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Updated SM3中的FF2和GG2函数 (markdown)

Sun Yimin 2023-09-26 08:35:15 +08:00
parent abfe1382c2
commit 8a7ec7c81d
1 changed files with 4 additions and 2 deletions
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SM3中的FF2和GG2函数.md

@ -63,11 +63,13 @@ $\lnot((X \land Y \land \lnot Z) \lor (X \land Z \land \lnot Y)) \land (Y \land
= $\lnot(X \land Y \land \lnot Z) \land \lnot(X \land Z \land \lnot Y) \land (Y \land Z)$
= $(\lnot X \lor \lnot Y \lor Z) \land (\lnot X \lor \lnot Z \lor Y) \land (Y \land Z)$
= $(\lnot X \lor (\lnot X \land \lnot Z) \lor (\lnot X \land Y) \lor (\lnot X \land \lnot Y) \lor (\lnot Z \land \lnot Y) \lor (Z \land \lnot X) \lor (Z \land Y)) \land (Y \land Z)$
= $(\lnot X \lor (\lnot X \land \lnot Z) \lor (Z \land \lnot X) \lor (\lnot X \land Y) \lor (\lnot X \land \lnot Y) \lor (\lnot Z \land \lnot Y)) \land (Y \land Z) $
= $(\lnot X \lor (\lnot X \land \lnot Z) \lor (Z \land \lnot X) \lor (\lnot X \land Y) \lor (\lnot X \land \lnot Y) \lor (\lnot Z \land \lnot Y)) \land
(Y \land Z) $
= $(\lnot X \lor ((\lnot X \land \lnot Z) \lor (Z \land \lnot X)) \lor ((\lnot X \land Y) \lor (\lnot X \land \lnot Y)) \lor (\lnot Z \land \lnot Y)) \land (Y \land Z) $
= $(\lnot X \lor (\lnot Z \land \lnot Y)) \land (Y \land Z)$
= $(\lnot X \lor (Z \lor Y)) \land (Y \land Z)$
= $(\lnot X \lor Z \lor Y) \land (Y \land Z)$
= $(Y \land Z$
= $(Y \land Z)$
$((X \land Y \land \lnot Z) \lor (X \land Z \land \lnot Y)) \land (\lnot Y \lor \lnot Z)$
= $(X \land Y \land \lnot Z) \lor (X \land Z \land \lnot Y)$