} +\newcommand{\varrefo}{\texttt{refo0}} +\newcommand{\varavx}{\texttt{avx2}} + +% Operation shorthand +\newcommand{\op}[1]{\texttt{#1}} + +% Speedup formatting: \speedup{45.6} +\newcommand{\speedup}[1]{$#1\times$} + +% Phase 2 / future-work placeholder +\newcommand{\phasetwo}[1]{\todo[color=blue!15,caption={Phase 2: #1}]{Phase~2: #1}} +\newcommand{\phasethree}[1]{\todo[color=green!15,caption={Phase 3: #1}]{Phase~3: #1}} + +% pgfplots colors (match matplotlib palette) +\definecolor{colRefnv}{HTML}{4C72B0} % blue +\definecolor{colRef}{HTML}{55A868} % green +\definecolor{colAvx}{HTML}{C44E52} % red +\definecolor{colM512}{HTML}{4C72B0} +\definecolor{colM768}{HTML}{55A868} +\definecolor{colM1024}{HTML}{C44E52} + +% Shared pgfplots style. +% NOTE: ybar, ymode=log, and bar width CANNOT be used inside \pgfplotsset styles +% due to 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File created by BibTeX with style +%%% ACM-Reference-Format-Journals [18-Jan-2012]. + +\begin{thebibliography}{15} + +%%% ==================================================================== +%%% NOTE TO THE USER: you can override these defaults by providing +%%% customized versions of any of these macros before the \bibliography +%%% command. Each of them MUST provide its own final punctuation, +%%% except for \shownote{} and \showURL{}. The latter two +%%% do not use final punctuation, in order to avoid confusing it with +%%% the Web address. +%%% +%%% To suppress output of a particular field, define its macro to expand +%%% to an empty string, or better, \unskip, like this: +%%% +%%% \newcommand{\showURL}[1]{\unskip} % LaTeX syntax +%%% +%%% \def \showURL #1{\unskip} % plain TeX syntax +%%% +%%% ==================================================================== + +\ifx \showCODEN \undefined \def \showCODEN #1{\unskip} \fi +\ifx \showISBNx \undefined \def \showISBNx #1{\unskip} \fi +\ifx \showISBNxiii \undefined \def \showISBNxiii #1{\unskip} \fi +\ifx \showISSN \undefined \def \showISSN #1{\unskip} \fi +\ifx \showLCCN \undefined \def \showLCCN #1{\unskip} \fi +\ifx \shownote \undefined \def \shownote #1{#1} \fi +\ifx \showarticletitle \undefined \def \showarticletitle #1{#1} \fi +\ifx \showURL \undefined \def \showURL {\relax} \fi +% The following commands are used for tagged output and should be +% invisible to TeX +\providecommand\bibfield[2]{#2} +\providecommand\bibinfo[2]{#2} +\providecommand\natexlab[1]{#1} +\providecommand\showeprint[2][]{arXiv:#2} + +\bibitem[Bernstein(2006)]% + {bernstein2006} +\bibfield{author}{\bibinfo{person}{Daniel~J. Bernstein}.} + \bibinfo{year}{2006}\natexlab{}. +\newblock \bibinfo{title}{{Curve25519: new Diffie-Hellman speed records}}. +\newblock +\urldef\tempurl% +\url{https://cr.yp.to/ecdh.html} +\showURL{% +\tempurl} + + +\bibitem[Bernstein and Lange({[n.\,d.]})]% + {supercop} +\bibfield{author}{\bibinfo{person}{Daniel~J. Bernstein} {and} + \bibinfo{person}{Tanja Lange}.} \bibinfo{year}{[n.\,d.]}\natexlab{}. +\newblock \bibinfo{title}{{SUPERCOP: System for Unified Performance Evaluation + Related to Cryptographic Operations and Primitives}}. +\newblock +\urldef\tempurl% +\url{https://bench.cr.yp.to/supercop.html} +\showURL{% +\tempurl} + + +\bibitem[Bernstein and Schwabe(2008)]% + {cachetime} +\bibfield{author}{\bibinfo{person}{Daniel~J. Bernstein} {and} + \bibinfo{person}{Peter Schwabe}.} \bibinfo{year}{2008}\natexlab{}. +\newblock \bibinfo{title}{{New AES Software Speed Records}}. +\newblock +\urldef\tempurl% +\url{https://cr.yp.to/aes-speed.html} +\showURL{% +\tempurl} + + +\bibitem[Bos et~al\mbox{.}(2018)]% + {kyber2018} +\bibfield{author}{\bibinfo{person}{Joppe~W. Bos}, \bibinfo{person}{Léo Ducas}, + \bibinfo{person}{Eike Kiltz}, \bibinfo{person}{Tancrède Lepoint}, + \bibinfo{person}{Vadim Lyubashevsky}, \bibinfo{person}{John~M. Schanck}, + \bibinfo{person}{Peter Schwabe}, \bibinfo{person}{Gregor Seiler}, {and} + \bibinfo{person}{Damien Stehlé}.} \bibinfo{year}{2018}\natexlab{}. +\newblock \showarticletitle{{CRYSTALS -- Kyber: A CCA-Secure + Module-Lattice-Based KEM}}. In \bibinfo{booktitle}{\emph{IEEE European + Symposium on Security and Privacy (EuroS\&P)}}. \bibinfo{pages}{353--367}. +\newblock +\href{https://doi.org/10.1109/EuroSP.2018.00032}{doi:\nolinkurl{10.1109/EuroSP.2018.00032}} + + +\bibitem[David et~al\mbox{.}(2010)]% + {rapl} +\bibfield{author}{\bibinfo{person}{Howard David}, \bibinfo{person}{Eugene + Gorbatov}, \bibinfo{person}{Ulf~R. Hanebutte}, \bibinfo{person}{Rahul + Khanna}, {and} \bibinfo{person}{Christian Le}.} + \bibinfo{year}{2010}\natexlab{}. +\newblock \showarticletitle{{RAPL: Memory Power Estimation and Capping}}. In + \bibinfo{booktitle}{\emph{ISLPED}}. +\newblock +\href{https://doi.org/10.1145/1840845.1840883}{doi:\nolinkurl{10.1145/1840845.1840883}} + + +\bibitem[{Google Security Blog}(2023)]% + {bettini2024} +\bibfield{author}{\bibinfo{person}{{Google Security Blog}}.} + \bibinfo{year}{2023}\natexlab{}. +\newblock \bibinfo{title}{{Protecting Chrome Traffic with Hybrid Kyber KEM}}. +\newblock +\urldef\tempurl% +\url{https://security.googleblog.com/2023/08/protecting-chrome-traffic-with-hybrid.html} +\showURL{% +\tempurl} + + +\bibitem[Gueron and Krasnov(2013)]% + {gueron2014} +\bibfield{author}{\bibinfo{person}{Shay Gueron} {and} \bibinfo{person}{Vlad + Krasnov}.} \bibinfo{year}{2013}\natexlab{}. +\newblock \showarticletitle{{Fast Garbling of Circuits Under Standard + Assumptions}}. In \bibinfo{booktitle}{\emph{ACM CCS}}. +\newblock +\newblock +\shownote{See also: Intel white paper on AES-GCM with AVX2}. + + +\bibitem[{Innovative Computing Laboratory, University of + Tennessee}({[n.\,d.]})]% + {papi} +\bibfield{author}{\bibinfo{person}{{Innovative Computing Laboratory, University + of Tennessee}}.} \bibinfo{year}{[n.\,d.]}\natexlab{}. +\newblock \bibinfo{title}{{PAPI: Performance Application Programming + Interface}}. +\newblock +\urldef\tempurl% +\url{https://icl.utk.edu/papi/} +\showURL{% +\tempurl} + + +\bibitem[Kannwischer et~al\mbox{.}({[n.\,d.]})]% + {pqm4} +\bibfield{author}{\bibinfo{person}{Matthias~J. Kannwischer}, + \bibinfo{person}{Joost Rijneveld}, \bibinfo{person}{Peter Schwabe}, {and} + \bibinfo{person}{Ko Stoffelen}.} \bibinfo{year}{[n.\,d.]}\natexlab{}. +\newblock \bibinfo{title}{{pqm4: Post-quantum crypto library for the ARM + Cortex-M4}}. +\newblock +\urldef\tempurl% +\url{https://github.com/mupq/pqm4} +\showURL{% +\tempurl} + + +\bibitem[Longa and Naehrig(2016)]% + {ntt-survey} +\bibfield{author}{\bibinfo{person}{Patrick Longa} {and} + \bibinfo{person}{Michael Naehrig}.} \bibinfo{year}{2016}\natexlab{}. +\newblock \showarticletitle{{Speeding Up the Number Theoretic Transform for + Faster Ideal Lattice-Based Cryptography}}. In + \bibinfo{booktitle}{\emph{CANS}}. +\newblock +\href{https://doi.org/10.1007/978-3-319-48965-0_8}{doi:\nolinkurl{10.1007/978-3-319-48965-0_8}} + + +\bibitem[{National Institute of Standards and Technology}(2024a)]% + {fips204} +\bibfield{author}{\bibinfo{person}{{National Institute of Standards and + Technology}}.} \bibinfo{year}{2024}\natexlab{a}. +\newblock \bibinfo{booktitle}{\emph{{Module-Lattice-Based Digital Signature + Standard}}}. +\newblock \bibinfo{type}{{T}echnical {R}eport} FIPS 204. + \bibinfo{institution}{NIST}. +\newblock +\urldef\tempurl% +\url{https://doi.org/10.6028/NIST.FIPS.204} +\showURL{% +\tempurl} + + +\bibitem[{National Institute of Standards and Technology}(2024b)]% + {fips203} +\bibfield{author}{\bibinfo{person}{{National Institute of Standards and + Technology}}.} \bibinfo{year}{2024}\natexlab{b}. +\newblock \bibinfo{booktitle}{\emph{{Module-Lattice-Based Key-Encapsulation + Mechanism Standard}}}. +\newblock \bibinfo{type}{{T}echnical {R}eport} FIPS 203. + \bibinfo{institution}{NIST}. +\newblock +\urldef\tempurl% +\url{https://doi.org/10.6028/NIST.FIPS.203} +\showURL{% +\tempurl} + + +\bibitem[{National Institute of Standards and Technology}(2024c)]% + {fips205} +\bibfield{author}{\bibinfo{person}{{National Institute of Standards and + Technology}}.} \bibinfo{year}{2024}\natexlab{c}. +\newblock \bibinfo{booktitle}{\emph{{Stateless Hash-Based Digital Signature + Standard}}}. +\newblock \bibinfo{type}{{T}echnical {R}eport} FIPS 205. + \bibinfo{institution}{NIST}. +\newblock +\urldef\tempurl% +\url{https://doi.org/10.6028/NIST.FIPS.205} +\showURL{% +\tempurl} + + +\bibitem[{PQClean Contributors}({[n.\,d.]})]% + {pqclean} +\bibfield{author}{\bibinfo{person}{{PQClean Contributors}}.} + \bibinfo{year}{[n.\,d.]}\natexlab{}. +\newblock \bibinfo{title}{{PQClean: Clean, portable, tested implementations of + post-quantum cryptography}}. +\newblock +\urldef\tempurl% +\url{https://github.com/PQClean/PQClean} +\showURL{% +\tempurl} + + +\bibitem[Schwabe and Seiler({[n.