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Use math/bits instead implementing arithmethic by hand

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This commit is contained in:
Henry Case 2019-06-26 11:12:43 +01:00
parent 8e0b3a2fa3
commit ec37e1f1bb
2 changed files with 34 additions and 101 deletions
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70
arith_utils.go
View File

@ -1,70 +0,0 @@
package sike
// Helpers
// uint128 representation
type uint128 struct {
H, L uint64
}
func addc64(cin, a, b uint64) (ret, cout uint64) {
ret = cin
ret = ret + a
if ret < a {
cout = 1
}
ret = ret + b
if ret < b {
cout = 1
}
return
}
func subc64(bIn, a, b uint64) (ret, bOut uint64) {
tmp := a - bIn
if tmp > a {
bOut = 1
}
ret = tmp - b
if ret > tmp {
bOut = 1
}
return
}
func mul64(a, b uint64) (res uint128) {
var al, bl, ah, bh, albl, albh, ahbl, ahbh uint64
var res1, res2, res3 uint64
var carry, maskL, maskH, temp uint64
maskL = (^maskL) >> 32
maskH = ^maskL
al = a & maskL
ah = a >> 32
bl = b & maskL
bh = b >> 32
albl = al * bl
albh = al * bh
ahbl = ah * bl
ahbh = ah * bh
res.L = albl & maskL
res1 = albl >> 32
res2 = ahbl & maskL
res3 = albh & maskL
temp = res1 + res2 + res3
carry = temp >> 32
res.L ^= temp << 32
res1 = ahbl >> 32
res2 = albh >> 32
res3 = ahbh & maskL
temp = res1 + res2 + res3 + carry
res.H = temp & maskL
carry = temp & maskH
res.H ^= (ahbh & maskH) + carry
return
}

