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Updated SM2 WWMM (2) (markdown)

Sun Yimin 2024-02-26 08:34:52 +08:00
parent 9bec042da7
commit 2af450584b
1 changed files with 53 additions and 50 deletions
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103
SM2-WWMM-(2).md

@ -446,32 +446,34 @@ $T_3=t_7 \ast 2^{448} + t_6 \ast 2^{384} + t_5 \ast 2^{320} + (t_4+Y) \ast 2^{25
**使用MULXQ**:
```asm
// First reduction step, [ord3, ord2, ord1, ord0] = [1, -0x100000000, -1, ord1, ord0]
MOVQ acc0, DX
MULXQ p256ordK0<>(SB), t0, AX
// calculate the positive part first: [1, 0, 0, ord1, ord0] * t0 + [0, acc3, acc2, acc1, acc0]
// the result is [acc0, acc3, acc2, acc1], last lowest limb is dropped.
MOVQ t0, DX // Y = t0 = (k0 * acc0) mod 2^64
MULXQ p256ord<>+0x00(SB), AX, t1
ADDQ AX, acc0 // (carry1, acc0) = acc0 + L(t0 * ord0)
ADCQ t1, acc1 // (carry2, acc1) = acc1 + H(t0 * ord0) + carry1
MOVQ t0, acc0 // acc0 = t0
// First reduction step, [ord3, ord2, ord1, ord0] = [1, -0x100000000, -1, ord1, ord0]
MOVQ acc0, DX
MULXQ p256ordK0<>(SB), t0, AX
// calculate the positive part first: [1, 0, 0, ord1, ord0] * t0 + [0, acc3, acc2, acc1, acc0]
// the result is [acc0, acc3, acc2, acc1], last lowest limb is dropped.
MOVQ t0, DX // Y = t0 = (k0 * acc0) mod 2^64
MULXQ p256ord<>+0x00(SB), AX, t1
ADDQ AX, acc0 // (carry1, acc0) = acc0 + L(t0 * ord0)
ADCQ t1, acc1 // (carry2, acc1) = acc1 + H(t0 * ord0) + carry1
MOVQ t0, acc0 // acc0 = t0
MULXQ p256ord<>+0x08(SB), AX, t1
ADCQ $0, t1 // t1 = carry2 + H(t0*ord1)
ADDQ AX, acc1 // (carry3, acc1) = acc1 + L(t0*ord1)
ADCQ t1, acc2 // (carry4, acc2) = acc2 + t1 + carry3
ADCQ $0, acc3 // (carry5, acc3) = acc3 + carry4
ADCQ $0, acc0 // acc0 = t0 + carry5
// calculate the negative part: [acc0, acc3, acc2, acc1] - [0, 0x100000000, 1, 0] * t0
MOVQ t0, AX
//MOVQ t0, DX // This is not required due to t0=DX already
SHLQ $32, AX
SHRQ $32, DX
// calculate the negative part: [acc0, acc3, acc2, acc1] - [0, 0x100000000, 1, 0] * t0
MOVQ t0, AX
SHLQ $32, AX
SHRQ $32, DX
SUBQ t0, acc2
SBBQ AX, acc3
SBBQ DX, acc0
MOVQ t0, DX
MULXQ p256ord<>+0x08(SB), AX, t1
ADCQ $0, t1 // t1 = carry2 + H(t0*ord1)
ADDQ AX, acc1 // (carry3, acc1) = acc1 + L(t0*ord1)
ADCQ t1, acc2 // (carry4, acc2) = acc2 + t1 + carry3
ADCQ $0, acc3 // (carry5, acc3) = acc3 + carry4
ADCQ $0, acc0 // acc0 = t0 + carry5
SUBQ t0, acc2
SBBQ AX, acc3
SBBQ DX, acc0
```
乘法: 3
移位：2
@ -633,47 +635,48 @@ $t_5=t_5 - 0$
乘法: 3
移位：2
加法：9
减法：4
减法：3
**使用MULXQ**:
```asm
// First reduction step
MOVQ acc0, DX
MULXQ p256ordK0<>(SB), t0, AX
// First reduction step
MOVQ acc0, DX
MULXQ p256ordK0<>(SB), t0, AX
MOVQ t0, DX
MULXQ p256ord<>+0x00(SB), AX, BX
ADDQ AX, acc0
ADCQ BX, acc1
MOVQ t0, DX
MULXQ p256ord<>+0x00(SB), AX, BX
ADDQ AX, acc0
ADCQ BX, acc1
MOVQ t0, acc0
MULXQ p256ord<>+0x08(SB), AX, BX
ADCQ $0, BX
ADDQ AX, acc1
ADCQ BX, acc2
ADCQ $0, acc3
ADCQ t0, acc4
ADCQ $0, acc5
MOVQ t0, AX
//MOVQ t0, DX // This is not required due to t0=DX already
SHLQ $32, AX
SHRQ $32, DX
MOVQ t0, AX
SHLQ $32, AX
SHRQ $32, DX
SUBQ t0, acc2
SBBQ AX, acc3
SBBQ DX, acc4
SBBQ $0, acc5
SUBQ t0, acc2
SBBQ AX, acc3
SBBQ DX, acc0
MOVQ t0, DX
MULXQ p256ord<>+0x08(SB), AX, BX
ADCQ $0, BX
ADDQ AX, acc1
ADCQ BX, acc2
ADCQ $0, acc3
ADCQ acc0, acc4
ADCQ $0, acc5
```
乘法: 3
移位：2
加法：8
减法：4
减法：3
| 方案 | 乘法 | 移位 | 加法 | 减法 |
| ----------- | ----------- | ----------- | ----------- | ----------- |
| 方案一 | 5 | 0 | 15 | 0 |
| 方案一（MULX/ADCX/ADOX） | 5 | 0 | 10 | 0 |
| 方案二 | 3 | 2 | 9 | 3 |
| 方案二（MULX） | 3 | 2 | 8 | 4 |
| 方案二（MULX） | 3 | 2 | 8 | 3 |
看来在支持**MULXQ/ADCXQ/ADOXQ**的情况下，使用方案一（MULX/ADCX/ADOX）更好！