auto: 2026-04-05T01:18:45Z

2026-04-04 21:18:45 -04:00 · 2026-04-04 21:18:45 -04:00 · 9a01c602bc
parent 9a3a5b62b6
commit 9a01c602bc
101 changed files with 9155 additions and 56 deletions
--- 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"
--- 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 :: [Text] -> Text -> Pandoc -> IO (Pandoc, Text, Text)
-applyCitations frKeys doc
+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 :: [Text] -> Text -> Pandoc -> Pandoc
-injectMeta frKeys (Pandoc meta blocks) =
+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"
--- 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).
--- 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 <p> 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
 -- ---------------------------------------------------------------------------
--- 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/<name>.svg.
 domainIcon :: Text -> Text
 domainIcon url
-    | "wikipedia.org" `T.isInfixOf` url = "wikipedia"
+    -- Scholarly / reference
-    | "arxiv.org"     `T.isInfixOf` url = "arxiv"
+    | "wikipedia.org"       `T.isInfixOf` url = "wikipedia"
-    | "doi.org"       `T.isInfixOf` url = "doi"
+    | "arxiv.org"           `T.isInfixOf` url = "arxiv"
-    | "github.com"    `T.isInfixOf` url = "github"
+    | "doi.org"             `T.isInfixOf` url = "doi"
-    | otherwise                          = "external"
+    | "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
--- 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
+    match allEssays $ do
-        route   $ gsubRoute "content/essays/" (const "essays/")
+        route $ customRoute $ \ident ->
-                  `composeRoutes` setExtension "html"
+            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
--- 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,
--- 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
@ -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)
--- 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
@ -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
--- 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
@ -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
--- 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
@ -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
--- 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
@ -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
--- 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
@ -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
--- 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
@ -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
--- 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
@ -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
--- 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
--- 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
@ -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)
--- 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
@ -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)
--- 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
@ -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)
--- 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
@ -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)
--- a/content/essays/where-does-simd-help-post-quantum-cryptography/index.md
+++ 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 <https://git.levineuwirth.org/where-simd-helps> 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.
 :::
--- a/data/simd-paper.bib
+++ 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},
 }
--- a/paper/figures/.gitkeep
+++ b/paper/figures/.gitkeep
--- a/paper/figures/cliffs_delta_heatmap.pdf
+++ b/paper/figures/cliffs_delta_heatmap.pdf
--- a/paper/figures/data/cliffs_delta.csv
+++ 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
--- a/paper/figures/data/cross_param.csv
+++ 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
--- a/paper/figures/data/decomp_mlkem1024.csv
+++ 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
--- a/paper/figures/data/decomp_mlkem512.csv
+++ 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
--- a/paper/figures/data/decomp_mlkem768.csv
+++ 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
--- a/paper/figures/data/hand_simd.csv
+++ 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
--- a/paper/figures/data/kem_level.csv
+++ 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
--- a/paper/figures/distributions.pdf
+++ b/paper/figures/distributions.pdf
--- a/paper/figures/fig_cross_param.tex
+++ 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}
--- a/paper/figures/fig_decomp.tex
+++ 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}
--- a/paper/figures/fig_hand_simd.tex
+++ 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}
--- a/paper/figures/fig_kem_level.tex
+++ 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}
--- a/paper/macros.tex
+++ 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 a pgfkeys namespace issue; apply them inline in each axis instead.
 \pgfplotsset{
  pqc bar/.style={
    ymajorgrids=true,
    yminorgrids=true,
    grid style={dashed, gray!30},
    xtick=data,
    x tick label style={rotate=45, anchor=east, font=\small},
    legend style={font=\small, at={(0.99,0.99)}, anchor=north east},
    error bars/error bar style={line width=0.5pt},
    error bars/error mark options={rotate=90, mark size=1.5pt},
  },
 }
--- a/paper/main.aux
+++ b/paper/main.aux
@ -0,0 +1,173 @@
 \relax 
 \providecommand\hyper@newdestlabel[2]{}
 \providecommand\HyField@AuxAddToFields[1]{}
 \providecommand\HyField@AuxAddToCoFields[2]{}
 \citation{fips203,fips204,fips205}
 \citation{bettini2024}
 \citation{kyber-avx2}
 \citation{fips203}
 \citation{ntt-survey}
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 \newblock \showarticletitle{{Fast Garbling of Circuits Under Standard
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 \newblock
 \newblock
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 \bibitem[{Innovative Computing Laboratory, University of
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--- a/paper/main.pdf
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 \documentclass[sigconf, nonacm]{acmart}
 % ── Packages ──────────────────────────────────────────────────────────────────
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 % ── 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}
 % ─────────────────────────────────────────────────────────────────────────────
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--- a/paper/refs.bib
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 % ── 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},
 }
--- a/paper/sections/abstract.tex
+++ 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.
