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Updated SM3中的FF2和GG2函数 (markdown)

Sun Yimin 2023-09-25 21:22:37 +08:00
parent a0e925a1e5
commit 06621c6f9d
1 changed files with 9 additions and 3 deletions
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SM3中的FF2和GG2函数.md

@ -55,10 +55,16 @@ $(X \land Y) \bigoplus (X \land Z) $
= $X \land ((Y \land \lnot Z) \lor (\lnot Y \land Z))$
= $(X \land Y \land \lnot Z) \lor (X \land Z \land \lnot Y)$
$\lnot((X \land Y \land \lnot Z) \lor (X \land Z \land \lnot Y))$
= $\lnot(X \land Y \land \lnot Z) \land \lnot(X \land Z \land \lnot Y)$
= $(\lnot X \lor \lnot Y \lor Z) \land (\lnot X \lor \lnot Z \lor Y)$
$\lnot((X \land Y \land \lnot Z) \lor (X \land Z \land \lnot Y)) \land (Y \land Z)$
= $\lnot(X \land Y \land \lnot Z) \land \lnot(X \land Z \land \lnot Y) \land (Y \land Z)$
= $(\lnot X \lor \lnot Y \lor Z) \land (\lnot X \lor \lnot Z \lor Y) \land (Y \land Z)$
= $(Y \land Z)$
$((X \land Y \land \lnot Z) \lor (X \land Z \land \lnot Y)) \land (\lnot Y \lor \lnot Z)$
= $(X \land Y \land \lnot Z) \lor (X \land Z \land \lnot Y)$
$(X \land Y \land \lnot Z) \lor (X \land Z \land \lnot Y) \lor (Y \land Z)$
= $(X \land Y \land \lnot Z) \lor (X \land Z \land \lnot Y) \lor (Y \land Z) \lor (X \land Y \land Z) \lor (X \land Y \land Z)$
= $(X \land Y \land \lnot Z) \lor (X \land Y \land Z) \lor (X \land Z \land \lnot Y) \lor (X \land Y \land Z) \lor (Y \land Z)$
= $(X \land Y) \lor (X \land Z) \lor (Y \land Z)$