65
fpP503.go
View File

@ -1,5 +1,9 @@
package sike package sike
import (
"math/bits"
)
// Fp implementation // Fp implementation
// Compute z = x + y (mod 2*p). // Compute z = x + y (mod 2*p).
@ -8,20 +12,20 @@ func fpAddRdc(z, x, y *Fp) {
// z=x+y % p503 // z=x+y % p503
for i := 0; i < FP_WORDS; i++ { for i := 0; i < FP_WORDS; i++ {
z[i], carry = addc64(carry, x[i], y[i]) z[i], carry = bits.Add64(x[i], y[i], carry)
} }
// z = z - p503x2 // z = z - p503x2
carry = 0 carry = 0
for i := 0; i < FP_WORDS; i++ { for i := 0; i < FP_WORDS; i++ {
z[i], carry = subc64(carry, z[i], p503x2[i]) z[i], carry = bits.Sub64(z[i], p503x2[i], carry)
} }
// if z<0 add p503x2 back // if z<0 add p503x2 back
mask := uint64(0 - carry) mask := uint64(0 - carry)
carry = 0 carry = 0
for i := 0; i < FP_WORDS; i++ { for i := 0; i < FP_WORDS; i++ {
z[i], carry = addc64(carry, z[i], p503x2[i]&mask) z[i], carry = bits.Add64(z[i], p503x2[i]&mask, carry)
} }
} }
@ -31,14 +35,14 @@ func fpSubRdc(z, x, y *Fp) {
// z = z - p503x2 // z = z - p503x2
for i := 0; i < FP_WORDS; i++ { for i := 0; i < FP_WORDS; i++ {
z[i], borrow = subc64(borrow, x[i], y[i]) z[i], borrow = bits.Sub64(x[i], y[i], borrow)
} }
// if z<0 add p503x2 back // if z<0 add p503x2 back
mask := uint64(0 - borrow) mask := uint64(0 - borrow)
borrow = 0 borrow = 0
for i := 0; i < FP_WORDS; i++ { for i := 0; i < FP_WORDS; i++ {
z[i], borrow = addc64(borrow, z[i], p503x2[i]&mask) z[i], borrow = bits.Add64(z[i], p503x2[i]&mask, borrow)
} }
} }
@ -46,14 +50,14 @@ func fpSubRdc(z, x, y *Fp) {
func fpRdcP(x *Fp) { func fpRdcP(x *Fp) {
var borrow, mask uint64 var borrow, mask uint64
for i := 0; i < FP_WORDS; i++ { for i := 0; i < FP_WORDS; i++ {
x[i], borrow = subc64(borrow, x[i], p503[i]) x[i], borrow = bits.Sub64(x[i], p503[i], borrow)
} }
// Sets all bits if borrow = 1 // Sets all bits if borrow = 1
mask = 0 - borrow mask = 0 - borrow
borrow = 0 borrow = 0
for i := 0; i < FP_WORDS; i++ { for i := 0; i < FP_WORDS; i++ {
x[i], borrow = addc64(borrow, x[i], p503[i]&mask) x[i], borrow = bits.Add64(x[i], p503[i]&mask, borrow)
} }
} }
@ -69,15 +73,14 @@ func fpSwapCond(x, y *Fp, mask uint8) {
// Compute z = x * y. // Compute z = x * y.
func fpMul(z *FpX2, x, y *Fp) { func fpMul(z *FpX2, x, y *Fp) {
var u, v, t uint64 var carry, t, u, v uint64
var carry uint64 var hi, lo uint64
var uv uint128
for i := uint64(0); i < FP_WORDS; i++ { for i := uint64(0); i < FP_WORDS; i++ {
for j := uint64(0); j <= i; j++ { for j := uint64(0); j <= i; j++ {
uv = mul64(x[j], y[i-j]) hi, lo = bits.Mul64(x[j], y[i-j])
v, carry = addc64(0, uv.L, v) v, carry = bits.Add64(lo, v, 0)
u, carry = addc64(carry, uv.H, u) u, carry = bits.Add64(hi, u, carry)
t += carry t += carry
} }
z[i] = v z[i] = v
@ -88,9 +91,9 @@ func fpMul(z *FpX2, x, y *Fp) {
for i := FP_WORDS; i < (2*FP_WORDS)-1; i++ { for i := FP_WORDS; i < (2*FP_WORDS)-1; i++ {
for j := i - FP_WORDS + 1; j < FP_WORDS; j++ { for j := i - FP_WORDS + 1; j < FP_WORDS; j++ {
uv = mul64(x[j], y[i-j]) hi, lo = bits.Mul64(x[j], y[i-j])
v, carry = addc64(0, uv.L, v) v, carry = bits.Add64(lo, v, 0)
u, carry = addc64(carry, uv.H, u) u, carry = bits.Add64(hi, u, carry)
t += carry t += carry
} }
z[i] = v z[i] = v
@ -105,7 +108,7 @@ func fpMul(z *FpX2, x, y *Fp) {
// with R=2^512. Destroys the input value. // with R=2^512. Destroys the input value.
func fpMontRdc(z *Fp, x *FpX2) { func fpMontRdc(z *Fp, x *FpX2) {
var carry, t, u, v uint64 var carry, t, u, v uint64
var uv uint128 var hi, lo uint64
var count int var count int
count = 3 // number of 0 digits in the least significat part of p503 + 1 count = 3 // number of 0 digits in the least significat part of p503 + 1
@ -113,14 +116,14 @@ func fpMontRdc(z *Fp, x *FpX2) {
for i := 0; i < FP_WORDS; i++ { for i := 0; i < FP_WORDS; i++ {
for j := 0; j < i; j++ { for j := 0; j < i; j++ {
if j < (i - count + 1) { if j < (i - count + 1) {
uv = mul64(z[j], p503p1[i-j]) hi, lo = bits.Mul64(z[j], p503p1[i-j])
v, carry = addc64(0, uv.L, v) v, carry = bits.Add64(lo, v, 0)
u, carry = addc64(carry, uv.H, u) u, carry = bits.Add64(hi, u, carry)
t += carry t += carry
} }
} }
v, carry = addc64(0, v, x[i]) v, carry = bits.Add64(v, x[i], 0)
u, carry = addc64(carry, u, 0) u, carry = bits.Add64(u, 0, carry)
t += carry t += carry
z[i] = v z[i] = v
@ -135,14 +138,14 @@ func fpMontRdc(z *Fp, x *FpX2) {
} }
for j := i - FP_WORDS + 1; j < FP_WORDS; j++ { for j := i - FP_WORDS + 1; j < FP_WORDS; j++ {
if j < (FP_WORDS - count) { if j < (FP_WORDS - count) {
uv = mul64(z[j], p503p1[i-j]) hi, lo = bits.Mul64(z[j], p503p1[i-j])
v, carry = addc64(0, uv.L, v) v, carry = bits.Add64(lo, v, 0)
u, carry = addc64(carry, uv.H, u) u, carry = bits.Add64(hi, u, carry)
t += carry t += carry
} }
} }
v, carry = addc64(0, v, x[i]) v, carry = bits.Add64(v, x[i], 0)
u, carry = addc64(carry, u, 0) u, carry = bits.Add64(u, 0, carry)
t += carry t += carry
z[i-FP_WORDS] = v z[i-FP_WORDS] = v
@ -150,7 +153,7 @@ func fpMontRdc(z *Fp, x *FpX2) {
u = t u = t
t = 0 t = 0
} }
v, carry = addc64(0, v, x[2*FP_WORDS-1]) v, carry = bits.Add64(v, x[2*FP_WORDS-1], 0)
z[FP_WORDS-1] = v z[FP_WORDS-1] = v
} }
@ -158,7 +161,7 @@ func fpMontRdc(z *Fp, x *FpX2) {
func fp2Add(z, x, y *FpX2) { func fp2Add(z, x, y *FpX2) {
var carry uint64 var carry uint64
for i := 0; i < 2*FP_WORDS; i++ { for i := 0; i < 2*FP_WORDS; i++ {
z[i], carry = addc64(carry, x[i], y[i]) z[i], carry = bits.Add64(x[i], y[i], carry)
} }
} }
@ -166,14 +169,14 @@ func fp2Add(z, x, y *FpX2) {
func fp2Sub(z, x, y *FpX2) { func fp2Sub(z, x, y *FpX2) {
var borrow, mask uint64 var borrow, mask uint64
for i := 0; i < 2*FP_WORDS; i++ { for i := 0; i < 2*FP_WORDS; i++ {
z[i], borrow = subc64(borrow, x[i], y[i]) z[i], borrow = bits.Sub64(x[i], y[i], borrow)
} }
// Sets all bits if borrow = 1 // Sets all bits if borrow = 1
mask = 0 - borrow mask = 0 - borrow
borrow = 0 borrow = 0
for i := FP_WORDS; i < 2*FP_WORDS; i++ { for i := FP_WORDS; i < 2*FP_WORDS; i++ {
z[i], borrow = addc64(borrow, z[i], p503[i-FP_WORDS]&mask) z[i], borrow = bits.Add64(z[i], p503[i-FP_WORDS]&mask, borrow)
} }
} }