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Updated SM2 WWMM (2) (markdown)
Sun Yimin
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SM2-WWMM-(2).md
130
SM2-WWMM-(2).md
@ -407,38 +407,39 @@ $T_3=t_7 \ast 2^{448} + t_6 \ast 2^{384} + t_5 \ast 2^{320} + (t_4+Y) \ast 2^{25
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**依然采用先减后加！**
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```asm
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// First reduction step
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MOVQ acc0, AX
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MULQ p256ordK0<>(SB)
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MOVQ AX, t0 // Y = t0 = (k0 * acc0) mod 2^64
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// First reduction step
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MOVQ acc0, AX
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MULQ p256ordK0<>(SB)
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MOVQ AX, t0 // Y = t0 = (k0 * acc0) mod 2^64
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MOVQ p256ord<>+0x00(SB), AX
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MULQ t0
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ADDQ AX, acc0 // (carry1, acc0) = acc0 + L(t0 * ord0)
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ADCQ $0, DX // DX = carry1 + H(t0 * ord0)
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MOVQ DX, t1 // t1 = carry1 + H(t0 * ord0)
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MOVQ t0, acc0 // acc0 = t0
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// 处理第一个加法，以便释放acc0
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MOVQ p256ord<>+0x00(SB), AX
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MULQ t0
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ADDQ AX, acc0 // (carry1, acc0) = acc0 + L(t0 * ord0)，acc0 可以被释放了。
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ADCQ $0, DX // DX = carry1 + H(t0 * ord0)
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MOVQ DX, t1 // t1 = carry1 + H(t0 * ord0)
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// calculate the negative part: [acc0, acc3, acc2, acc1] - [0, 0x100000000, 1, 0] * t0
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// 处理减法
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MOVQ t0, acc0 // acc0 = t0
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MOVQ t0, AX
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MOVQ t0, DX
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SHLQ $32, AX
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SHRQ $32, DX
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// calculate the negative part: [acc0, acc3, acc2, acc1] - [0, 0x100000000, 1, 0] * t0
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MOVQ t0, AX
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MOVQ t0, DX
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SHLQ $32, AX
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SHRQ $32, DX
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SUBQ t0, acc2
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SBBQ AX, acc3
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SBBQ DX, acc0
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MOVQ p256ord<>+0x08(SB), AX
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MULQ t0
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ADDQ t1, acc1 // (carry2, acc1) = acc1 + t1
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ADCQ $0, DX // DX = carry2 + H(t0*ord1)
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ADDQ AX, acc1 // (carry3, acc1) = acc1 + t1 + L(t0*ord1)
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ADCQ DX, acc2
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ADCQ $0, acc3
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ADCQ $0, acc0
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SUBQ t0, acc2
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SBBQ AX, acc3
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SBBQ DX, acc0
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// 处理加法
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MOVQ p256ord<>+0x08(SB), AX
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MULQ t0
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ADDQ t1, acc1 // (carry2, acc1) = acc1 + t1
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ADCQ $0, DX // DX = carry2 + H(t0*ord1)
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ADDQ AX, acc1 // (carry3, acc1) = acc1 + t1 + L(t0*ord1)
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ADCQ DX, acc2
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ADCQ $0, acc3
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ADCQ $0, acc0
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```
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乘法: 3
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移位：2
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@ -450,15 +451,15 @@ $T_3=t_7 \ast 2^{448} + t_6 \ast 2^{384} + t_5 \ast 2^{320} + (t_4+Y) \ast 2^{25
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// First reduction step, [ord3, ord2, ord1, ord0] = [1, -0x100000000, -1, ord1, ord0]
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MOVQ acc0, DX
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MULXQ p256ordK0<>(SB), t0, AX
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// calculate the positive part first: [1, 0, 0, ord1, ord0] * t0 + [0, acc3, acc2, acc1, acc0]
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// the result is [acc0, acc3, acc2, acc1], last lowest limb is dropped.
