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\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 ) =
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\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 . 
 []


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\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][]
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[][]\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
 $\OML/cmm/m/it/10.95 w \OT1/cmr/m/n/10.95 = [1\OML/cmm/m/it/10.95 ; \OT1/cmr/m
/n/10.95 4\OML/cmm/m/it/10.95 ; \OT1/cmr/m/n/10.95 16\OML/cmm/m/it/10.95 ; \OT1
/cmr/m/n/10.95 64]$
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[5]
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[][]\T1/cmr/bx/n/10.95 Theorem 4.4 \T1/cmr/m/n/10.95 (M�bius Bridge Mem-ory Re-
duc-tion)\T1/cmr/bx/n/10.95 . [][]\T1/cmr/m/it/10.95 [MACHINE-CHECKED][] [][NOV
ELTY-CANDIDATE][]The
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\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 na�ve MITM. [][MACHINE-CHECKED][] \T1/cmtt/m/it/10.95 AES_Mobius_Bridge_Theo
rems.lean
 []


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\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
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[][]\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
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[][]\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
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[][]\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]
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[]\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 . 
 []

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