From aca73e2d79ca84ac57498d3520cce3ce9ae95260 Mon Sep 17 00:00:00 2001 From: Sun Yimin Date: Thu, 22 Feb 2024 11:04:39 +0800 Subject: [PATCH] Updated SM2 MFMM (2) (markdown) --- SM2-MFMM-(2).md | 14 ++++++++------ 1 file changed, 8 insertions(+), 6 deletions(-) diff --git a/SM2-MFMM-(2).md b/SM2-MFMM-(2).md index 2ff4fe0..34e82ab 100644 --- a/SM2-MFMM-(2).md +++ b/SM2-MFMM-(2).md @@ -97,6 +97,8 @@ $t_2=t_2 - a_1$ $t_3=t_3 - a_0$ $t_0=t_0 - a_1$ +**减法显然是安全的（因为第四步的结果显然是>=0的，而且为零的情况仅限于 $t_0==0$ 的情况 ），所以调整为先做减法，再做加法，确保第四步加法不会产生进位。**。 + 伪代码： ```asm \ // First reduction step, [p3, p2, p1, p0] = [1, -0x100000000, 0, (1 - 0x100000000), -1] @@ -104,17 +106,17 @@ $t_0=t_0 - a_1$ MOVQ acc0, DX \ SHLQ $32, AX \ // AX = L(acc0 * 2^32), low part SHRQ $32, DX \ // DX = H(acc0 * 2^32), high part - \ // calculate the positive part first: [1, 0, 0, 1] * acc0 + [0, acc3, acc2, acc1], - \ // due to (-1) * acc0 + acc0 == 0, so last lowest lamb 0 is dropped directly, no carry. - ADDQ acc0, acc1 \ // acc1' = L (acc0 + acc1) - ADCQ $0, acc2 \ // acc2' = acc2 + carry1 - ADCQ $0, acc3 \ // acc3' = acc3 + carry2 - ADCQ $0, acc0 \ // acc0' = acc0 + carry3 \// calculate the negative part: [0, -0x100000000, 0, -0x100000000] * acc0 SUBQ AX, acc1 \ SBBQ DX, acc2 \ SBBQ AX, acc3 \ SBBQ DX, acc0 \ + \ // calculate the positive part: [1, 0, 0, 1] * acc0 + [0, acc3, acc2, acc1], + \ // due to (-1) * acc0 + acc0 == 0, so last lowest lamb 0 is dropped directly, no carry. + ADDQ acc0, acc1 \ // acc1' = L (acc0 + acc1) + ADCQ $0, acc2 \ // acc2' = acc2 + carry1 + ADCQ $0, acc3 \ // acc3' = acc3 + carry2 + ADCQ $0, acc0 \ // acc0' = acc0 + carry3 ``` 移位: 2 加法：4