--- a/paper/sections/background.tex
+++ 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.
--- a/paper/sections/conclusion.tex
+++ 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.
--- a/paper/sections/discussion.tex
+++ 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.}
--- a/paper/sections/intro.tex
+++ 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.
--- a/paper/sections/methodology.tex
+++ 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.
--- a/paper/sections/related.tex
+++ 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.
--- a/paper/sections/results.tex
+++ 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.}
--- a/paper/sections/supplementary.tex
+++ 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.}
--- 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 `<span class="citation">` 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.
--- 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 {
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    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;
 }
--- a/static/css/popups.css
+++ b/static/css/popups.css
@ -53,6 +53,9 @@
 /* Source label ("Wikipedia", "arXiv") */
 .popup-source {
    display: flex;
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    gap: 0.3em;
    font-size: 0.65rem;
    font-weight: 600;
    font-variant-caps: all-small-caps;
@ -61,6 +64,61 @@
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 }
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    content: '';
    display: inline-block;
    flex-shrink: 0;
    width:  0.85em;
    height: 0.85em;
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    mask-position: center;
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--- a/static/css/typography.css
+++ b/static/css/typography.css
@ -625,3 +625,78 @@ a[data-link-icon="github"]::after {
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--- a/static/images/link-icons/worldcat.svg
+++ b/static/images/link-icons/worldcat.svg
@ -0,0 +1 @@
 <svg xmlns="http://www.w3.org/2000/svg" width="174.46" height="168.206" viewBox="0 0 177.525 171.162" xmlns:v="https://vecta.io/nano"><path d="M100.26.831c9.76-1.34 19.63-.63 29.45-.74 5.17-.12 10.18 3.69 10.97 8.89 1.49 6.53-4.35 13.32-11.03 12.8-13.51-.72-27.67-1.39-40.44 3.85-9.54 4.01-15.41 13.69-17.11 23.6-1.58 5.71-.43 13.39-6.51 16.71-6.64 4.43-16.7-.88-16.52-8.91 1.29-14.8 5.8-30.16 16.57-40.91 9.13-9.25 21.94-13.76 34.62-15.29zm-70.23 6.74c5.65-1.98 12.33 1.72 13.78 7.5 1.4 4.97-1.69 9.53-2.97 14.16-3.91 11.79-7.82 24.71-4.37 37.08 3.2 10.86 13.4 17.39 23.26 21.58 5.15 1.66 8.67 7.33 7.36 12.69-1.16 6.02-8.06 10.07-13.87 7.95-12.81-5.38-25.32-13.27-32.63-25.45-6.76-11.04-8.11-24.62-6.1-37.22 1.49-10.8 5.1-21.14 8.55-31.44 1.02-3.29 3.72-5.85 6.99-6.85zm74.19 27.23c15.27-2.9 32.25-.95 44.79 8.85 13.45 10.41 20.4 26.7 25.34 42.5 1.33 4.91 4.53 9.99 2.54 15.18-1.99 6.04-9.74 9.09-15.27 5.88-2.86-1.4-4.8-4.17-5.56-7.21-3.2-11.39-6.81-22.96-13.76-32.7-3.75-5.34-9.26-9.51-15.6-11.2-7.64-2.07-15.68-.92-23.28.74-5.16 1.53-11.36-1.38-13.08-6.57-1.7-4.25-.17-9.34 3.26-12.25 2.99-2.43 7-2.54 10.62-3.22zm14.84 36.63c4.34-1.28 9.54.14 12.12 4 7.71 12.94 13.47 28.12 10.82 43.4-2.51 15.96-13.69 28.85-25.91 38.64a375.65 375.65 0 0 1-15.48 11.5c-4.47 3.48-11.67 2.75-15.2-1.74-3.83-4.49-2.93-12.16 1.94-15.54 11.91-8.27 25.09-16.59 31.59-30.1 5.26-11.43.36-24.11-5.71-34.14-3.85-5.61-.69-14.16 5.83-16.02zM6.83 102.491c3.6-1.56 8.02-1.09 11.13 1.34 10.53 7.92 21.53 16.1 34.57 19.19 9.67 2.31 19.78-1.58 26.78-8.29 2.9-2.42 5.32-5.32 7.84-8.11 3.94-4.63 11.88-4.49 15.89-.03 3.59 3.81 3.91 10.37.39 14.32-8.13 9.01-17.49 17.55-29.2 21.48-12.76 4.73-27.1 2.85-39.3-2.64-10.75-4.65-20.28-11.54-29.73-18.35-3.09-2.09-4.8-5.77-5.2-9.38.95-3.87 2.83-8.01 6.83-9.53z"/></svg>