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// 处理第一个加法，以便释放acc0
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MOVQ t0, DX // Y = t0 = (k0 * acc0) mod 2^64
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MULXQ p256ord<>+0x00(SB), AX, t1
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ADDQ AX, acc0 // (carry1, acc0) = acc0 + L(t0 * ord0)
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ADDQ AX, acc0 // (carry1, acc0) = acc0 + L(t0 * ord0)，acc0 可以被释放了。
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ADCQ t1, acc1 // (carry2, acc1) = acc1 + H(t0 * ord0) + carry1
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MOVQ t0, acc0 // acc0 = t0
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// calculate the negative part: [acc0, acc3, acc2, acc1] - [0, 0x100000000, 1, 0] * t0
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// 处理减法
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MOVQ t0, acc0 // acc0 = t0
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MOVQ t0, AX
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SHLQ $32, AX
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SHRQ $32, DX
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@ -467,6 +468,7 @@ $T_3=t_7 \ast 2^{448} + t_6 \ast 2^{384} + t_5 \ast 2^{320} + (t_4+Y) \ast 2^{25
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SBBQ AX, acc3
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SBBQ DX, acc0
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// 处理加法
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MOVQ t0, DX
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MULXQ p256ord<>+0x08(SB), AX, t1
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ADCQ $0, t1 // t1 = carry2 + H(t0*ord1)
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@ -589,36 +591,39 @@ $T_3=(t_4+Y) \ast 2^{256}+(t_3 - Y \ast 2^{32}) \ast 2^{192} + (t_2 - Y) \ast 2^
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伪代码：
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```asm
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// First reduction step
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MOVQ acc0, AX
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MULQ p256ordK0<>(SB)
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MOVQ AX, t0
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// First reduction step
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MOVQ acc0, AX
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MULQ p256ordK0<>(SB)
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MOVQ AX, t0
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MOVQ p256ord<>+0x00(SB), AX
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MULQ t0
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ADDQ AX, acc0
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ADCQ $0, DX
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MOVQ DX, BX
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// 处理第一个加法，以便释放acc0
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MOVQ p256ord<>+0x00(SB), AX
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MULQ t0
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ADDQ AX, acc0 // acc0 可以被释放了
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ADCQ $0, DX
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MOVQ DX, BX
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MOVQ t0, acc0
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MOVQ t0, AX
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MOVQ t0, DX
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SHLQ $32, AX
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SHRQ $32, DX
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// 开始处理减法
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MOVQ t0, acc0
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MOVQ t0, AX
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MOVQ t0, DX
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SHLQ $32, AX
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SHRQ $32, DX
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SUBQ t0, acc2
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SBBQ AX, acc3
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SBBQ DX, acc0
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SUBQ t0, acc2
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SBBQ AX, acc3
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SBBQ DX, acc0
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MOVQ p256ord<>+0x08(SB), AX
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MULQ t0
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ADDQ BX, acc1
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ADCQ $0, DX
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ADDQ AX, acc1
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ADCQ DX, acc2
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ADCQ $0, acc3
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ADCQ acc0, acc4
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ADCQ $0, acc5
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// 处理加法
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MOVQ p256ord<>+0x08(SB), AX
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MULQ t0
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ADDQ BX, acc1
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ADCQ $0, DX
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ADDQ AX, acc1
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ADCQ DX, acc2
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ADCQ $0, acc3
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ADCQ acc0, acc4
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ADCQ $0, acc5
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```
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乘法: 3
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移位：2
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@ -631,12 +636,14 @@ $T_3=(t_4+Y) \ast 2^{256}+(t_3 - Y \ast 2^{32}) \ast 2^{192} + (t_2 - Y) \ast 2^
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MOVQ acc0, DX
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MULXQ p256ordK0<>(SB), t0, AX
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// 处理第一个加法，以便释放acc0
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MOVQ t0, DX
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MULXQ p256ord<>+0x00(SB), AX, BX
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ADDQ AX, acc0
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ADDQ AX, acc0 // acc0 可以被释放了
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ADCQ BX, acc1
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MOVQ t0, acc0
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// 开始处理减法
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MOVQ t0, acc0
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MOVQ t0, AX
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SHLQ $32, AX
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SHRQ $32, DX
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@ -645,6 +652,7 @@ $T_3=(t_4+Y) \ast 2^{256}+(t_3 - Y \ast 2^{32}) \ast 2^{192} + (t_2 - Y) \ast 2^
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SBBQ AX, acc3
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SBBQ DX, acc0
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// 处理加法
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MOVQ t0, DX
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MULXQ p256ord<>+0x08(SB), AX, BX
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ADCQ $0, BX
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