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Created SM3中的FF2和GG2函数 (markdown)

Sun Yimin 2023-09-22 15:33:38 +08:00
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SM3中的FF2和GG2函数.md Normal file

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# 定义
$FF2(X, Y, Z) = (X \land Y) \lor (X \land Z) \lor (Y \land Z)$
$GG2(X, Y, Z) = (X \land Y) \lor (\lnot X \land Z)$
# 等价公式
$FF2(X, Y, Z) = (X \land Y) \bigoplus (X \land Z) \bigoplus (Y \land Z)$
$GG2(X, Y, Z) = (Y \bigoplus Z) \land X \bigoplus Z$
# 验证
|X|Y|Z|$(X \land Y) \lor (X \land Z) \lor (Y \land Z)$ |$(X \land Y) \bigoplus (X \land Z) \bigoplus (Y \land Z)$|$(X \land Y) \lor (\lnot X \land Z)$|$(Y \bigoplus Z) \land X \bigoplus Z$|
|----|----|----|----|----|----|----|
|0|0|0|0|0|0|0|
|0|0|1|0|0|1|1|
|0|1|0|0|0|0|0|
|0|1|1|1|1|1|1|
|1|0|0|0|0|0|0|
|1|0|1|1|1|0|0|
|1|1|0|1|1|1|1|
|1|1|1|1|1|1|1|
# 证明
TODO