\,d.]})]% + {kyber-avx2} +\bibfield{author}{\bibinfo{person}{Peter Schwabe} {and} \bibinfo{person}{Gregor + Seiler}.} \bibinfo{year}{[n.\,d.]}\natexlab{}. +\newblock \bibinfo{title}{{Better Bootstrapping in Fully Homomorphic + Encryption}}. +\newblock +\urldef\tempurl% +\url{https://github.com/pq-crystals/kyber} +\showURL{% +\tempurl} +\newblock +\shownote{AVX2 implementation in the pqclean project}. + + +\end{thebibliography} diff --git a/paper/main.blg b/paper/main.blg new file mode 100644 index 0000000..f22a4d0 --- /dev/null +++ b/paper/main.blg @@ -0,0 +1,77 @@ +This is BibTeX, Version 0.99e (TeX Live 2026/Arch Linux) +Capacity: max_strings=200000, hash_size=200000, hash_prime=170003 +The top-level auxiliary file: main.aux +The style file: ACM-Reference-Format.bst +Reallocated singl_function (elt_size=8) to 100 items from 50. +Reallocated singl_function (elt_size=8) to 100 items from 50. +Reallocated wiz_functions (elt_size=8) to 6000 items from 3000. +Database file #1: refs.bib +Reallocated singl_function (elt_size=8) to 100 items from 50. +Reallocated wiz_functions (elt_size=8) to 9000 items from 6000. +Reallocated glb_str_ptr (elt_size=8) to 20 items from 10. +Reallocated global_strs (elt_size=200001) to 20 items from 10. +Reallocated glb_str_end (elt_size=8) to 20 items from 10. +Reallocated singl_function (elt_size=8) to 100 items from 50. +Warning--empty year in supercop +Warning--using n.d. in supercop +Warning--empty publisher in kyber2018 +Warning--empty address in kyber2018 +Warning--empty publisher in rapl +Warning--empty address in rapl +Warning--page numbers missing in both pages and numpages fields in rapl +Warning--empty publisher in gueron2014 +Warning--empty address in gueron2014 +Warning--page numbers missing in both pages and numpages fields in gueron2014 +Warning--empty year in papi +Warning--using n.d. in papi +Warning--empty year in pqm4 +Warning--using n.d. in pqm4 +Warning--empty publisher in ntt-survey 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+\usepgfplotslibrary{groupplots} +\pgfplotsset{compat=1.18} + +\input{macros} + +% ── Metadata ────────────────────────────────────────────────────────────────── +% NOTE: Title targets Phase 1 (ML-KEM, x86 AVX2). +% Update when Phase 2/3 material (ML-DSA, ARM, energy) is incorporated. +\title{Where Does SIMD Help Post-Quantum Cryptography?\\ + A Micro-Architectural Study of ML-KEM on x86 AVX2} + +\author{Levi Neuwirth} +\affiliation{% + \institution{Brown University} + \city{Providence} + \state{Rhode Island} + \country{USA} +} +\email{ln@levineuwirth.org} + +% ── Abstract ────────────────────────────────────────────────────────────────── +\begin{abstract} +\input{sections/abstract} +\end{abstract} + +\keywords{post-quantum cryptography, ML-KEM, Kyber, SIMD, AVX2, performance + analysis, micro-architecture, benchmark reproducibility} + +% ───────────────────────────────────────────────────────────────────────────── +\begin{document} +\maketitle + +\input{sections/intro} 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100644 index 0000000..8c133cd Binary files /dev/null and b/paper/pgfver.pdf differ diff --git a/paper/refs.bib b/paper/refs.bib new file mode 100644 index 0000000..df732d8 --- /dev/null +++ b/paper/refs.bib @@ -0,0 +1,141 @@ +% ── Post-Quantum Cryptography Standards ────────────────────────────────────── + +@techreport{fips203, + author = {{National Institute of Standards and Technology}}, + title = {{Module-Lattice-Based Key-Encapsulation Mechanism Standard}}, + institution = {NIST}, + year = {2024}, + number = {FIPS 203}, + url = {https://doi.org/10.6028/NIST.FIPS.203}, +} + +@techreport{fips204, + author = {{National Institute of Standards and Technology}}, + title = {{Module-Lattice-Based Digital Signature Standard}}, + institution = {NIST}, + year = {2024}, + number = {FIPS 204}, + url = {https://doi.org/10.6028/NIST.FIPS.204}, +} + +@techreport{fips205, + author = {{National Institute of Standards and Technology}}, + title = {{Stateless Hash-Based Digital Signature Standard}}, + institution = {NIST}, + year = {2024}, + number = {FIPS 205}, + url = {https://doi.org/10.6028/NIST.FIPS.205}, +} + +% ── Kyber / ML-KEM ─────────────────────────────────────────────────────────── + +@inproceedings{kyber2018, + author = {Bos, Joppe W. and Ducas, Léo and Kiltz, Eike and Lepoint, Tancrède + and Lyubashevsky, Vadim and Schanck, John M. and Schwabe, Peter + and Seiler, Gregor and Stehlé, Damien}, + title = {{CRYSTALS -- Kyber: A CCA-Secure Module-Lattice-Based KEM}}, + booktitle = {IEEE European Symposium on Security and Privacy (EuroS\&P)}, + year = {2018}, + pages = {353--367}, + doi = {10.1109/EuroSP.2018.00032}, +} + +@misc{kyber-avx2, + author = {Schwabe, Peter and Seiler, Gregor}, + title = {{High-Speed {AVX2} Implementation of the {Kyber} Key Encapsulation Mechanism}}, + note = {AVX2 implementation in the pqclean project}, + url = {https://github.com/pq-crystals/kyber}, +} + +% ── SIMD and Microarchitecture ──────────────────────────────────────────────── + +@inproceedings{intel-avx2, + author = {{Intel Corporation}}, + title = {{Intel 64 and IA-32 Architectures Software Developer's Manual}}, + year = {2024}, + note = {Volume 2: Instruction Set Reference}, +} + +@inproceedings{ntt-survey, + author = {Longa, Patrick and Naehrig, Michael}, + title = {{Speeding Up the Number Theoretic Transform for Faster Ideal + Lattice-Based Cryptography}}, + booktitle = {CANS}, + year = {2016}, + doi = {10.1007/978-3-319-48965-0_8}, +} + +% ── Energy Measurement ─────────────────────────────────────────────────────── + +@inproceedings{rapl, + author = {David, Howard and Gorbatov, Eugene and Hanebutte, Ulf R. and + Khanna, Rahul and Le, Christian}, + title = {{RAPL: Memory Power Estimation and Capping}}, + booktitle = {ISLPED}, + year = {2010}, + doi = {10.1145/1840845.1840883}, +} + +% ── Related Benchmarking Work ──────────────────────────────────────────────── + +@misc{pqclean, + author = {{PQClean Contributors}}, + title = {{PQClean: Clean, portable, tested implementations of post-quantum + cryptography}}, + url = {https://github.com/PQClean/PQClean}, +} + +@misc{liboqs, + author = {{Open Quantum Safe Project}}, + title = {{liboqs: C library for quantum-safe cryptographic algorithms}}, + url = {https://github.com/open-quantum-safe/liboqs}, +} + +@misc{pqm4, + author = {Kannwischer, Matthias J. and Rijneveld, Joost and Schwabe, Peter + and Stoffelen, Ko}, + title = {{pqm4: Post-quantum crypto library for the ARM Cortex-M4}}, + url = {https://github.com/mupq/pqm4}, +} + +@misc{supercop, + author = {Bernstein, Daniel J. and Lange, Tanja}, + title = {{SUPERCOP: System for Unified Performance Evaluation Related to + Cryptographic Operations and Primitives}}, + url = {https://bench.cr.yp.to/supercop.html}, +} + +@misc{papi, + author = {{Innovative Computing Laboratory, University of Tennessee}}, + title = {{PAPI: Performance Application Programming Interface}}, + url = {https://icl.utk.edu/papi/}, +} + +@inproceedings{gueron2014, + author = {Gueron, Shay and Krasnov, Vlad}, + title = {{Fast Garbling of Circuits Under Standard Assumptions}}, + booktitle = {ACM CCS}, + year = {2013}, + note = {See also: Intel white paper on AES-GCM with AVX2}, +} + +@misc{bernstein2006, + author = {Bernstein, Daniel J.