62 lines
1.2 KiB
Go
62 lines
1.2 KiB
Go
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package crypto
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import "math/big"
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// addMod computes z = (x + y) % p.
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func addMod(x *big.Int, y *big.Int, p *big.Int) (z *big.Int) {
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z = new(big.Int).Add(x, y)
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z.Mod(z, p)
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return z
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}
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// subMod computes z = (x - y) % p.
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func subMod(x *big.Int, y *big.Int, p *big.Int) (z *big.Int) {
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z = new(big.Int).Sub(x, y)
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z.Mod(z, p)
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return z
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}
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// mulMod computes z = (x * y) % p.
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func mulMod(x *big.Int, y *big.Int, p *big.Int) (z *big.Int) {
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n := new(big.Int).Set(x)
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z = big.NewInt(0)
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for i := 0; i < y.BitLen(); i++ {
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if y.Bit(i) == 1 {
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z = addMod(z, n, p)
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}
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n = addMod(n, n, p)
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}
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return z
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}
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// invMod computes z = (1/x) % p.
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func invMod(x *big.Int, p *big.Int) (z *big.Int) {
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z = new(big.Int).ModInverse(x, p)
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return z
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}
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// expMod computes z = (x^e) % p.
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func expMod(x *big.Int, y *big.Int, p *big.Int) (z *big.Int) {
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z = new(big.Int).Exp(x, y, p)
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return z
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}
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// sqrtMod computes z = sqrt(x) % p.
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func sqrtMod(x *big.Int, p *big.Int) (z *big.Int) {
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/* assert that p % 4 == 3 */
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if new(big.Int).Mod(p, big.NewInt(4)).Cmp(big.NewInt(3)) != 0 {
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panic("p is not equal to 3 mod 4!")
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}
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/* z = sqrt(x) % p = x^((p+1)/4) % p */
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/* e = (p+1)/4 */
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e := new(big.Int).Add(p, big.NewInt(1))
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e = e.Rsh(e, 2)
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z = expMod(x, e, p)
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return z
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}
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