move to lib

internal/lib/discreteLog.go

@@ -0,0 +1,79 @@
+/*
+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")
+}