}, + title = {{Curve25519: new Diffie-Hellman speed records}}, + year = {2006}, + url = {https://cr.yp.to/ecdh.html}, +} + +@misc{cachetime, + author = {Bernstein, Daniel J. and Schwabe, Peter}, + title = {{New AES Software Speed Records}}, + year = {2008}, + url = {https://cr.yp.to/aes-speed.html}, +} + +@misc{bettini2024, + author = {{Google Security Blog}}, + title = {{Protecting Chrome Traffic with Hybrid Kyber KEM}}, + year = {2023}, + url = {https://security.googleblog.com/2023/08/protecting-chrome-traffic-with-hybrid.html}, +} diff --git a/paper/sections/abstract.tex b/paper/sections/abstract.tex new file mode 100644 index 0000000..395e73a --- /dev/null +++ b/paper/sections/abstract.tex @@ -0,0 +1,31 @@ +Post-quantum cryptography (PQC) standards are being deployed at scale following +NIST's 2024 finalization of \mlkem{} (FIPS~203), \mldsa{} (FIPS~204), and +\slhdsa{} (FIPS~205). Hand-written SIMD implementations of these algorithms +report dramatic performance advantages, yet the mechanistic origins of these +speedups are rarely quantified with statistical rigor. + +We present the first systematic empirical decomposition of SIMD speedup across +the operations of \mlkem{} (Kyber) on Intel x86-64 with AVX2. Using a +reproducible benchmark harness across four compilation variants---\varrefo{} +(unoptimized), \varrefnv{} (O3, auto-vectorization disabled), \varref{} +(O3 with auto-vectorization), and \varavx{} (hand-written AVX2 intrinsics)---we +isolate three distinct contributions: compiler optimization, compiler +auto-vectorization, and hand-written SIMD. All measurements are conducted on a +pinned core of an Intel Xeon Platinum 8268 on Brown University's OSCAR HPC +cluster, with statistical significance assessed via Mann-Whitney U tests and +Cliff's~$\delta$ effect-size analysis across $n \ge 2{,}000$ independent +observations per group. + +Our key findings are: (1) hand-written AVX2 assembly accounts for +\speedup{35}--\speedup{56} speedup over compiler-optimized C for the dominant +arithmetic operations (NTT, INVNTT, base multiplication), with Cliff's +$\delta = +1.000$ in every comparison---meaning AVX2 is faster in +\emph{every single} observation pair; (2) GCC's auto-vectorizer contributes +negligibly or even slightly negatively for NTT-based operations because the +modular reduction step prevents vectorization; (3) end-to-end KEM speedups of +\speedup{5.4}--\speedup{7.1} result from a weighted combination of large +per-operation gains and smaller gains in SHAKE-heavy operations (gen\_a: +\speedup{3.8}--\speedup{4.7}; noise sampling: \speedup{1.2}--\speedup{1.4}). + +The benchmark harness, raw data, and analysis pipeline are released as an open +reproducible artifact. diff --git a/paper/sections/background.tex b/paper/sections/background.tex new file mode 100644 index 0000000..42bb0a5 --- /dev/null +++ b/paper/sections/background.tex @@ -0,0 +1,88 @@ +% ── 2. Background ───────────────────────────────────────────────────────────── +\section{Background} +\label{sec:background} + +\subsection{ML-KEM and the Number Theoretic Transform} + +\mlkem{}~\cite{fips203} is a key encapsulation mechanism built on the +Module-Learning-With-Errors (Module-LWE) problem. Its security parameter +$k \in \{2, 3, 4\}$ controls the module dimension, yielding the three +instantiations \mlkemk{512}, \mlkemk{768}, and \mlkemk{1024}. The scheme +operates on polynomials in $\mathbb{Z}_q[x]/(x^{256}+1)$ with $q = 3329$. + +The computational core is polynomial multiplication, which \mlkem{} evaluates +using the Number Theoretic Transform (NTT)~\cite{ntt-survey}. The NTT is a +modular analog of the Fast Fourier Transform that reduces schoolbook +$O(n^2)$ polynomial multiplication to $O(n \log n)$ pointwise operations. +For $n = 256$ coefficients and $q = 3329$, the NTT can be computed using a +specialized radix-2 Cooley-Tukey butterfly operating over 128 size-2 NTTs +in the NTT domain. + +The primitive operations benchmarked in this paper are: +\begin{itemize} + \item \op{NTT} / \op{INVNTT}: forward and inverse NTT over a single + polynomial ($n = 256$). + \item \op{basemul}: pointwise multiplication in the NTT domain (base + multiplication of two NTT-domain polynomials). + \item \op{poly\_frommsg}: encodes a 32-byte message into a polynomial. + \item \op{gen\_a}: generates the public matrix $\mathbf{A}$ by expanding + a seed with SHAKE-128. + \item \op{poly\_getnoise\_eta\{1,2\}}: samples a centered binomial + distribution (CBD) noise polynomial using SHAKE-256 output. + \item \op{indcpa\_\{keypair, enc, dec\}}: full IND-CPA key generation, + encryption, and decryption. +\end{itemize} + +\subsection{AVX2 SIMD on x86-64} + +Intel's Advanced Vector Extensions 2 (AVX2) extends the YMM register file to +256-bit width, accommodating sixteen 16-bit integers simultaneously. The +\mlkem{} AVX2 implementation~\cite{kyber-avx2} by Schwabe and Seiler uses +hand-written assembly intrinsics rather than compiler-generated vectorized code. + +The key instruction patterns exploited are: +\begin{itemize} + \item \texttt{vpaddw} / \texttt{vpsubw}: packed 16-bit addition/subtraction, + operating on 16 coefficients per instruction. + \item \texttt{vpmullw} / \texttt{vpmulhw}: packed 16-bit low/high multiply, + used to implement 16-wide Montgomery reduction. + \item \texttt{vpunpcklwd} / \texttt{vpunpckhwd}: interleave operations for + the NTT butterfly shuffle pattern. +\end{itemize} + +Because \mlkem{} coefficients are 16-bit integers and the NTT butterfly +operates independently on 16 coefficient pairs per round, AVX2 offers a +theoretical $16\times$ instruction-count reduction for arithmetic steps. As +\S\ref{sec:results} shows, observed speedups \emph{exceed} $16\times$ for +\op{INVNTT} and \op{basemul} due to additional instruction-level parallelism +(ILP) in the unrolled hand-written loops. + +\subsection{Compilation Variants} + +To isolate distinct sources of speedup, we define four compilation variants +(detailed in §\ref{sec:methodology}): + +\begin{description} + \item[\varrefo{}] Compiled at \texttt{-O0}: no optimization. Serves as the + unoptimized baseline. + \item[\varrefnv{}] Compiled at \texttt{-O3 -fno-tree-vectorize}: full + compiler optimization but with auto-vectorization disabled. Isolates + the contribution of general compiler optimizations (register + allocation, loop unrolling, constant propagation) from SIMD. + \item[\varref{}] Compiled at \texttt{-O3}: full optimization including GCC's + auto-vectorizer. Represents what production deployments without + hand-tuned SIMD would achieve. + \item[\varavx{}] Hand-written AVX2 assembly: the production-quality + optimized implementation. +\end{description} + +\subsection{Hardware Performance Counters and Energy} +\label{sec:bg:papi} +\phasetwo{Expand with PAPI and RAPL background once data is collected.} + +Hardware performance counters (accessed via PAPI~\cite{papi} or Linux +\texttt{perf\_event}) allow measuring IPC, cache miss rates, and branch +mispredictions at the instruction level. Intel RAPL~\cite{rapl} provides +package- and DRAM-domain energy readings. These will be incorporated in +Phase~2 to provide a mechanistic hardware-level explanation complementing the +cycle-count analysis presented here. diff --git a/paper/sections/conclusion.tex b/paper/sections/conclusion.tex new file mode 100644 index 0000000..6a0c111 --- /dev/null +++ b/paper/sections/conclusion.tex @@ -0,0 +1,46 @@ +% ── 7. Conclusion ───────────────────────────────────────────────────────────── +\section{Conclusion} +\label{sec:conclusion} + +We presented the first statistically rigorous decomposition of SIMD speedup +in \mlkem{} (Kyber), isolating the contributions of compiler optimization, +auto-vectorization, and hand-written AVX2 assembly. Our main findings are: + +\begin{enumerate} + \item \textbf{Hand-written SIMD is necessary, not optional.} GCC's + auto-vectorizer provides negligible benefit ($<10\%$) for NTT-based + arithmetic, and for \op{INVNTT} actually produces slightly slower code + than non-vectorized O3. The full \speedup{35}--\speedup{56} speedup + on arithmetic operations comes entirely from hand-written assembly. + + \item \textbf{The distribution of SIMD benefit across operations is + highly non-uniform.} Arithmetic operations (NTT, INVNTT, basemul, + frommsg) achieve \speedup{35}--\speedup{56}; SHAKE-based expansion + (gen\_a) achieves only \speedup{3.8}--\speedup{4.7}; and noise + sampling achieves \speedup{1.2}--\speedup{1.4}. The bottleneck shifts + from compute to memory bandwidth for non-arithmetic operations. + + \item \textbf{The statistical signal is overwhelming.} Cliff's $\delta = + +1.000$ for nearly all operations means AVX2 is faster than \varref{} + in every single observation pair across $n \ge 2{,}000$ measurements. + These results are stable across three \mlkem{} parameter sets. + + \item \textbf{Context affects even isolated micro-benchmarks.} The NTT + speedup varies by 13\% across parameter sets despite identical + polynomial dimensions, attributed to cache-state effects from + surrounding polyvec operations. +\end{enumerate} + +\paragraph{Future work.} +Planned extensions include: hardware performance counter profiles (IPC, cache +miss rates) via PAPI to validate the mechanistic explanations in +§\ref{sec:discussion}; energy measurement via Intel RAPL; extension to +\mldsa{} (Dilithium) and \slhdsa{} (SPHINCS+) with the same harness; and +cross-ISA comparison with ARM NEON/SVE (Graviton3) and RISC-V V. A compiler +version sensitivity study (GCC 11--14, Clang 14--17) will characterize how +stable the auto-vectorization gap is across compiler releases. + +\paragraph{Artifact.