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Package microtype Info: Applying patch `item' on input line 55. Package microtype Info: Applying patch `toc' on input line 55. Package microtype Info: Applying patch `eqnum' on input line 55. Package microtype Info: Applying patch `footnote' on input line 55. Package microtype Info: Applying patch `verbatim' on input line 55. LaTeX Info: Redefining \microtypesetup on input line 55. Package microtype Info: Generating PDF output. Package microtype Info: Character protrusion enabled (level 2). Package microtype Info: Using default protrusion set `alltext'. Package microtype Info: No font expansion. Package microtype Info: No adjustment of tracking. Package microtype Info: No adjustment of interword spacing. Package microtype Info: No adjustment of character kerning. (C:\Users\jessi\AppData\Local\Programs\MiKTeX\tex/latex/microtype\mt-cmr.cfg File: mt-cmr.cfg 2013/05/19 v2.2 microtype config. file: Computer Modern Roman (RS) ) Package hyperref Info: Link coloring ON on input line 55. (aes_cryptanalysis.out) (aes_cryptanalysis.out) \@outlinefile=\write3 \openout3 = `aes_cryptanalysis.out'. (C:\Users\jessi\AppData\Local\Programs\MiKTeX\tex/context/base/mkii\supp-pdf.mk ii [Loading MPS to PDF converter (version 2006.09.02).] \scratchcounter=\count344 \scratchdimen=\dimen262 \scratchbox=\box67 \nofMPsegments=\count345 \nofMParguments=\count346 \everyMPshowfont=\toks37 \MPscratchCnt=\count347 \MPscratchDim=\dimen263 \MPnumerator=\count348 \makeMPintoPDFobject=\count349 \everyMPtoPDFconversion=\toks38 ) (C:\Users\jessi\AppData\Local\Programs\MiKTeX\tex/latex/epstopdf-pkg\epstopdf-b ase.sty Package: epstopdf-base 2020-01-24 v2.11 Base part for package epstopdf Package epstopdf-base Info: Redefining graphics rule for `.eps' on input line 4 85. 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(C:\Users\jessi\AppData\Local\Programs\MiKTeX\tex/latex/amsfonts\umsb.fd File: umsb.fd 2013/01/14 v3.01 AMS symbols B ) (C:\Users\jessi\AppData\Local\Programs\MiKTeX\tex/latex/microtype\mt-msb.cfg File: mt-msb.cfg 2005/06/01 v1.0 microtype config. file: AMS symbols (b) (RS) ) Package microtype Info: Loading generic protrusion settings for font family (microtype) `cmtt' (encoding: T1). (microtype) For optimal results, create family-specific settings. (microtype) See the microtype manual for details. Overfull \hbox (21.92322pt too wide) in paragraph at lines 60--67 \T1/cmr/m/n/10 prior MITM ap-proaches), and a machine-checked proof that the co n-straint sys-tem $\OMS/cmsy/m/n/10 C\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 K; X[]; [] ; X[]\OT1/cmr/m/n/10 ) = [] (aes_cryptanalysis.toc [1 {C:/Users/jessi/AppData/Local/MiKTeX/fonts/map/pdftex/pdftex.map}]) \tf@toc=\write4 \openout4 = `aes_cryptanalysis.toc'. [2] Package mdframed Info: mdframed detected package amsthm changed the theorem header of amsthm (mdframed) on input line 95. [3] Package hyperref Warning: Token not allowed in a PDF string (Unicode): (hyperref) removing `\@textsuperscript' on input line 109. Overfull \hbox (195.31322pt too wide) in paragraph at lines 129--143 [] [] [4] Overfull \hbox (39.82985pt too wide) in paragraph at lines 198--210 [] [] Overfull \hbox (126.86444pt too wide) in paragraph at lines 221--224 \T1/cmr/m/it/10.95 ter-is-tic is at most $\OT1/cmr/m/n/10.95 2[]$\T1/cmr/m/it/1 0.95 , far be-low the $\OT1/cmr/m/n/10.95 2[]$ \T1/cmr/m/it/10.95 se-cu-rity th resh-old. [][MACHINE-CHECKED][] \T1/cmtt/m/it/10.95 AES_10Round_Terminal_Result .lean\T1/cmr/m/it/10.95 . [] Overfull \hbox (18.69676pt too wide) in paragraph at lines 248--252 \OMS/cmsy/m/n/10.95 f[]g$ \T1/cmr/m/it/10.95 onto $\OMS/cmsy/m/n/10.95 f\OT1/cm r/m/n/10.95 0\OML/cmm/m/it/10.95 ; [] ; \OT1/cmr/m/n/10.95 254\OMS/cmsy/m/n/10. 