mirror of
https://github.com/emmansun/gmsm.git
synced 2025-09-18 21:03:49 +08:00
Updated MFMM (markdown)
parent
c71e06e625
commit
d52a2af3b0
33
MFMM.md
33
MFMM.md
@ -283,36 +283,3 @@ acc0, acc1, acc2, acc3, acc4, acc5是64位寄存器
|
|||||||
PASS
|
PASS
|
||||||
ok github.com/emmansun/gmsm/sm2 4.753s
|
ok github.com/emmansun/gmsm/sm2 4.753s
|
||||||
|
|
||||||
### 续1:平方的模约减优化
|
|
||||||
SM2 256 的素数P=0xfffffffeffffffffffffffffffffffffffffffff00000000ffffffffffffffff,也可以表示为
|
|
||||||
|
|
||||||
$P = 2^{256}-(2^{32} \ast 2^{192} + 0 \ast 2^{128} + (2^{32} - 1) \ast 2^{64} + 1)$
|
|
||||||
|
|
||||||
这样,可以通过移位和加减操作来实现模约减。
|
|
||||||
假设:
|
|
||||||
$T=t_7 \ast 2^{448} + t_6 \ast 2^{384} + t_5 \ast 2^{320} + t_4 \ast 2^{256} + t_3 \ast 2^{192} + t_2 \ast 2^{128} + t_1 \ast 2^{64} + t_0 $
|
|
||||||
则共四次约减,第一次约减为:
|
|
||||||
|
|
||||||
$T_1=t_0$
|
|
||||||
|
|
||||||
$T_2=T_1 \ast P=t_0 \ast P= t_0 \ast (2^{256}-(2^{32} \ast 2^{192} + 0 \ast 2^{128} + (2^{32} - 1) \ast 2^{64} + 1))$
|
|
||||||
$T_2=t_0 \ast 2^{256} - t_0 \ast 2^{32} \ast 2^{192} - t_0 \ast (2^{32} - 1) \ast 2^{64} - t_0$
|
|
||||||
|
|
||||||
$T_3=T + T_2=t_7 \ast 2^{448} + t_6 \ast 2^{384} + t_5 \ast 2^{320} + t_4 \ast 2^{256} + t_3 \ast 2^{192} + t_2 \ast 2^{128} + t_1 \ast 2^{64} + t_0 \ast 2^{256} - t_0 \ast 2^{32} \ast 2^{192} - t_0 \ast (2^{32} - 1) \ast 2^{64} - t_0 $
|
|
||||||
$T_3=t_7 \ast 2^{448} + t_6 \ast 2^{384} + t_5 \ast 2^{320} + (t_4+t_0) \ast 2^{256}+(t_3 - t_0 \ast 2^{32}) \ast 2^{192} + t_2 \ast 2^{128} + (t_1 + t_0 - t_0 \ast 2^{32}) \ast 2^{64} $
|
|
||||||
|
|
||||||
先处理加法,后处理减法,后三个加法是带进位加法
|
|
||||||
$t_1=t_0 + t_1$
|
|
||||||
$t_2=t_2 + 0$
|
|
||||||
$t_3=t_3 + 0$
|
|
||||||
$t_0=t_0 + 0$
|
|
||||||
t<sub>0</sub>,t<sub>2</sub>,t<sub>3</sub>会不会同时是0xffffffffffffffff呢?
|
|
||||||
|
|
||||||
接着处理减法,假定a<sub>0</sub>是 $t_0 \ast 2^{32}$ 的低64位,a<sub>1</sub>是 $t_0 \ast 2^{32}$ 的高64位。后三个减法是带借位减法:
|
|
||||||
$t_1=t_1 - a_0$
|
|
||||||
$t_2=t_2 - a_1$
|
|
||||||
$t_3=t_3 - a_0$
|
|
||||||
$t_0=t_0 - a_1$
|
|
||||||
t<sub>0</sub>会不会不够减呢?简单可证也不会(因为其本身就是乘法和加法的变形而已)。
|
|
||||||
|
|
||||||
### 续2:乘法的模约减优化
|
|
||||||
|
Loading…
x
Reference in New Issue
Block a user