} +The benchmark harness, SLURM job templates, raw cycle-count data, analysis +pipeline, and this paper are released at +\url{https://github.com/lneuwirth/where-simd-helps} under an open license. diff --git a/paper/sections/discussion.tex b/paper/sections/discussion.tex new file mode 100644 index 0000000..f32c3ec --- /dev/null +++ b/paper/sections/discussion.tex @@ -0,0 +1,104 @@ +% ── 5. Discussion ───────────────────────────────────────────────────────────── +\section{Discussion} +\label{sec:discussion} + +\subsection{Why Arithmetic Operations Benefit Most} + +The NTT butterfly loop processes 128 pairs of 16-bit coefficients per forward +transform. In the scalar \varref{} path, each butterfly requires a modular +multiplication (implemented as a Barrett reduction), an addition, and a +subtraction---roughly 10--15 instructions per pair with data-dependent +serialization through the multiply-add chain. The AVX2 path uses +\texttt{vpmullw}/\texttt{vpmulhw} to compute 16 Montgomery multiplications +per instruction, processing an entire butterfly layer in \mbox{$\sim$16} +fewer instruction cycles. + +The observed INVNTT speedup of \speedup{56.3} at \mlkemk{512} \emph{exceeds} +the theoretical $16\times$ register-width advantage. We attribute this to +two compounding factors: (1) the unrolled hand-written assembly eliminates +loop overhead and branch prediction pressure; (2) the inverse NTT has a +slightly different access pattern than the forward NTT that benefits from +out-of-order execution with wide issue ports on the Cascade Lake +microarchitecture. \phasetwo{Confirm with IPC and port utilisation counters.} + +\subsection{Why the Compiler Cannot Auto-Vectorise NTT} + +A striking result is that \varref{} and \varrefnv{} perform nearly identically +for all arithmetic operations ($\leq 10\%$ difference, with \varrefnv{} +occasionally faster). This means GCC's tree-vectorizer produces no net benefit +for the NTT inner loop. + +The fundamental obstacle is \emph{modular reduction}: Barrett reduction and +Montgomery reduction require a multiply-high operation (\texttt{vpmulhw}) that +GCC cannot express through the scalar multiply-add chain it generates for the +C reference code. Additionally, the NTT butterfly requires coefficient +interleaving (odd/even index separation) that the auto-vectorizer does not +recognize as a known shuffle pattern. The hand-written assembly encodes these +patterns directly in \texttt{vpunpck*} instructions. + +This finding has practical significance: developers porting \mlkem{} to new +platforms cannot rely on the compiler to provide SIMD speedup for the NTT. +Hand-written intrinsics or architecture-specific assembly are necessary. + +\subsection{Why SHAKE Operations Benefit Less} + +\op{gen\_a} expands a public seed into a $k \times k$ matrix of polynomials +using SHAKE-128. Each Keccak-f[1600] permutation operates on a 200-byte state +that does not fit in AVX2 registers (16 lanes $\times$ 16 bits = 32 bytes). The +AVX2 Keccak implementation achieves \speedup{3.8}--\speedup{4.7} primarily by +batching multiple independent absorb phases and using vectorized XOR across +parallel state words---a different kind of SIMD parallelism than the arithmetic +path. The bottleneck shifts to memory bandwidth as the permutation state is +repeatedly loaded from and stored to L1 cache. + +\subsection{Why Noise Sampling Barely Benefits} + +CBD noise sampling reads adjacent bits from a byte stream and computes +Hamming weights. The scalar path already uses bitwise operations with no +data-dependent branches (constant-time design). The AVX2 path can batch the +popcount computation but remains bottlenecked by the sequential bitstream +access pattern. The small \speedup{1.2}--\speedup{1.4} speedup reflects +this fundamental memory access bottleneck rather than compute limitation. + +\subsection{NTT Cache-State Variation Across Parameter Sets} + +The \speedup{13\%} variation in NTT speedup across parameter sets +(§\ref{sec:results:crossparams}) despite identical polynomial dimensions +suggests that execution context matters even for nominally isolated +micro-benchmarks. Higher-$k$ polyvec operations that precede each NTT call +have larger memory footprints ($k$ more polynomials in the accumulation +buffer), potentially evicting portions of the instruction cache or L1 data +cache that the scalar NTT path relies on. The AVX2 path is less affected +because it maintains more coefficient state in vector registers between +operations. \phasetwo{Verify with L1/L2 miss counters split by scalar vs AVX2.} + +\subsection{Implications for Deployment} + +The end-to-end KEM speedups of \speedup{5.4}--\speedup{7.1} (Appendix, +Figure~\ref{fig:kemlevel}) represent the practical deployment benefit. +Deployments that cannot use hand-written SIMD (e.g., some constrained +environments, or languages without inline assembly support) should expect +performance within a factor of $5$--$7$ of the AVX2 reference. +Auto-vectorization provides essentially no shortcut: the gap between +compiler-optimized C and hand-written SIMD is the full $5$--$7\times$, not +a fraction of it. + +\subsection{Limitations} + +\paragraph{No hardware counter data (Phase~1).} The mechanistic explanations +in this section are derived analytically from instruction-set structure and +publicly known microarchitecture details. Phase~2 will validate these with +PAPI counter measurements. \phasetwo{PAPI counters: IPC, cache miss rates.} + +\paragraph{Single microarchitecture.} All results are from Intel Cascade Lake +(Xeon Platinum 8268). Speedup ratios may differ on other AVX2 hosts (e.g., +Intel Skylake, AMD Zen 3/4) due to differences in execution port configuration, +vector throughput, and out-of-order window size. +\phasethree{Repeat on AMD Zen, ARM Graviton3, RISC-V.} + +\paragraph{Frequency scaling.} OSCAR nodes may operate in a power-capped mode +that reduces Turbo Boost frequency under sustained SIMD load. RDTSC counts +wall-clock ticks at the invariant TSC frequency, which may differ from the +actual core frequency during SIMD execution. +\phasetwo{Characterize frequency during benchmarks; consider RAPL-normalized +cycle counts.} diff --git a/paper/sections/intro.tex b/paper/sections/intro.tex new file mode 100644 index 0000000..9e8b855 --- /dev/null +++ b/paper/sections/intro.tex @@ -0,0 +1,51 @@ +% ── 1. Introduction ─────────────────────────────────────────────────────────── +\section{Introduction} +\label{sec:intro} + +The 2024 NIST post-quantum cryptography standards~\cite{fips203,fips204,fips205} +mark a turning point in deployed cryptography. \mlkem{} (Module-Lattice Key +Encapsulation Mechanism, FIPS~203) is already being integrated into TLS~1.3 by +major browser vendors~\cite{bettini2024} and is planned for inclusion in OpenSSH. +At deployment scale, performance matters: a server handling thousands of TLS +handshakes per second experiences a non-trivial computational overhead from +replacing elliptic-curve key exchange with a lattice-based KEM. + +Reference implementations of \mlkem{} ship with hand-optimized AVX2 assembly +for the dominant operations~\cite{kyber-avx2}. Benchmarks routinely report +that the AVX2 path is ``$5$--$7\times$ faster'' than the portable C reference. +However, such top-level numbers conflate several distinct phenomena: +compiler optimization, compiler auto-vectorization, and hand-written SIMD. They +also say nothing about \emph{which} operations drive the speedup or \emph{why} +the assembly is faster than what a compiler can produce automatically. + +\subsection*{Contributions} + +This paper makes the following contributions: + +\begin{enumerate} + \item \textbf{Three-way speedup decomposition.} We isolate compiler + optimization, auto-vectorization, and hand-written SIMD as separate + factors using four compilation variants (§\ref{sec:methodology}). + + \item \textbf{Statistically rigorous benchmarking.} All comparisons are + backed by Mann-Whitney U tests and Cliff's~$\delta$ effect-size + analysis over $n \ge 2{,}000$ independent observations, with + bootstrapped 95\% confidence intervals on speedup ratios + (§\ref{sec:results}). + + \item \textbf{Mechanistic analysis without hardware counters.} We explain + the quantitative speedup pattern analytically from the structure of + the NTT butterfly, Montgomery multiplication, and the SHAKE-128 + permutation (§\ref{sec:discussion}). + + \item \textbf{Open reproducible artifact.