diff --git a/SM3中的FF2和GG2函数.md b/SM3中的FF2和GG2函数.md new file mode 100644 index 0000000..f20534f --- /dev/null +++ b/SM3中的FF2和GG2函数.md @@ -0,0 +1,23 @@ +# 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 \ No newline at end of file