Updated SM2 MFMM (2) (markdown)

Sun Yimin 2024-02-22 09:29:16 +08:00
parent a3180f9b6e
commit ed40a7a221

@ -1,10 +1,14 @@
## SM2 P256 P表示
SM2 256 的素数P=0xfffffffeffffffffffffffffffffffffffffffff00000000ffffffffffffffff也可以表示为
$p_0=0xFFFFFFFEFFFFFFFF$
$p_1=0xFFFFFFFF00000000$
$p_2=0xFFFFFFFFFFFFFFFF$
$p_3=0xFFFFFFFEFFFFFFFF$
$$P = 2^{256} - 2^{224} - 2^{96} + 2^{64} - 1$$
$$P = 0xFFFFFFFEFFFFFFF \ast 2^{192} + 0xFFFFFFFFFFFFFFFFF \ast 2^{128} + 0xFFFFFFFF00000000 \ast 2^{64} + 0xFFFFFFFFFFFFFFFFF$$
$$P = p_3 \ast 2^{192} + p_2 \ast 2^{128} + p_1 \ast 2^{64} + p_0$$
$$P = 2^{256}-(2^{32} \ast 2^{192} + 0 \ast 2^{128} + (2^{32} - 1) \ast 2^{64} + 1)$$
@ -17,8 +21,8 @@ $T_1=t_0$
### 方案一:(乘法、加法)
这个是最原始方法。
$T_2=T_1 \ast P=t_0 \ast P= (t_0 \ast 0xFFFFFFFEFFFFFFF) \ast 2^{192} + (t_0 \ast 0xFFFFFFFFFFFFFFFFF) \ast 2^{128} + (t_0 \ast 0xFFFFFFFF00000000) \ast 2^{64} + (t_0 \ast 0xFFFFFFFFFFFFFFFFF)$
$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+t_0 \ast 0xFFFFFFFEFFFFFFF) \ast 2^{192} + (t_2+t_0 \ast 0xFFFFFFFFFFFFFFFFF) \ast 2^{128} + (t_1+t_0 \ast 0xFFFFFFFF00000000) \ast 2^{64} + t_0 \ast 2^{64} $
$T_2=T_1 \ast P=t_0 \ast P= (t_0 \ast p_3) \ast 2^{192} + (t_0 \ast p_2) \ast 2^{128} + (t_0 \ast p_1) \ast 2^{64} + (t_0 \ast p_0)$
$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+t_0 \ast p_3) \ast 2^{192} + (t_2+t_0 \ast p_2) \ast 2^{128} + (t_1+t_0 \ast p_1) \ast 2^{64} + t_0 \ast 2^{64} $
$t_1=t_1 + t_0 \ast 0xFFFFFFFF00000001$