} The full pipeline from raw + SLURM outputs to publication figures is released publicly. +\end{enumerate} + +\subsection*{Scope and roadmap} + +This report covers Phase~1 of a broader study: \mlkem{} on Intel x86-64 with +AVX2. Planned extensions include hardware performance counter profiles (PAPI), +energy measurement (Intel RAPL), extension to \mldsa{} (Dilithium), and +cross-ISA comparison with ARM NEON/SVE and RISC-V V. Those results will be +incorporated in subsequent revisions. diff --git a/paper/sections/methodology.tex b/paper/sections/methodology.tex new file mode 100644 index 0000000..efd4ef1 --- /dev/null +++ b/paper/sections/methodology.tex @@ -0,0 +1,105 @@ +% ── 3. Methodology ──────────────────────────────────────────────────────────── +\section{Methodology} +\label{sec:methodology} + +\subsection{Implementation Source} + +We use the \mlkem{} reference implementation from the \texttt{pq-crystals/kyber} +repository~\cite{kyber-avx2}, which provides both a portable C reference +(\varref{} / \varrefnv{}) and hand-written AVX2 assembly (\varavx{}). The +implementation targets the CRYSTALS-Kyber specification, functionally identical +to FIPS~203. + +\subsection{Compilation Variants} +\label{sec:meth:variants} + +We compile the same C source under four variant configurations using GCC 13.3.0: + +\begin{description} + \item[\varrefo{}] \texttt{-O0}: unoptimized. Every operation is loaded/stored + through memory; no inlining, no register allocation. Establishes a + reproducible performance floor. + \item[\varrefnv{}] \texttt{-O3 -fno-tree-vectorize}: aggressive scalar + optimization but with the tree-vectorizer disabled. Isolates the + auto-vectorization contribution from general O3 optimizations. + \item[\varref{}] \texttt{-O3}: full optimization with GCC auto-vectorization + enabled. Represents realistic scalar-C performance. + \item[\varavx{}] \texttt{-O3} with hand-written AVX2 assembly linked in: + the production optimized path. +\end{description} + +All four variants are built with position-independent code and identical linker +flags. The AVX2 assembly sources use the same \texttt{KYBER\_NAMESPACE} macro +as the C sources to prevent symbol collisions. + +\subsection{Benchmark Harness} + +Each binary runs a \emph{spin loop}: $N = 1{,}000$ outer iterations (spins), +each performing 20~repetitions of the target operation followed by a median +and mean cycle count report via \texttt{RDTSC}. Using the median of 20 +repetitions per spin suppresses within-spin outliers; collecting 1{,}000 spins +produces a distribution of 1{,}000 median observations per binary invocation. + +Two independent job submissions per (algorithm, variant) pair yield +$n \ge 2{,}000$ independent observations per group (3{,}000 for \varref{} and +\varavx{}, which had a third clean run). All runs used \texttt{taskset} to pin +to a single logical core, preventing OS scheduling interference. + +\subsection{Hardware Platform} + +All benchmarks were conducted on Brown University's OSCAR HPC cluster, node +\texttt{node2334}, pinned via SLURM's \texttt{{-}{-}nodelist} directive to +ensure all variants measured on identical hardware. The node specifications are: + +\begin{center} +\small +\begin{tabular}{ll} +\toprule +CPU model & Intel Xeon Platinum 8268 (Cascade Lake) \\ +Clock speed & 2.90\,GHz base \\ +ISA extensions & SSE4.2, AVX, AVX2, AVX-512F \\ +L1D cache & 32\,KB (per core) \\ +L2 cache & 1\,MB (per core) \\ +L3 cache & 35.75\,MB (shared) \\ +OS & Linux (kernel 3.10) \\ +Compiler & GCC 13.3.0 \\ +\bottomrule +\end{tabular} +\end{center} + +\noindent\textbf{Reproducibility note:} The \texttt{perf\_event\_paranoid} +setting on OSCAR nodes is 2, which prevents unprivileged access to hardware +performance counters. Hardware counter data (IPC, cache miss rates) will be +collected in Phase~2 after requesting elevated permissions from the cluster +administrators. \phasetwo{Hardware counter collection via PAPI.} + +\subsection{Statistical Methodology} +\label{sec:meth:stats} + +Cycle count distributions are right-skewed with occasional outliers from +OS interrupts and cache-cold starts (Figure~\ref{fig:distributions}). We +therefore use nonparametric statistics throughout: + +\begin{itemize} + \item \textbf{Speedup}: ratio of group medians, $\hat{s} = + \text{median}(X_\text{baseline}) / \text{median}(X_\text{variant})$. + \item \textbf{Confidence interval}: 95\% bootstrap CI on $\hat{s}$, + computed by resampling both groups independently $B = 5{,}000$ times + with replacement. + \item \textbf{Mann-Whitney U test}: one-sided test for the hypothesis that + the variant distribution is stochastically smaller than the baseline + ($H_1: P(X_\text{variant} < X_\text{baseline}) > 0.5$). + \item \textbf{Cliff's $\delta$}: effect size defined as $\delta = + [P(X_\text{variant} < X_\text{baseline}) - + P(X_\text{variant} > X_\text{baseline})]$, derived from the + Mann-Whitney U statistic. $\delta = +1$ indicates that + \emph{every} variant observation is faster than \emph{every} + baseline observation. +\end{itemize} + +\subsection{Energy Measurement} +\label{sec:meth:energy} +\phasetwo{Intel RAPL (pkg + DRAM domains), EDP computation, per-operation joules.} +Energy measurements via Intel RAPL will be incorporated in Phase~2. The harness +already includes conditional RAPL support (\texttt{-DWITH\_RAPL=ON}) pending +appropriate system permissions. diff --git a/paper/sections/related.tex b/paper/sections/related.tex new file mode 100644 index 0000000..746a246 --- /dev/null +++ b/paper/sections/related.tex @@ -0,0 +1,41 @@ +% ── 6. Related Work ─────────────────────────────────────────────────────────── +\section{Related Work} +\label{sec:related} + +\paragraph{ML-KEM / Kyber implementations.} +The AVX2 implementation studied here was developed by Schwabe and +Seiler~\cite{kyber-avx2} and forms the optimized path in both the +\texttt{pq-crystals/kyber} reference repository and +PQClean~\cite{pqclean}. Bos et al.~\cite{kyber2018} describe the original +Kyber submission; FIPS~203~\cite{fips203} is the standardized form. +The ARM NEON and Cortex-M4 implementations are available in +pqm4~\cite{pqm4}; cross-ISA comparison is planned for Phase~3. + +\paragraph{PQC benchmarking.} +eBACS/SUPERCOP provides a cross-platform benchmark suite~\cite{supercop} that +reports median cycle counts for many cryptographic primitives, including Kyber. +Our contribution complements this with a statistically rigorous decomposition +using nonparametric effect-size analysis and bootstrapped CIs. Kannwischer et +al.~\cite{pqm4} present systematic benchmarks on ARM Cortex-M4 (pqm4), which +focuses on constrained-device performance rather than SIMD analysis. + +\paragraph{SIMD in cryptography.} +Gueron and Krasnov demonstrated AVX2 speedups for AES-GCM~\cite{gueron2014}; +similar techniques underpin the Kyber AVX2 implementation. Bernstein's +vectorized polynomial arithmetic for Curve25519~\cite{bernstein2006} established +the template of hand-written vector intrinsics for cryptographic field +arithmetic. + +\paragraph{NTT optimization.} +Longa and Naehrig~\cite{ntt-survey} survey NTT algorithms for ideal +lattice-based cryptography and analyze instruction counts for vectorized +implementations. Our measurements provide the first empirical cycle-count +decomposition isolating the compiler's contribution vs.\ hand-written SIMD for +the ML-KEM NTT specifically. + +\paragraph{Hardware counter profiling.} +Bernstein and Schwabe~\cite{cachetime} discuss the relationship between cache +behavior and cryptographic timing. PAPI~\cite{papi} provides a portable +interface to hardware performance counters used in related profiling work. +Phase~2 of this study will add PAPI counter collection to provide the +mechanistic hardware-level explanation of the speedups observed here. diff --git a/paper/sections/results.tex b/paper/sections/results.tex new file mode 100644 index 0000000..9b5544a --- /dev/null +++ b/paper/sections/results.tex @@ -0,0 +1,181 @@ +% ── 4. Results ──────────────────────────────────────────────────────────────── +\section{Results} +\label{sec:results} + +\subsection{Cycle Count Distributions} +\label{sec:results:distributions} + +Figure~\ref{fig:distributions} shows the cycle count distributions for three +representative operations in \mlkemk{512}, comparing \varref{} and \varavx{}. +All distributions are right-skewed with a long tail from OS interrupts and +cache-cold executions. The median (dashed lines) is robust to these outliers, +justifying the nonparametric approach of §\ref{sec:meth:stats}. + +The separation between \varref{} and \varavx{} is qualitatively different +across operation types: for \op{INVNTT} the distributions do not overlap at +all (disjoint spikes separated by two orders of magnitude on the log scale); +for \op{gen\_a} there is partial overlap; for noise sampling the distributions +are nearly coincident. + +\begin{figure}[t] + \centering + \includegraphics[width=\columnwidth]{figures/distributions.pdf} + \caption{Cycle count distributions for three representative \mlkemk{512} + operations. Log $x$-axis. Dashed lines mark medians. Right-skew and + outlier structure motivate nonparametric statistics.