neo-go/pkg/crypto/modular_arithmetic.go

package crypto

import "math/big"

// addMod computes z = (x + y) % p.
func addMod(x *big.Int, y *big.Int, p *big.Int) (z *big.Int) {
	z = new(big.Int).Add(x, y)
	z.Mod(z, p)
	return z
}

// subMod computes z = (x - y) % p.
func subMod(x *big.Int, y *big.Int, p *big.Int) (z *big.Int) {
	z = new(big.Int).Sub(x, y)
	z.Mod(z, p)
	return z
}

// mulMod computes z = (x * y) % p.
func mulMod(x *big.Int, y *big.Int, p *big.Int) (z *big.Int) {
	n := new(big.Int).Set(x)
	z = big.NewInt(0)

	for i := 0; i < y.BitLen(); i++ {
		if y.Bit(i) == 1 {
			z = addMod(z, n, p)
		}
		n = addMod(n, n, p)
	}

	return z
}

// invMod computes z = (1/x) % p.
func invMod(x *big.Int, p *big.Int) (z *big.Int) {
	z = new(big.Int).ModInverse(x, p)
	return z
}

// expMod computes z = (x^e) % p.
func expMod(x *big.Int, y *big.Int, p *big.Int) (z *big.Int) {
	z = new(big.Int).Exp(x, y, p)
	return z
}

// sqrtMod computes z = sqrt(x) % p.
func sqrtMod(x *big.Int, p *big.Int) (z *big.Int) {
	/* assert that p % 4 == 3 */
	if new(big.Int).Mod(p, big.NewInt(4)).Cmp(big.NewInt(3)) != 0 {
		panic("p is not equal to 3 mod 4!")
	}

	/* z = sqrt(x) % p = x^((p+1)/4) % p */

	/* e = (p+1)/4 */
	e := new(big.Int).Add(p, big.NewInt(1))
	e = e.Rsh(e, 2)

	z = expMod(x, e, p)
	return z
}