--- a/static/images/link-icons/youtube.svg
+++ b/static/images/link-icons/youtube.svg
@ -0,0 +1 @@
 <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 576 512"><path d="M549.655 124.083c-6.281-23.65-24.787-42.276-48.284-48.597C458.781 64 288 64 288 64S117.22 64 74.629 75.486c-23.497 6.322-42.003 24.947-48.284 48.597-11.412 42.867-11.412 132.305-11.412 132.305s0 89.438 11.412 132.305c6.281 23.65 24.787 41.5 48.284 47.821C117.22 448 288 448 288 448s170.78 0 213.371-11.486c23.497-6.321 42.003-24.171 48.284-47.821 11.412-42.867 11.412-132.305 11.412-132.305s0-89.438-11.412-132.305zm-317.51 213.508V175.185l142.739 81.205-142.739 81.201z"></path></svg>
--- 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,
                    '<div class="popup-wikipedia">'
-                    + '<div class="popup-source">Wikipedia</div>'
+                    + srcHtml('wikipedia', 'Wikipedia')
                    + '<div class="popup-title">'   + esc(page.title) + '</div>'
                    + '<div class="popup-extract">' + esc(text)       + '</div>'
                    + '</div>');
@ -339,7 +339,7 @@
                if (authors.length > 3) authorStr += ' et\u00a0al.';
                return store(href,
                    '<div class="popup-arxiv">'
-                    + '<div class="popup-source">arXiv</div>'
+                    + srcHtml('arxiv', 'arXiv')
                    + '<div class="popup-title">'    + esc(title)     + '</div>'
                    + (authorStr ? '<div class="popup-authors">'  + esc(authorStr) + '</div>' : '')
                    + '<div class="popup-abstract">' + esc(summary)   + '</div>'
@ -375,7 +375,7 @@
                var meta = [journal, year].filter(Boolean).join(', ');
                return store(href,
                    '<div class="popup-doi">'
-                    + '<div class="popup-source">CrossRef</div>'
+                    + srcHtml('doi', 'CrossRef')
                    + '<div class="popup-title">'    + esc(title)    + '</div>'
                    + (authors  ? '<div class="popup-authors">'  + esc(authors)  + '</div>' : '')
                    + (meta     ? '<div class="popup-meta">'     + esc(meta)     + '</div>' : '')
@ -402,7 +402,7 @@
                    .filter(Boolean).join(' \u00b7 ');
                return store(href,
                    '<div class="popup-github">'
-                    + '<div class="popup-source">GitHub</div>'
+                    + srcHtml('github', 'GitHub')
                    + '<div class="popup-title">'    + esc(data.full_name)   + '</div>'
                    + (data.description ? '<div class="popup-abstract">' + esc(data.description) + '</div>' : '')
                    + (meta ? '<div class="popup-meta">' + esc(meta) + '</div>' : '')
@ -429,7 +429,7 @@
                if (desc.length > 300) desc = desc.slice(0, 300).replace(/\s\S+$/, '') + '\u2026';
                return store(href,
                    '<div class="popup-openlibrary">'
-                    + '<div class="popup-source">Open Library</div>'
+                    + srcHtml('openlibrary', 'Open Library')
                    + '<div class="popup-title">'    + esc(data.title) + '</div>'
                    + (desc ? '<div class="popup-abstract">' + esc(desc) + '</div>' : '')
                    + '</div>');
@ -464,7 +464,7 @@
                }
                return store(href,
                    '<div class="popup-biorxiv">'
-                    + '<div class="popup-source">' + esc(label) + '</div>'
+                    + srcHtml(server, label)