95 g$ \T1/cmr/m/it/10.95 with max-i-mum en-tropy (100% uni-for-mity). [][VERIFI ED-COMPUTATIONAL][] [] Overfull \hbox (14.3675pt too wide) in paragraph at lines 254--258 [][]\T1/cmr/bx/n/10.95 Definition 4.3 \T1/cmr/m/n/10.95 (Per-Round Weighted Gau ge)\T1/cmr/bx/n/10.95 . [][]\T1/cmr/m/it/10.95 [NOVELTY-CANDIDATE][]Let weights $\OML/cmm/m/it/10.95 w \OT1/cmr/m/n/10.95 = [1\OML/cmm/m/it/10.95 ; \OT1/cmr/m /n/10.95 4\OML/cmm/m/it/10.95 ; \OT1/cmr/m/n/10.95 16\OML/cmm/m/it/10.95 ; \OT1 /cmr/m/n/10.95 64]$ [] [5] Overfull \hbox (47.53549pt too wide) in paragraph at lines 279--284 [][]\T1/cmr/bx/n/10.95 Theorem 4.4 \T1/cmr/m/n/10.95 (Möbius Bridge Mem-ory Re- duc-tion)\T1/cmr/bx/n/10.95 . [][]\T1/cmr/m/it/10.95 [MACHINE-CHECKED][] [][NOV ELTY-CANDIDATE][]The [] Overfull \hbox (71.46558pt too wide) in paragraph at lines 279--284 \T1/cmr/m/it/10.95 duc-tion lower bound of $\OT1/cmr/m/n/10.95 256\OMS/cmsy/m/n /10.95 ^^B$ \T1/cmr/m/it/10.95 ($\OT1/cmr/m/n/10.95 2[]$\T1/cmr/m/it/10.95 ) ov er naïve MITM. [][MACHINE-CHECKED][] \T1/cmtt/m/it/10.95 AES_Mobius_Bridge_Theo rems.lean [] Package hyperref Warning: Token not allowed in a PDF string (Unicode): (hyperref) removing `math shift' on input line 313. Package hyperref Warning: Token not allowed in a PDF string (Unicode): (hyperref) removing `subscript' on input line 313. Package hyperref Warning: Token not allowed in a PDF string (Unicode): (hyperref) removing `math shift' on input line 313. Overfull \hbox (18.07191pt too wide) in paragraph at lines 322--327 \T1/cmr/m/it/10.95 at-tack can be built on this lin-eariza-tion. [][MACHINE-CHE CKED][] \T1/cmtt/m/it/10.95 AES_10Round_Terminal_Result.lean [] Overfull \hbox (21.5956pt too wide) in paragraph at lines 329--333 [][]\T1/cmr/bx/n/10.95 Theorem 5.3 \T1/cmr/m/n/10.95 (Rank vs. In-ver-sion Boun d-ary)\T1/cmr/bx/n/10.95 . [][]\T1/cmr/m/it/10.95 [MACHINE-CHECKED][] [][NOVELT Y-CANDIDATE][]The [] [6] Overfull \hbox (182.04147pt too wide) in paragraph at lines 411--429 [] [] [7] Overfull \hbox (58.19208pt too wide) in paragraph at lines 453--457 [][]\T1/cmr/bx/n/10.95 Proposition 8.1 \T1/cmr/m/n/10.95 (AES S-box Braid Depth )\T1/cmr/bx/n/10.95 . [][]\T1/cmr/m/it/10.95 [VERIFIED-COMPUTATIONAL][] [][NOVE LTY-CANDIDATE][]The [] Overfull \hbox (25.35147pt too wide) in paragraph at lines 459--463 [][]\T1/cmr/bx/n/10.95 Proposition 8.2 \T1/cmr/m/n/10.95 (Grover Or-a-cle Cost) \T1/cmr/bx/n/10.95 . [][]\T1/cmr/m/it/10.95 [VERIFIED-COMPUTATIONAL][] [][NOVEL TY-CANDIDATE][]A [] [8] Overfull \hbox (157.0416pt too wide) in paragraph at lines 525--527 []\T1/cmr/m/n/10.95 All code, Lean proofs, and MILP for-mu-la-tions are in the open-source repos-i-tory \T1/cmtt/m/n/10.95 github.com/SNAPKITTYWEST/ahmad-foun dations\T1/cmr/m/n/10.95 . [] [9] [10] (aes_cryptanalysis.aux) *********** LaTeX2e <2026-06-01> L3 programming layer <2026-06-18> *********** LaTeX Warning: Label(s) may have changed. Rerun to get cross-references right. Package rerunfilecheck Info: File `aes_cryptanalysis.out' has not changed. (rerunfilecheck) Checksum: DEE582115B8C35213D9B403CD6908C9D;3817. ) Here is how much of TeX's memory you used: 16859 strings out of 467510 270791 string characters out of 5408794 749179 words of memory out of 5000000 45767 multiletter control sequences out of 15000+600000 652880 words of font info for 104 fonts, out of 8000000 for 9000 1141 hyphenation exceptions out of 8191 75i,9n,79p,1016b,638s stack positions out of 10000i,1000n,20000p,200000b,200000s Output written on aes_cryptanalysis.pdf (10 pages, 411021 bytes). PDF statistics: 1012 PDF objects out of 1200 (max. 8388607) 78 named destinations out of 1000 (max. 500000) 20145 words of extra memory for PDF output out of 20736 (max. 10000000)