chore: vendor

vendor/github.com/cloudflare/circl/math/fp448/fp.go

@@ -0,0 +1,164 @@
+// Package fp448 provides prime field arithmetic over GF(2^448-2^224-1).
+package fp448
+
+import (
+	"errors"
+
+	"github.com/cloudflare/circl/internal/conv"
+)
+
+// Size in bytes of an element.
+const Size = 56
+
+// Elt is a prime field element.
+type Elt [Size]byte
+
+func (e Elt) String() string { return conv.BytesLe2Hex(e[:]) }
+
+// p is the prime modulus 2^448-2^224-1.
+var p = Elt{
+	0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+	0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+	0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+	0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff,
+	0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+	0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+	0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+}
+
+// P returns the prime modulus 2^448-2^224-1.
+func P() Elt { return p }
+
+// ToBytes stores in b the little-endian byte representation of x.
+func ToBytes(b []byte, x *Elt) error {
+	if len(b) != Size {
+		return errors.New("wrong size")
+	}
+	Modp(x)
+	copy(b, x[:])
+	return nil
+}
+
+// IsZero returns true if x is equal to 0.
+func IsZero(x *Elt) bool { Modp(x); return *x == Elt{} }
+
+// IsOne returns true if x is equal to 1.
+func IsOne(x *Elt) bool { Modp(x); return *x == Elt{1} }
+
+// SetOne assigns x=1.
+func SetOne(x *Elt) { *x = Elt{1} }
+
+// One returns the 1 element.
+func One() (x Elt) { x = Elt{1}; return }
+
+// Neg calculates z = -x.
+func Neg(z, x *Elt) { Sub(z, &p, x) }
+
+// Modp ensures that z is between [0,p-1].
+func Modp(z *Elt) { Sub(z, z, &p) }
+
+// InvSqrt calculates z = sqrt(x/y) iff x/y is a quadratic-residue. If so,
+// isQR = true; otherwise, isQR = false, since x/y is a quadratic non-residue,
+// and z = sqrt(-x/y).
+func InvSqrt(z, x, y *Elt) (isQR bool) {
+	// First note that x^(2(k+1)) = x^(p-1)/2 * x = legendre(x) * x
+	// so that's x if x is a quadratic residue and -x otherwise.
+	// Next, y^(6k+3) = y^(4k+2) * y^(2k+1) = y^(p-1) * y^((p-1)/2) = legendre(y).
+	// So the z we compute satisfies z^2 y = x^(2(k+1)) y^(6k+3) = legendre(x)*legendre(y).
+	// Thus if x and y are quadratic residues, then z is indeed sqrt(x/y).
+	t0, t1 := &Elt{}, &Elt{}
+	Mul(t0, x, y)         // x*y
+	Sqr(t1, y)            // y^2
+	Mul(t1, t0, t1)       // x*y^3
+	powPminus3div4(z, t1) // (x*y^3)^k
+	Mul(z, z, t0)         // z = x*y*(x*y^3)^k = x^(k+1) * y^(3k+1)
+
+	// Check if x/y is a quadratic residue
+	Sqr(t0, z)     // z^2
+	Mul(t0, t0, y) // y*z^2
+	Sub(t0, t0, x) // y*z^2-x
+	return IsZero(t0)
+}
+
+// Inv calculates z = 1/x mod p.
+func Inv(z, x *Elt) {
+	// Calculates z = x^(4k+1) = x^(p-3+1) = x^(p-2) = x^-1, where k = (p-3)/4.
+	t := &Elt{}
+	powPminus3div4(t, x) // t = x^k
+	Sqr(t, t)            // t = x^2k
+	Sqr(t, t)            // t = x^4k
+	Mul(z, t, x)         // z = x^(4k+1)
+}
+
+// powPminus3div4 calculates z = x^k mod p, where k = (p-3)/4.
+func powPminus3div4(z, x *Elt) {
+	x0, x1 := &Elt{}, &Elt{}
+	Sqr(z, x)
+	Mul(z, z, x)
+	Sqr(x0, z)
+	Mul(x0, x0, x)
+	Sqr(z, x0)
+	Sqr(z, z)
+	Sqr(z, z)
+	Mul(z, z, x0)
+	Sqr(x1, z)
+	for i := 0; i < 5; i++ {
+		Sqr(x1, x1)
+	}
+	Mul(x1, x1, z)
+	Sqr(z, x1)
+	for i := 0; i < 11; i++ {
+		Sqr(z, z)
+	}
+	Mul(z, z, x1)
+	Sqr(z, z)
+	Sqr(z, z)
+	Sqr(z, z)
+	Mul(z, z, x0)
+	Sqr(x1, z)
+	for i := 0; i < 26; i++ {
+		Sqr(x1, x1)
+	}
+	Mul(x1, x1, z)
+	Sqr(z, x1)
+	for i := 0; i < 53; i++ {
+		Sqr(z, z)
+	}
+	Mul(z, z, x1)
+	Sqr(z, z)
+	Sqr(z, z)
+	Sqr(z, z)
+	Mul(z, z, x0)
+	Sqr(x1, z)
+	for i := 0; i < 110; i++ {
+		Sqr(x1, x1)
+	}
+	Mul(x1, x1, z)
+	Sqr(z, x1)
+	Mul(z, z, x)
+	for i := 0; i < 223; i++ {
+		Sqr(z, z)
+	}
+	Mul(z, z, x1)
+}
+
+// Cmov assigns y to x if n is 1.
+func Cmov(x, y *Elt, n uint) { cmov(x, y, n) }
+
+// Cswap interchanges x and y if n is 1.
+func Cswap(x, y *Elt, n uint) { cswap(x, y, n) }
+
+// Add calculates z = x+y mod p.
+func Add(z, x, y *Elt) { add(z, x, y) }
+
+// Sub calculates z = x-y mod p.
+func Sub(z, x, y *Elt) { sub(z, x, y) }
+
+// AddSub calculates (x,y) = (x+y mod p, x-y mod p).
+func AddSub(x, y *Elt) { addsub(x, y) }
+
+// Mul calculates z = x*y mod p.
+func Mul(z, x, y *Elt) { mul(z, x, y) }
+
+// Sqr calculates z = x^2 mod p.
+func Sqr(z, x *Elt) { sqr(z, x) }