                    + '<div class="popup-title">'    + esc(paper.title) + '</div>'
                    + (authorStr ? '<div class="popup-authors">'  + esc(authorStr)  + '</div>' : '')
                    + (abstract  ? '<div class="popup-abstract">' + esc(abstract)   + '</div>' : '')
@ -484,7 +484,7 @@
                if (!data || !data.title) return null;
                return store(href,
                    '<div class="popup-youtube">'
-                    + '<div class="popup-source">YouTube</div>'
+                    + srcHtml('youtube', 'YouTube')
                    + '<div class="popup-title">'   + esc(data.title)       + '</div>'
                    + (data.author_name ? '<div class="popup-authors">' + esc(data.author_name) + '</div>' : '')
                    + '</div>');
@ -516,7 +516,7 @@
                var byline = [creator, year].filter(Boolean).join(', ');
                return store(href,
                    '<div class="popup-archive">'
-                    + '<div class="popup-source">Internet Archive</div>'
+                    + srcHtml('internet-archive', 'Internet Archive')
                    + '<div class="popup-title">'    + esc(title) + '</div>'
                    + (byline ? '<div class="popup-authors">' + esc(byline) + '</div>' : '')
                    + (desc   ? '<div class="popup-abstract">' + esc(desc) + '</div>' : '')
@ -550,7 +550,7 @@
                var meta    = [journal, year].filter(Boolean).join(', ');
                return store(href,
                    '<div class="popup-pubmed">'
-                    + '<div class="popup-source">PubMed</div>'
+                    + srcHtml('pubmed', 'PubMed')
                    + '<div class="popup-title">'    + esc(paper.title) + '</div>'
                    + (authors ? '<div class="popup-authors">' + esc(authors) + '</div>' : '')
                    + (meta    ? '<div class="popup-meta">'    + esc(meta)    + '</div>' : '')
@ -633,5 +633,11 @@
            .replace(/"/g, '&quot;');
    }
    /* 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 '<div class="popup-source" data-popup-source="' + esc(key) + '">' + esc(label) + '</div>';
    }
    document.addEventListener('DOMContentLoaded', init);
 }());
--- a/templates/partials/metadata.html
+++ b/templates/partials/metadata.html
@ -22,5 +22,6 @@
        $if(status)$<a href="#epistemic">$if(overall-score)$<span class="ep-link-label">Epistemic</span><span class="meta-overall-score" title="Overall score: $overall-score$/100">$overall-score$%</span>$else$Epistemic$endif$</a>$endif$
        $if(bibliography)$<a href="#bibliography">Bibliography</a>$endif$
        $if(backlinks)$<a href="#backlinks">Backlinks</a>$endif$
        $if(repository)$<a href="$repository$">Repository</a>$endif$
    </nav>
 </div>
--- a/Show More
+++ b/Show More
		`@ -0,0 +1 @@`
							<svg xmlns="http://www.w3.org/2000/svg" viewBox="23 35 205 180"><path d="M47.1 124.4l-30.1 76c0 .3 7.6.6 16.9.6h16.9l3.6-9.2 6-15.8 2.4-6.5 31.5-.3 31.5-.2 3 7.7 6.2 16 3.2 8.3h16.9c9.3 0 16.9-.2 16.9-.4s-8.5-21.7-18.9-47.8L123 77.2 111.8 49H94.5 77.2l-30.1 75.4zm57.3-10.4l9.6 25.2c0 .5-8.8.8-19.5.8s-19.5-.3-19.5-.8c0-.4 3.4-9.5 7.6-20.2l9.6-24.8c1.1-2.9 2.1-5.2 2.3-5s4.7 11.3 9.9 24.8zM140 50.2c0 .7 13.4 34.8 29.8 75.8l29.7 74.5 16.9.3c9.9.1 16.6-.1 16.4-.7-.1-.5-13.8-34.7-30.2-76l-30-75.1h-16.3c-12.4 0-16.3.3-16.3 1.2z"/></svg>
		`@ -0,0 +1 @@`
							`<svg xmlns="http://www.w3.org/2000/svg" viewBox="30 30 448 448"><path d="M 30,30 V 478 H 478 V 30 Z"/><path fill="#fff" stroke="#fff" stroke-width="6" d="M 269.2,281.1 V 382 H 237.8 V 279.3 L 158,126 h 37.3 c 52.5,98.3 49.2,101.2 59.3,125.6 12.3,-27 5.8,-24.4 60.6,-125.6 H 350 Z"/></svg>`