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filifa
2025-09-30 23:58:28 -04:00
parent 5c42040e34
commit a760093f9d
12 changed files with 62 additions and 3 deletions
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12
internal/lib/primitiveRoot.go
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@@ -21,6 +21,9 @@ import (
"math/big"
)
/*
Totient is a naive implementation of Euler's totient function.
*/
func Totient(n *big.Int) *big.Int {
N := new(big.Int).Set(n)
@@ -52,6 +55,9 @@ func Totient(n *big.Int) *big.Int {
return phi
}
/*
MultiplicativeOrder computes the smallest integer k such that g^k = 1 (mod modulus).
*/
func MultiplicativeOrder(g *big.Int, modulus *big.Int) *big.Int {
e := new(big.Int).Set(g)
var k *big.Int
@@ -63,6 +69,9 @@ func MultiplicativeOrder(g *big.Int, modulus *big.Int) *big.Int {
return k
}
/*
PrimitiveRoot computes a primitive root modulo modulus.
*/
func PrimitiveRoot(modulus *big.Int) (*big.Int, error) {
if modulus.Cmp(big.NewInt(1)) == 0 {
return big.NewInt(0), nil
@@ -85,6 +94,9 @@ func PrimitiveRoot(modulus *big.Int) (*big.Int, error) {
return nil, errors.New("no primitive root")
}
/*
PrimitiveRootFast computes a primitive root modulo modulus, utilizing the prime factorization of the totient of the modulus to find a solution more efficiently.
*/
func PrimitiveRootFast(modulus *big.Int, tpf map[string]*big.Int) (*big.Int, error) {
phi := big.NewInt(1)
for p, exp := range tpf {