add discrete log command

cmd/discreteLog.go

@@ -0,0 +1,120 @@
+/*
+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 cmd
+
+import (
+	"fmt"
+	"math/big"
+
+	"github.com/spf13/cobra"
+)
+
+var discreteLogOrder string
+var discreteLogGenerator string
+var discreteLogElement string
+
+// 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
+}
+
+func babyStepGiantStep(n, g, x *big.Int) *big.Int {
+	m := ceilSqrt(n)
+
+	table := make(map[string]*big.Int)
+	for j := big.NewInt(0); j.Cmp(m) == -1; j.Add(j, big.NewInt(1)) {
+		a := new(big.Int).Exp(g, j, n)
+		table[a.String()] = new(big.Int).Set(j)
+	}
+
+	// p = g^-m modulo n
+	p := new(big.Int).Neg(m)
+	p.Exp(g, 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
+		}
+
+		gamma.Mul(gamma, p)
+		gamma.Mod(gamma, n)
+	}
+
+	return nil
+}
+
+func discreteLog(cmd *cobra.Command, args []string) {
+	n, ok := new(big.Int).SetString(discreteLogOrder, 10)
+	if !ok {
+		cobra.CheckErr("invalid order " + discreteLogOrder)
+	}
+
+	g, ok := new(big.Int).SetString(discreteLogGenerator, 10)
+	if !ok {
+		cobra.CheckErr("invalid generator " + discreteLogGenerator)
+	}
+
+	x, ok := new(big.Int).SetString(discreteLogElement, 10)
+	if !ok {
+		cobra.CheckErr("invalid element " + discreteLogElement)
+	}
+
+	k := babyStepGiantStep(n, g, x)
+	fmt.Println(k)
+}
+
+// discreteLogCmd represents the discreteLog command
+var discreteLogCmd = &cobra.Command{
+	Use:   "discrete-log",
+	Short: "Compute the discrete logarithm",
+	Long:  `Compute the discrete logarithm`,
+	Run:   discreteLog,
+}
+
+func init() {
+	rootCmd.AddCommand(discreteLogCmd)
+
+	// Here you will define your flags and configuration settings.
+
+	// Cobra supports Persistent Flags which will work for this command
+	// and all subcommands, e.g.:
+	// discreteLogCmd.PersistentFlags().String("foo", "", "A help for foo")
+
+	// Cobra supports local flags which will only run when this command
+	// is called directly, e.g.:
+	// discreteLogCmd.Flags().BoolP("toggle", "t", false, "Help message for toggle")
+
+	discreteLogCmd.Flags().StringVarP(&discreteLogOrder, "order", "n", "", "order of the cyclic group")
+	discreteLogCmd.MarkFlagRequired("order")
+
+	discreteLogCmd.Flags().StringVarP(&discreteLogGenerator, "generator", "g", "", "generator of the cyclic group")
+	discreteLogCmd.MarkFlagRequired("generator")
+
+	discreteLogCmd.Flags().StringVarP(&discreteLogElement, "element", "e", "", "element of the cyclic group to compute logarithm of")
+	discreteLogCmd.MarkFlagRequired("element")
+}