80 lines
1.9 KiB
Go
80 lines
1.9 KiB
Go
/*
|
|
Copyright © 2025 filifa
|
|
|
|
This program is free software: you can redistribute it and/or modify
|
|
it under the terms of the GNU General Public License as published by
|
|
the Free Software Foundation, either version 3 of the License, or
|
|
(at your option) any later version.
|
|
|
|
This program is distributed in the hope that it will be useful,
|
|
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
|
GNU General Public License for more details.
|
|
|
|
You should have received a copy of the GNU General Public License
|
|
along with this program. If not, see <http://www.gnu.org/licenses/>.
|
|
*/
|
|
package lib
|
|
|
|
import (
|
|
"errors"
|
|
"fmt"
|
|
"math/big"
|
|
)
|
|
|
|
// whyyyy doesn't math/big have a ceil functionnnn
|
|
func ceilSqrt(x *big.Int) *big.Int {
|
|
z := new(big.Int).Sqrt(x)
|
|
s := new(big.Int).Exp(z, big.NewInt(2), nil)
|
|
if s.Cmp(x) != 0 {
|
|
z.Add(z, big.NewInt(1))
|
|
}
|
|
|
|
return z
|
|
}
|
|
|
|
// TODO: this can be extended to work with n, b not coprime
|
|
// https://cp-algorithms.com/algebra/discrete-log.html
|
|
func BabyStepGiantStep(n, b, x, order *big.Int) (*big.Int, error) {
|
|
z := new(big.Int).GCD(nil, nil, b, n)
|
|
if z.Cmp(big.NewInt(1)) != 0 {
|
|
return nil, fmt.Errorf("base %v and modulus %v are not coprime", b, n)
|
|
}
|
|
|
|
var m *big.Int
|
|
if order == nil {
|
|
// m = ceil(sqrt(n - 1))
|
|
z := big.NewInt(1)
|
|
z.Sub(n, z)
|
|
m = ceilSqrt(z)
|
|
} else {
|
|
m = ceilSqrt(order)
|
|
}
|
|
|
|
table := make(map[string]*big.Int)
|
|
for j := big.NewInt(1); j.Cmp(m) <= 0; j.Add(j, big.NewInt(1)) {
|
|
a := new(big.Int).Exp(b, j, n)
|
|
table[a.String()] = new(big.Int).Set(j)
|
|
}
|
|
|
|
// p = b^-m modulo n
|
|
p := new(big.Int).Neg(m)
|
|
p.Exp(b, p, n)
|
|
|
|
gamma := new(big.Int).Set(x)
|
|
|
|
for i := big.NewInt(0); i.Cmp(m) == -1; i.Add(i, big.NewInt(1)) {
|
|
j, ok := table[gamma.String()]
|
|
if ok {
|
|
i.Mul(i, m)
|
|
i.Add(i, j)
|
|
return i, nil
|
|
}
|
|
|
|
gamma.Mul(gamma, p)
|
|
gamma.Mod(gamma, n)
|
|
}
|
|
|
|
return nil, errors.New("no solution")
|
|
}
|