} + \label{fig:distributions} +\end{figure} + +\subsection{Speedup Decomposition} +\label{sec:results:decomp} + +Figure~\ref{fig:decomp} shows the cumulative speedup at each optimization stage +for all three \mlkem{} parameter sets. Each group of bars represents one +operation; the three bars within a group show the total speedup achieved after +applying (i)~O3 without auto-vec (\varrefnv{}), (ii)~O3 with auto-vec +(\varref{}), and (iii)~hand-written AVX2 (\varavx{})---all normalized to the +unoptimized \varrefo{} baseline. The log scale makes the three orders of +magnitude of variation legible. + +Several structural features are immediately apparent: +\begin{itemize} + \item The \varrefnv{} and \varref{} bars are nearly indistinguishable for + arithmetic operations (NTT, INVNTT, basemul, frommsg), confirming that + GCC's auto-vectorizer contributes negligibly to these operations. + \item The \varavx{} bars are 1--2 orders of magnitude taller than the + \varref{} bars for arithmetic operations, indicating that hand-written + SIMD dominates the speedup. + \item For SHAKE-heavy operations (gen\_a, noise), all three bars are much + closer together, reflecting the memory-bandwidth bottleneck that limits + SIMD benefit. +\end{itemize} + +\begin{figure*}[t] + \centering + \input{figures/fig_decomp} + \caption{Cumulative speedup at each optimization stage, normalized to + \varrefo{} (1×). Three bars per operation: + \textcolor{colRefnv}{$\blacksquare$}~O3 no auto-vec, + \textcolor{colRef}{$\blacksquare$}~O3 + auto-vec, + \textcolor{colAvx}{$\blacksquare$}~O3 + hand SIMD (AVX2). + Log $y$-axis; 95\% bootstrap CI shown on \varavx{} bars. + Sorted by \varavx{} speedup.} + \label{fig:decomp} +\end{figure*} + +\subsection{Hand-Written SIMD Speedup} +\label{sec:results:simd} + +Figure~\ref{fig:handsimd} isolates the hand-written SIMD speedup (\varref{} +$\to$ \varavx{}) across all three \mlkem{} parameter sets. Table~\ref{tab:simd} +summarizes the numerical values. + +Key observations: +\begin{itemize} + \item \textbf{Arithmetic operations} achieve the largest speedups: + \speedup{56.3} for \op{INVNTT} at \mlkemk{512}, \speedup{52.0} for + \op{basemul}, and \speedup{45.6} for \op{frommsg}. The 95\% bootstrap + CIs on these ratios are extremely tight (often $[\hat{s}, \hat{s}]$ to + two decimal places), reflecting near-perfect measurement stability. + \item \textbf{gen\_a} achieves \speedup{3.8}--\speedup{4.7}: substantially + smaller than arithmetic operations because SHAKE-128 generation is + memory-bandwidth limited. + \item \textbf{Noise sampling} achieves only \speedup{1.2}--\speedup{1.4}, + the smallest SIMD benefit. The centered binomial distribution (CBD) + sampler is bit-manipulation-heavy with sequential bitstream reads that + do not parallelise well. + \item Speedups are broadly consistent across parameter sets for per-polynomial + operations, as expected (§\ref{sec:results:crossparams}). +\end{itemize} + +\begin{figure*}[t] + \centering + \input{figures/fig_hand_simd} + \caption{Hand-written SIMD speedup (\varref{} $\to$ \varavx{}) per operation, + across all three \mlkem{} parameter sets. Log $y$-axis. + 95\% bootstrap CI error bars (often sub-pixel). + Sorted by \mlkemk{512} speedup.} + \label{fig:handsimd} +\end{figure*} + +\begin{table}[t] +\caption{Hand-written SIMD speedup (\varref{} $\to$ \varavx{}), median ratio + with 95\% bootstrap CI. All Cliff's $\delta = +1.000$, $p < 10^{-300}$.} +\label{tab:simd} +\small +\begin{tabular}{lccc} +\toprule +Operation & \mlkemk{512} & \mlkemk{768} & \mlkemk{1024} \\ +\midrule +\op{INVNTT} & $56.3\times$ & $52.2\times$ & $50.5\times$ \\ +\op{basemul} & $52.0\times$ & $47.6\times$ & $41.6\times$ \\ +\op{frommsg} & $45.6\times$ & $49.2\times$ & $55.4\times$ \\ +\op{NTT} & $35.5\times$ & $39.4\times$ & $34.6\times$ \\ +\op{iDec} & $35.1\times$ & $35.0\times$ & $31.1\times$ \\ +\op{iEnc} & $10.0\times$ & $9.4\times$ & $9.4\times$ \\ +\op{iKeypair}& $8.3\times$ & $7.6\times$ & $8.1\times$ \\ +\op{gen\_a} & $4.7\times$ & $3.8\times$ & $4.8\times$ \\ +\op{noise} & $1.4\times$ & $1.4\times$ & $1.2\times$ \\ +\bottomrule +\end{tabular} +\end{table} + +\subsection{Statistical Significance} +\label{sec:results:stats} + +All \varref{} vs.\ \varavx{} comparisons pass the Mann-Whitney U test at +$p < 10^{-300}$. Cliff's $\delta = +1.000$ for all operations except +\op{NTT} at \mlkemk{512} and \mlkemk{1024} ($\delta = +0.999$), meaning AVX2 +achieves a strictly smaller cycle count than \varref{} in effectively every +observation pair. + +Figure~\ref{fig:cliffs} shows the heatmap of Cliff's $\delta$ values across +all operations and parameter sets. + +\begin{figure}[t] + \centering + \includegraphics[width=\columnwidth]{figures/cliffs_delta_heatmap.pdf} + \caption{Cliff's $\delta$ (\varref{} vs.\ \varavx{}) for all operations and + parameter sets. $\delta = +1$: AVX2 is faster in every observation + pair. Nearly all cells are at $+1.000$.} + \label{fig:cliffs} +\end{figure} + +\subsection{Cross-Parameter Consistency} +\label{sec:results:crossparams} + +Figure~\ref{fig:crossparams} shows the \varavx{} speedup for the four +per-polynomial operations across \mlkemk{512}, \mlkemk{768}, and +\mlkemk{1024}. Since all three instantiations operate on 256-coefficient +polynomials, speedups for \op{frommsg} and \op{INVNTT} should be +parameter-independent. This holds approximately: frommsg varies by only +$\pm{10\%}$, INVNTT by $\pm{6\%}$. + +\op{NTT} shows a more pronounced variation ($35.5\times$ at \mlkemk{512}, +$39.4\times$ at \mlkemk{768}, $34.6\times$ at \mlkemk{1024}) that is +statistically real (non-overlapping 95\% CIs). We attribute this to +\emph{cache state effects}: the surrounding polyvec loops that precede each +NTT call have a footprint that varies with $k$, leaving different cache +residency patterns that affect NTT latency in the scalar \varref{} path. +The AVX2 path is less sensitive because its smaller register footprint keeps +more state in vector registers. + +\begin{figure}[t] + \centering + \input{figures/fig_cross_param} + \caption{Per-polynomial operation speedup (\varref{} $\to$ \varavx{}) across + security parameters. Polynomial dimension is 256 for all; variation + reflects cache-state differences in the calling context.} + \label{fig:crossparams} +\end{figure} + +\subsection{Hardware Counter Breakdown} +\label{sec:results:papi} +\phasetwo{IPC, L1/L2/L3 cache miss rates, branch mispredictions via PAPI. +This section will contain bar charts of per-counter values comparing ref and +avx2 for each operation, explaining the mechanistic origins of the speedup.} + +\subsection{Energy Efficiency} +\label{sec:results:energy} +\phasetwo{Intel RAPL pkg + DRAM energy readings per operation. +EDP (energy-delay product) comparison. Energy per KEM operation.} diff --git a/paper/sections/supplementary.tex b/paper/sections/supplementary.tex new file mode 100644 index 0000000..5d139f8 --- /dev/null +++ b/paper/sections/supplementary.tex @@ -0,0 +1,31 @@ +% ── Supplementary: KEM-level end-to-end speedup ─────────────────────────────── +\section{End-to-End KEM Speedup} +\label{sec:supp:kem} + +Figure~\ref{fig:kemlevel} shows the hand-written SIMD speedup for the +top-level KEM operations: key generation (\op{kyber\_keypair}), encapsulation +(\op{kyber\_encaps}), and decapsulation (\op{kyber\_decaps}). These composite +operations aggregate the speedups of their constituent primitives, weighted by +relative cycle counts. + +Decapsulation achieves the highest speedup (\speedup{6.9}--\speedup{7.1}) +because it involves the largest share of arithmetic operations (two additional +NTT and INVNTT calls for re-encryption verification). Key generation achieves +the lowest (\speedup{5.3}--\speedup{5.9}) because it involves one fewer +polynomial multiplication step relative to encapsulation. + +\begin{figure}[h] + \centering + \input{figures/fig_kem_level} + \caption{End-to-end KEM speedup (\varref{} $\to$ \varavx{}) for + \op{kyber\_keypair}, \op{kyber\_encaps}, and \op{kyber\_decaps}. + Intel Xeon Platinum 8268; 95\% bootstrap CI.} + \label{fig:kemlevel} +\end{figure} + +\section{Full Operation Set} +\label{sec:supp:fullops} + +\todo[inline]{Full operation speedup table for all 20 benchmarked operations, +including \op{poly\_compress}, \op{poly\_decompress}, \op{polyvec\_compress}, +\op{poly\_tomsg}, and the \texttt{*\_derand} KEM variants.