mirror/gmsm
1
0
Fork 0
mirror of https://github.com/emmansun/gmsm.git synced 2025-05-11 03:26:17 +08:00
Code Issues Packages Projects Releases Wiki Activity

Updated SM3中的FF2和GG2函数 (markdown)

Sun Yimin 2023-09-25 16:42:01 +08:00
parent ff9ccf829d
commit 73b1ca903e
1 changed files with 9 additions and 1 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

10
SM3中的FF2和GG2函数.md

@ -39,4 +39,12 @@ GG2等价公式初次见于[Intel® Integrated Performance Primitives Cryptograp
|1|1|1|1|1|1|1|
# 证明
Ask help https://math.stackexchange.com/questions/4775054/how-to-prove-below-two-logic-formulas
Ask help https://math.stackexchange.com/questions/4775054/how-to-prove-below-two-logic-formulas
GG2(X,Y,Z)
= $(X \land Y) \bigoplus (\lnot X \land Z)$
= $(\lnot (X \land Y) \land (\lnot X \land Z)) \lor ((X \land Y) \land (\lnot (\lnot X \land Z)))$
= $((\lnot X \lor \lnot Y) \land (\lnot X \land Z)) \lor ((X \land Y) \land (X \lor \lnot Z))$
= $(\lnot X \land Z) \lor (\lnot X \land \lnot Y \land Z) \lor (X \land Y) \lor (X \land Y \land \lnot Z) $
= $((\lnot X \land Z) \lor (\lnot X \land Z \land \lnot Y)) \lor ((X \land Y) \lor (X \land Y \land \lnot Z))$
= $((X \land Y) \land (1 \lor \lnot Z)) \lor ((\lnot X \land Z) \land (1 \lor \lnot Y))$
= $(X \land Y) \lor (\lnot X \land Z)$