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Updated MFMM (markdown)

Sun Yimin 2021-12-19 20:47:17 +08:00
parent 1a70e815f4
commit fe929e491c
1 changed files with 23 additions and 1 deletions
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MFMM.md

@ -30,7 +30,7 @@ acc0, acc1, acc2, acc3, acc4, acc5是64位寄存器
(carry3, acc3) = carry2 + acc3 + acc0 * p3 (carry3, acc3) = carry2 + acc3 + acc0 * p3
(carry4, acc4) = carry3 + acc4 (carry4, acc4) = carry3 + acc4
acc5 = carry4 acc5 = carry4
进位处理后，结果表示成 tmp = acc5 * 2^256 + acc4 * 2^192 + acc3 * 2^128 + acc2 * 2 ^ 64 + acc1 进位处理后，结果表示成 tmp = acc5 * 2^256 + acc4 * 2^192 + acc3 * 2^128 + acc2 * 2 ^ 64 + acc1
H = high64(acc0*2^32) 超出64位宽部分 , L = low64(acc0*2^32) H = high64(acc0*2^32) 超出64位宽部分 , L = low64(acc0*2^32)
@ -43,6 +43,28 @@ acc0, acc1, acc2, acc3, acc4, acc5是64位寄存器
=acc4 * 2^192 + (acc0 * p3 + acc3) * 2^128 + acc2 * 2^64 + acc1 + acc0* 2^32 =acc4 * 2^192 + (acc0 * p3 + acc3) * 2^128 + acc2 * 2^64 + acc1 + acc0* 2^32
=acc4 * 2^192 + (acc0 * p3 + acc3) * 2^128 + (acc2 + H(acc0* 2^32))* 2^64 + acc1 + L(acc0* 2^32) =acc4 * 2^192 + (acc0 * p3 + acc3) * 2^128 + (acc2 + H(acc0* 2^32))* 2^64 + acc1 + L(acc0* 2^32)
amd64 汇编表示为：
MOVQ acc0, AX
MOVQ acc0, t1
SHLQ $32, acc0 // L(acc0 * 2^32)
MULQ p256const1<>(SB) // acc0 * p3 = (DX, AX), DX为高64位
SHRQ $32, t1 // t1 = H(acc0 * 2^32)
ADDQ acc0, acc1 // (carry1, acc1) = acc1 + L(acc0 * 2^32)
ADCQ t1, acc2 // (carry2, acc2) = carry1 + acc2 + H(acc0 * 2^32)
ADCQ AX, acc3 // (carry3, acc3) = carry2 + acc3 + L(acc0 * p3)
ADCQ DX, acc4 // (carry4, acc4) = carry3 + acc4 + H(acc0 * p3)
ADCQ $0, acc5 // acc5 = carry4
XORQ acc0, acc0 // acc0 = 0
arm64 汇编表示为：
ADDS acc0<<32, acc1, acc1 // (carry1, acc1) = acc1 + L(acc0 * 2^32)
LSR $32, acc0, t0 // t0 = H(acc0 * 2^32)
MUL acc0, const1, t1 // t1 = L(acc0 * p3)
UMULH acc0, const1, acc0 // acc0 = H(acc0 * p3)
ADCS t0, acc2 // (carry2, acc2) = carry1 + acc2 + H(acc0 * 2^32)
ADCS t1, acc3 // (carry3, acc3) = carry2 + acc3 + L(acc0 * p3)
ADC $0, acc0 // acc0 = carry3 + H(acc0 * p3), why?
SM2曲线 SM2曲线
p = 0x fffffffeffffffff ffffffffffffffff ffffffff00000000 ffffffffffffffff p = 0x fffffffeffffffff ffffffffffffffff ffffffff00000000 ffffffffffffffff
= (2^64 - 2^32 - 1) * 2^192 + (2^64 - 1) * 2^128 + (2^64 - 2^32) * 2^64 + (2^64 - 1) = (2^64 - 2^32 - 1) * 2^192 + (2^64 - 1) * 2^128 + (2^64 - 2^32) * 2^64 + (2^64 - 1)