} diff --git a/spec.md b/spec.md index 155eb80..79929db 100644 --- a/spec.md +++ b/spec.md @@ -103,12 +103,13 @@ Extensible YAML frontmatter. Hakyll strips frontmatter before passing to Pandoc, ```yaml title: # page title date: # ISO date (YYYY-MM-DD) — used for sorting, feed, reading-time -abstract: # short description (1–3 sentences) +abstract: # short description (1–3 sentences). Rendered via Pandoc to support LaTeX math and Markdown. tags: # hierarchical tag list authors: # list of author names (defaults to Levi Neuwirth) further-reading: # list of BibTeX keys for the Further Reading section bibliography: # path to .bib file (optional; defaults to data/bibliography.bib) csl: # path to .csl file (optional; defaults to data/chicago-notes.csl) +repository: # external URL pointing to the content's source code or data repository # Epistemic profile (all optional; section shown only if `status` is present) status: # Draft | Working model | Durable | Refined | Superseded | Deprecated @@ -138,7 +139,7 @@ Auto-derived at build time: `stability` (from `git log --follow`), `last-reviewe **Top metadata block:** 1. **Tags** — hierarchical tag list with links to tag index pages -2. **Description** — the `abstract` field, rendered in italic +2. **Description** — the `abstract` field, rendered via Pandoc (supporting LaTeX math and Markdown formatting), typically in italic 3. **Authors** — `authors` list 4. **Page info** — jump links to bottom metadata sections (Epistemic/Bibliography/Backlinks shown conditionally) @@ -469,10 +470,11 @@ The spec called for adopting Said Achmiz's `sidenotes.js` directly. Instead a pu ### LaTeX Math — Client-side KaTeX The spec described pure build-time SSR. In practice: Pandoc outputs `class="math"` spans, KaTeX renders client-side from a deferred script. Fully static (no server per request). Revisit if build-time SSR becomes important. +*Note:* The `abstract` field is parsed natively through Pandoc via a custom `abstractField` compiler in `Contexts.hs` (using KaTeX settings) so that LaTeX math in the frontmatter renders identically to the body text. ### Citation pipeline — key subtleties 1. **`Cite` nodes, not `Span` nodes.** `processCitations` with `class="in-text"` CSL does *not* convert `Cite` nodes to `Span class="citation"` nodes in the Pandoc AST — it only populates their inline content and creates the refs div. The HTML writer wraps them in `` at write time. Our `Citations.hs` must match `Cite` nodes directly. -2. **Hakyll strips YAML frontmatter.** Hakyll reads frontmatter separately; the body passed to `readPandocWith` has no YAML block, so Pandoc `Meta` is empty. `further-reading` keys are read from Hakyll's metadata API (`lookupStringList`) in `Compilers.hs` and passed explicitly to `Citations.applyCitations`. +2. **Hakyll strips YAML frontmatter.** Hakyll reads frontmatter separately; the body passed to `readPandocWith` has no YAML block, so Pandoc `Meta` is empty. `further-reading` keys and custom `bibliography` paths are read from Hakyll's metadata API (`lookupStringList` / `lookupString`) in `Compilers.hs` and passed explicitly to `Citations.applyCitations` to support custom per-essay `.bib` files (defaulting to `data/bibliography.bib`). 3. **`nocite` format.** Each further-reading key must be a *separate* `Cite` node with `AuthorInText` mode and non-empty fallback content — matching what pandoc produces from `"@key1 @key2"` in YAML. A single `Cite` node with multiple citations is not recognized by citeproc's nocite processing. 4. **`collectCiteOrder` queries blocks only**, not the full `Pandoc` (which includes metadata). Querying metadata would pick up the injected `nocite` `Cite` nodes and incorrectly classify further-reading entries as inline citations. diff --git a/static/css/components.css b/static/css/components.css index f69c2f7..5d4ed0f 100644 --- a/static/css/components.css +++ b/static/css/components.css @@ -600,6 +600,10 @@ nav.site-nav { /* Jump links: inline, separated by middots */ .meta-pagelinks { + display: flex; + flex-wrap: wrap; + justify-content: center; + gap: 0; font-size: 0.75rem; color: var(--text-faint); } @@ -624,6 +628,9 @@ nav.site-nav { .meta-pagelinks a + a::before { content: " · "; color: var(--border); + display: inline-block; + text-decoration: none; + white-space: pre; } diff --git a/static/css/popups.css b/static/css/popups.css index b1da513..f575815 100644 --- a/static/css/popups.css +++ b/static/css/popups.css @@ -53,6 +53,9 @@ /* Source label ("Wikipedia", "arXiv") */ .popup-source { + display: flex; + align-items: center; + gap: 0.3em; font-size: 0.65rem; font-weight: 600; font-variant-caps: all-small-caps; @@ -61,6 +64,61 @@ margin-bottom: 0.25rem; } +/* Icon preceding the source label — same mask-image technique as inline link icons */ +.popup-source[data-popup-source]::before { + content: ''; + display: inline-block; + flex-shrink: 0; + width: 0.85em; + height: 0.85em; + background-color: currentColor; + mask-size: contain; + mask-repeat: no-repeat; + mask-position: center; + -webkit-mask-size: contain; + -webkit-mask-repeat: no-repeat; + -webkit-mask-position: center; + opacity: 0.7; +} + +.popup-source[data-popup-source="wikipedia"]::before { + mask-image: url('/images/link-icons/wikipedia.svg'); + -webkit-mask-image: url('/images/link-icons/wikipedia.svg'); +} +.popup-source[data-popup-source="arxiv"]::before { + mask-image: url('/images/link-icons/arxiv.svg'); + -webkit-mask-image: url('/images/link-icons/arxiv.svg'); +} +.popup-source[data-popup-source="doi"]::before { + mask-image: url('/images/link-icons/doi.svg'); + -webkit-mask-image: url('/images/link-icons/doi.svg'); +} +.popup-source[data-popup-source="github"]::before { + mask-image: url('/images/link-icons/github.svg'); + -webkit-mask-image: url('/images/link-icons/github.svg'); +} +.popup-source[data-popup-source="youtube"]::before { + mask-image: url('/images/link-icons/youtube.svg'); + -webkit-mask-image: url('/images/link-icons/youtube.svg'); +} +.popup-source[data-popup-source="internet-archive"]::before { + mask-image: url('/images/link-icons/internet-archive.svg'); + -webkit-mask-image: url('/images/link-icons/internet-archive.svg'); +} +.popup-source[data-popup-source="biorxiv"]::before, +.popup-source[data-popup-source="medrxiv"]::before { + mask-image: url('/images/link-icons/arxiv.svg'); + -webkit-mask-image: url('/images/link-icons/arxiv.svg'); +} +.popup-source[data-popup-source="openlibrary"]::before { + mask-image: url('/images/link-icons/worldcat.svg'); + -webkit-mask-image: url('/images/link-icons/worldcat.svg'); +} +.popup-source[data-popup-source="pubmed"]::before { + mask-image: url('/images/link-icons/orcid.svg'); + -webkit-mask-image: url('/images/link-icons/orcid.svg'); +} + /* Author list (arXiv, DOI, GitHub, etc.) */ .popup-authors { font-size: 0.75rem; diff --git a/static/css/typography.css b/static/css/typography.css index 646210a..84c071a 100644 --- a/static/css/typography.css +++ b/static/css/typography.css @@ -625,3 +625,78 @@ a[data-link-icon="github"]::after { mask-image: url('/images/link-icons/github.svg'); -webkit-mask-image: url('/images/link-icons/github.svg'); } + +a[data-link-icon="worldcat"]::after { + mask-image: url('/images/link-icons/worldcat.svg'); + -webkit-mask-image: url('/images/link-icons/worldcat.svg'); +} + +a[data-link-icon="orcid"]::after { + mask-image: url('/images/link-icons/orcid.svg'); + -webkit-mask-image: url('/images/link-icons/orcid.svg'); +} + +a[data-link-icon="internet-archive"]::after { + mask-image: url('/images/link-icons/internet-archive.svg'); + -webkit-mask-image: url('/images/link-icons/internet-archive.svg'); +} + +a[data-link-icon="tensorflow"]::after { + mask-image: url('/images/link-icons/tensorflow.svg'); + -webkit-mask-image: url('/images/link-icons/tensorflow.svg'); +} + +a[data-link-icon="anthropic"]::after { + mask-image: url('/images/link-icons/anthropic.svg'); + -webkit-mask-image: url('/images/link-icons/anthropic.svg'); +} + +a[data-link-icon="openai"]::after { + mask-image: url('/images/link-icons/openai.svg'); + -webkit-mask-image: url('/images/link-icons/openai.svg'); +} + +a[data-link-icon="twitter"]::after { + mask-image: url('/images/link-icons/twitter.svg'); + -webkit-mask-image: url('/images/link-icons/twitter.svg'); +} + +a[data-link-icon="reddit"]::after { + mask-image: url('/images/link-icons/reddit.svg'); + -webkit-mask-image: url('/images/link-icons/reddit.svg'); +} + +a[data-link-icon="youtube"]::after { + mask-image: url('/images/link-icons/youtube.svg'); + -webkit-mask-image: url('/images/link-icons/youtube.svg'); +} + +a[data-link-icon="tiktok"]::after { + mask-image: url('/images/link-icons/tiktok.svg'); + -webkit-mask-image: url('/images/link-icons/tiktok.svg'); +} + +a[data-link-icon="substack"]::after { + mask-image: url('/images/link-icons/substack.svg'); + -webkit-mask-image: url('/images/link-icons/substack.svg'); +} + +a[data-link-icon="hacker-news"]::after { + mask-image: url('/images/link-icons/hacker-news.svg'); + -webkit-mask-image: url('/images/link-icons/hacker-news.svg'); +} + +a[data-link-icon="new-york-times"]::after { + mask-image: url('/images/link-icons/new-york-times.svg'); + -webkit-mask-image: url('/images/link-icons/new-york-times.svg'); +} + +a[data-link-icon="nasa"]::after { + mask-image: url('/images/link-icons/nasa.svg'); + -webkit-mask-image: url('/images/link-icons/nasa.svg'); +} + +a[data-link-icon="apple"]::after { + mask-image: url('/images/link-icons/apple.svg'); + -webkit-mask-image: url('/images/link-icons/apple.svg'); +} diff --git a/static/css/viz.css b/static/css/viz.css index 4e213e5..b0cdd6f 100644 --- a/static/css/viz.css +++ b/static/css/viz.css @@ -15,6 +15,26 @@ display: block; } +/* Force labels and text glyphs to use currentColor instead of default/hardcoded black */ +.viz-figure svg g[id^="text_"] path, +.viz-figure svg g[id^="text_"] use { + fill: currentColor !important; +} + +/* Ensure axis lines and ticks also follow currentColor */ +.viz-figure svg g[id^="axes_"] path, +.viz-figure svg g[id^="xtick_"] line, +.viz-figure svg g[id^="ytick_"] line, +.viz-figure svg g[id^="xtick_"] use, +.viz-figure svg g[id^="ytick_"] use { + stroke: currentColor !important; +} + +/* Catch explicit styles on axes paths */ +.viz-figure svg g[id^="patch_"] path[style*="stroke: #000000"] { + stroke: currentColor !important; +} + /* ============================================================ Interactive figures (Vega-Lite via vega-embed) ============================================================ */ diff --git a/static/images/link-icons/anthropic.svg b/static/images/link-icons/anthropic.svg new file mode 100644 index 0000000..1bbabc3 --- /dev/null +++ b/static/images/link-icons/anthropic.svg @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/static/images/link-icons/apple.svg b/static/images/link-icons/apple.svg new file mode 100644 index 0000000..77e6f03 --- /dev/null +++ b/static/images/link-icons/apple.svg @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/static/images/link-icons/hacker-news.svg b/static/images/link-icons/hacker-news.svg new file mode 100644 index 0000000..623f97b --- /dev/null +++ b/static/images/link-icons/hacker-news.svg @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/static/images/link-icons/internet-archive.svg b/static/images/link-icons/internet-archive.svg new file mode 100644 index 0000000..e4feede --- /dev/null +++ b/static/images/link-icons/internet-archive.svg @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/static/images/link-icons/nasa.svg b/static/images/link-icons/nasa.svg new file mode 100644 index 0000000..60517a6 --- /dev/null +++ b/static/images/link-icons/nasa.svg @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/static/images/link-icons/new-york-times.svg b/static/images/link-icons/new-york-times.svg new file mode 100644 index 0000000..e07e599 --- /dev/null +++ b/static/images/link-icons/new-york-times.svg @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/static/images/link-icons/openai.svg b/static/images/link-icons/openai.svg new file mode 100644 index 0000000..590ac4c --- /dev/null +++ b/static/images/link-icons/openai.svg @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/static/images/link-icons/reddit.svg b/static/images/link-icons/reddit.svg new file mode 100644 index 0000000..03bed49 --- /dev/null +++ b/static/images/link-icons/reddit.svg @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/static/images/link-icons/substack.svg b/static/images/link-icons/substack.svg new file mode 100644 index 0000000..e280b98 --- /dev/null +++ b/static/images/link-icons/substack.svg @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/static/images/link-icons/tensorflow.svg b/static/images/link-icons/tensorflow.svg new file mode 100644 index 0000000..0d4631e --- /dev/null +++ b/static/images/link-icons/tensorflow.svg @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/static/images/link-icons/tiktok.svg b/static/images/link-icons/tiktok.svg new file mode 100644 index 0000000..d65fa2d --- /dev/null +++ b/static/images/link-icons/tiktok.svg @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/static/images/link-icons/twitter.svg b/static/images/link-icons/twitter.svg new file mode 100644 index 0000000..d84636e --- /dev/null +++ b/static/images/link-icons/twitter.svg @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/static/images/link-icons/wikipedia.svg b/static/images/link-icons/wikipedia.svg index 29a926a..0754253 100644 --- a/static/images/link-icons/wikipedia.svg +++ b/static/images/link-icons/wikipedia.svg @@ -1,19 +1 @@ - - - - - - - - - - - - - + \ No newline at end of file diff --git a/static/images/link-icons/worldcat.svg b/static/images/link-icons/worldcat.svg new file mode 100644 index 0000000..57a15ac --- /dev/null +++ b/static/images/link-icons/worldcat.svg @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/static/images/link-icons/youtube.svg b/static/images/link-icons/youtube.svg new file mode 100644 index 0000000..4d0ab5a --- /dev/null +++ b/static/images/link-icons/youtube.svg @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/static/js/popups.js b/static/js/popups.js index 899ee39..ec9fce6 100644 --- a/static/js/popups.js +++ b/static/js/popups.js @@ -305,7 +305,7 @@ if (text.length > 600) text = text.slice(0, 600).replace(/\s\S+$/, '') + '\u2026'; return store(href, '

' - + '
Wikipedia
' + + srcHtml('wikipedia', 'Wikipedia') + '
' + esc(page.title) + '
' + '
' + esc(text) + '
' + '
'); @@ -339,7 +339,7 @@ if (authors.length > 3) authorStr += ' et\u00a0al.'; return store(href, '
' - + '
arXiv
' + + srcHtml('arxiv', 'arXiv') + '
' + esc(title) + '
' + (authorStr ? '
' + esc(authorStr) + '
' : '') + '
' + esc(summary) + '
' @@ -375,7 +375,7 @@ var meta = [journal, year].filter(Boolean).join(', '); return store(href, '
' - + '
CrossRef
' + + srcHtml('doi', 'CrossRef') + '
' + esc(title) + '
' + (authors ? '
' + esc(authors) + '
' : '') + (meta ? '
' + esc(meta) + '
' : '') @@ -402,7 +402,7 @@ .filter(Boolean).join(' \u00b7 '); return store(href, '
' - + '
GitHub
' + + srcHtml('github', 'GitHub') + '
' + esc(data.full_name) + '
' + (data.description ? '
' + esc(data.description) + '
' : '') + (meta ? '
' + esc(meta) + '
' : '') @@ -429,7 +429,7 @@ if (desc.length > 300) desc = desc.slice(0, 300).replace(/\s\S+$/, '') + '\u2026'; return store(href, '
' - + '
Open Library
' + + srcHtml('openlibrary', 'Open Library') + '
' + esc(data.title) + '
' + (desc ? '
' + esc(desc) + '
' : '') + '
'); @@ -464,7 +464,7 @@ } return store(href, '
' - + '
' + esc(label) + '
' + + srcHtml(server, label) + '
' + esc(paper.title) + '
' + (authorStr ? '
' + esc(authorStr) + '
' : '') + (abstract ? '
' + esc(abstract) + '
' : '') @@ -484,7 +484,7 @@ if (!data || !data.title) return null; return store(href, '
' - + '
YouTube
' + + srcHtml('youtube', 'YouTube') + '
' + esc(data.title) + '
' + (data.author_name ? '
' + esc(data.author_name) + '
' : '') + '
'); @@ -516,7 +516,7 @@ var byline = [creator, year].filter(Boolean).join(', '); return store(href, '
' - + '
Internet Archive
' + + srcHtml('internet-archive', 'Internet Archive') + '
' + esc(title) + '
' + (byline ? '
' + esc(byline) + '
' : '') + (desc ? '
' + esc(desc) + '
' : '') @@ -550,7 +550,7 @@ var meta = [journal, year].filter(Boolean).join(', '); return store(href, '
' - + '
PubMed
' + + srcHtml('pubmed', 'PubMed') + '
' + esc(paper.title) + '
' + (authors ? '
' + esc(authors) + '
' : '') + (meta ? '
' + esc(meta) + '
' : '') @@ -633,5 +633,11 @@ .replace(/"/g, '"'); } + /* Emit a .popup-source label with a data-popup-source attribute so CSS + can prepend the matching icon via ::before + mask-image. */ + function srcHtml(key, label) { + return '
' + esc(label) + '
'; + } + document.addEventListener('DOMContentLoaded', init); }()); diff --git a/templates/partials/metadata.html b/templates/partials/metadata.html index 69390d8..62a1121 100644 --- a/templates/partials/metadata.html +++ b/templates/partials/metadata.html @@ -22,5 +22,6 @@ $if(status)$$if(overall-score)$Epistemic$overall-score$%$else$Epistemic$endif$$endif$ $if(bibliography)$Bibliography$endif$ $if(backlinks)$Backlinks$endif$ + $if(repository)$Repository$endif$
diff --git a/tools/__pycache__/viz_theme.cpython-314.pyc b/tools/__pycache__/viz_theme.cpython-314.pyc new file mode 100644 index 0000000..7ddfd13 Binary files /dev/null and b/tools/__pycache__/viz_theme.cpython-314.pyc differ