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83 lines
2.7 KiB
Go
83 lines
2.7 KiB
Go
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package native
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// SswuParams for computing the Simplified SWU mapping
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// for hash to curve implementations
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type SswuParams struct {
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C1, C2, A, B, Z [FieldLimbs]uint64
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}
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// Osswu3mod4 computes the simplified map optmized for 3 mod 4 primes
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// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-11#appendix-G.2.1
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func (p *SswuParams) Osswu3mod4(u *Field) (x, y *Field) {
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var tv1, tv2, tv3, tv4, xd, x1n, x2n, gxd, gx1, aNeg, zA, y1, y2 [FieldLimbs]uint64
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var wasInverted int
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u.Arithmetic.Mul(&tv1, &u.Value, &u.Value) // tv1 = u^2
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u.Arithmetic.Mul(&tv3, &p.Z, &tv1) // tv3 = z * tv1
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u.Arithmetic.Square(&tv2, &tv3) // tv2 = tv3^2
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u.Arithmetic.Add(&xd, &tv2, &tv3) // xd = tv2 + tv3
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u.Arithmetic.Add(&x1n, &u.Params.R, &xd) // x1n = (xd + 1)
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u.Arithmetic.Mul(&x1n, &x1n, &p.B) // x1n * B
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u.Arithmetic.Neg(&aNeg, &p.A)
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u.Arithmetic.Mul(&xd, &xd, &aNeg) // xd = -A * xd
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xdIsZero := (&Field{
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Value: xd,
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}).IsZero()
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u.Arithmetic.Mul(&zA, &p.Z, &p.A)
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u.Arithmetic.Selectznz(&xd, &xd, &zA, xdIsZero) // xd = z * A if xd == 0
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u.Arithmetic.Square(&tv2, &xd) // tv2 = xd^2
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u.Arithmetic.Mul(&gxd, &tv2, &xd) // gxd = tv2 * xd
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u.Arithmetic.Mul(&tv2, &tv2, &p.A) // tv2 = A * tv2
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u.Arithmetic.Square(&gx1, &x1n) // gx1 = x1n^2
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u.Arithmetic.Add(&gx1, &gx1, &tv2) // gx1 = gx1 + tv2
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u.Arithmetic.Mul(&gx1, &gx1, &x1n) // gx1 = gx1 * x1n
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u.Arithmetic.Mul(&tv2, &gxd, &p.B) // tv2 = B * gxd
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u.Arithmetic.Add(&gx1, &gx1, &tv2) // gx1 = gx1 + tv2
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u.Arithmetic.Square(&tv4, &gxd) // tv4 = gxd^2
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u.Arithmetic.Mul(&tv2, &gx1, &gxd) // tv2 = gx1 * gxd
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u.Arithmetic.Mul(&tv4, &tv4, &tv2) // tv4 = tv4 * tv2
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Pow(&y1, &tv4, &p.C1, u.Params, u.Arithmetic) // y1 = tv4^C1
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u.Arithmetic.Mul(&y1, &y1, &tv2) //y1 = y1 * tv2
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u.Arithmetic.Mul(&x2n, &tv3, &x1n) // x2n = tv3 * x1n
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u.Arithmetic.Mul(&y2, &y1, &p.C2) // y2 = y1 * c2
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u.Arithmetic.Mul(&y2, &y2, &tv1) // y2 = y2 * tv1
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u.Arithmetic.Mul(&y2, &y2, &u.Value) // y2 = y2 * u
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u.Arithmetic.Square(&tv2, &y1) // tv2 = y1^2
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u.Arithmetic.Mul(&tv2, &tv2, &gxd) // tv2 = tv2 * gxd
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e2 := (&Field{Value: tv2}).Equal(&Field{Value: gx1})
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x = new(Field).Set(u)
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y = new(Field).Set(u)
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// If e2, x = x1, else x = x2
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u.Arithmetic.Selectznz(&x.Value, &x2n, &x1n, e2)
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// xn / xd
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u.Arithmetic.Invert(&wasInverted, &tv1, &xd)
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u.Arithmetic.Mul(&tv1, &x.Value, &tv1)
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u.Arithmetic.Selectznz(&x.Value, &x.Value, &tv1, wasInverted)
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// If e2, y = y1, else y = y2
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u.Arithmetic.Selectznz(&y.Value, &y2, &y1, e2)
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uBytes := u.Bytes()
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yBytes := y.Bytes()
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usign := uBytes[0] & 1
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ysign := yBytes[0] & 1
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// Fix sign of y
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if usign != ysign {
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y.Neg(y)
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}
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return
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}
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