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// +build noasm !amd64,!arm64
package p503
import (
. "github.com/cloudflare/sidh/internal/arith"
. "github.com/cloudflare/sidh/internal/isogeny"
)
// Compute z = x + y (mod p).
func fp503AddReduced(z, x, y *FpElement) {
var carry uint64
// z=x+y % p503
for i := 0; i < NumWords; i++ {
z[i], carry = Addc64(carry, x[i], y[i])
}
// z = z - p503x2
carry = 0
for i := 0; i < NumWords; i++ {
z[i], carry = Subc64(carry, z[i], p503x2[i])
}
// if z<0 add p503x2 back
mask := uint64(0 - carry)
carry = 0
for i := 0; i < NumWords; i++ {
z[i], carry = Addc64(carry, z[i], p503x2[i]&mask)
}
}
// Compute z = x - y (mod p).
func fp503SubReduced(z, x, y *FpElement) {
var borrow uint64
// z = z - p503x2
for i := 0; i < NumWords; i++ {
z[i], borrow = Subc64(borrow, x[i], y[i])
}
// if z<0 add p503x2 back
mask := uint64(0 - borrow)
borrow = 0
for i := 0; i < NumWords; i++ {
z[i], borrow = Addc64(borrow, z[i], p503x2[i]&mask)
}
}
// Conditionally swaps bits in x and y in constant time.
// mask indicates bits to be swapped (set bits are swapped)
// For details see "Hackers Delight, 2.20"
//
// Implementation doesn't actually depend on a prime field.
func fp503ConditionalSwap(x, y *FpElement, mask uint8) {
var tmp, mask64 uint64
mask64 = 0 - uint64(mask)
for i := 0; i < NumWords; i++ {
tmp = mask64 & (x[i] ^ y[i])
x[i] = tmp ^ x[i]
y[i] = tmp ^ y[i]
}
}
// Perform Montgomery reduction: set z = x R^{-1} (mod 2*p)
// with R=2^512. Destroys the input value.
func fp503MontgomeryReduce(z *FpElement, x *FpElementX2) {
var carry, t, u, v uint64
var uv Uint128
var count int
count = 3 // number of 0 digits in the least significat part of p503 + 1
for i := 0; i < NumWords; i++ {
for j := 0; j < i; j++ {
if j < (i - count + 1) {
uv = Mul64(z[j], p503p1[i-j])
v, carry = Addc64(0, uv.L, v)
u, carry = Addc64(carry, uv.H, u)
t += carry
}
}
v, carry = Addc64(0, v, x[i])
u, carry = Addc64(carry, u, 0)
t += carry
z[i] = v
v = u
u = t
t = 0
}
for i := NumWords; i < 2*NumWords-1; i++ {
if count > 0 {
count--
}
for j := i - NumWords + 1; j < NumWords; j++ {
if j < (NumWords - count) {
uv = Mul64(z[j], p503p1[i-j])
v, carry = Addc64(0, uv.L, v)
u, carry = Addc64(carry, uv.H, u)
t += carry
}
}
v, carry = Addc64(0, v, x[i])
u, carry = Addc64(carry, u, 0)
t += carry
z[i-NumWords] = v
v = u
u = t
t = 0
}
v, carry = Addc64(0, v, x[2*NumWords-1])
z[NumWords-1] = v
}
// Compute z = x * y.
func fp503Mul(z *FpElementX2, x, y *FpElement) {
var u, v, t uint64
var carry uint64
var uv Uint128
for i := uint64(0); i < NumWords; i++ {
for j := uint64(0); j <= i; j++ {
uv = Mul64(x[j], y[i-j])
v, carry = Addc64(0, uv.L, v)
u, carry = Addc64(carry, uv.H, u)
t += carry
}
z[i] = v
v = u
u = t
t = 0
}
for i := NumWords; i < (2*NumWords)-1; i++ {
for j := i - NumWords + 1; j < NumWords; j++ {
uv = Mul64(x[j], y[i-j])
v, carry = Addc64(0, uv.L, v)
u, carry = Addc64(carry, uv.H, u)
t += carry
}
z[i] = v
v = u
u = t
t = 0
}
z[2*NumWords-1] = v
}
// Compute z = x + y, without reducing mod p.
func fp503AddLazy(z, x, y *FpElement) {
var carry uint64
for i := 0; i < NumWords; i++ {
z[i], carry = Addc64(carry, x[i], y[i])
}
}
// Compute z = x + y, without reducing mod p.
func fp503X2AddLazy(z, x, y *FpElementX2) {
var carry uint64
for i := 0; i < 2*NumWords; i++ {
z[i], carry = Addc64(carry, x[i], y[i])
}
}
// Reduce a field element in [0, 2*p) to one in [0,p).
func fp503StrongReduce(x *FpElement) {
var borrow, mask uint64
for i := 0; i < NumWords; i++ {
x[i], borrow = Subc64(borrow, x[i], p503[i])
}
// Sets all bits if borrow = 1
mask = 0 - borrow
borrow = 0
for i := 0; i < NumWords; i++ {
x[i], borrow = Addc64(borrow, x[i], p503[i]&mask)
}
}
// Compute z = x - y, without reducing mod p.
func fp503X2SubLazy(z, x, y *FpElementX2) {
var borrow, mask uint64
for i := 0; i < 2*NumWords; i++ {
z[i], borrow = Subc64(borrow, x[i], y[i])
}
// Sets all bits if borrow = 1
mask = 0 - borrow
borrow = 0
for i := NumWords; i < 2*NumWords; i++ {
z[i], borrow = Addc64(borrow, z[i], p503[i-NumWords]&mask)
}
}
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