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Updated SM3中的FF2和GG2函数 (markdown)

Sun Yimin 2023-09-25 17:14:50 +08:00
parent 0d2048a58c
commit 8a35082fe9
1 changed files with 7 additions and 1 deletions
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SM3中的FF2和GG2函数.md

@ -47,4 +47,10 @@ $GG2(X,Y,Z)$
= $(\lnot X \land Z) \lor (\lnot X \land \lnot Y \land Z) \lor (X \land Y) \lor (X \land Y \land \lnot Z) $
= $((\lnot X \land Z) \lor (\lnot X \land Z \land \lnot Y)) \lor ((X \land Y) \lor (X \land Y \land \lnot Z))$
= $((X \land Y) \land (1 \lor \lnot Z)) \lor ((\lnot X \land Z) \land (1 \lor \lnot Y))$
= $(X \land Y) \lor (\lnot X \land Z)$
= $(X \land Y) \lor (\lnot X \land Z)$
$FF2(X, Y, Z) = (X \land Y) \bigoplus (X \land Z) \bigoplus (Y \land Z)$
$(X \land Y) \bigoplus (X \land Z) $
= $X \land (Y \bigoplus Z)$
= $X \land ((Y \land \lnot Z) \lor (\lnot Y \land Z))$
= $(X \land Y \land \lnot Z) \lor (X \land Z \land \lnot Y)$