152 lines
4.0 KiB
Go
152 lines
4.0 KiB
Go
/*
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Copyright © 2025 filifa
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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package cmd
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import (
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"errors"
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"fmt"
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"math/big"
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"github.com/spf13/cobra"
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)
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var discreteLogModulus string
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var discreteLogBase string
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var discreteLogElement string
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var discreteLogOrder string
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// whyyyy doesn't math/big have a ceil functionnnn
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func ceilSqrt(x *big.Int) *big.Int {
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z := new(big.Int).Sqrt(x)
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s := new(big.Int).Exp(z, big.NewInt(2), nil)
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if s.Cmp(x) != 0 {
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z.Add(z, big.NewInt(1))
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}
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return z
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}
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// TODO: this can be extended to work with n, b not coprime
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// https://cp-algorithms.com/algebra/discrete-log.html
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func babyStepGiantStep(n, b, x, order *big.Int) (*big.Int, error) {
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z := new(big.Int).GCD(nil, nil, b, n)
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if z.Cmp(big.NewInt(1)) != 0 {
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return nil, fmt.Errorf("base %v is not invertible modulo %v", b, n)
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}
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var m *big.Int
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if order == nil {
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// m = ceil(sqrt(n - 1))
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z := big.NewInt(1)
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z.Sub(n, z)
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m = ceilSqrt(z)
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} else {
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m = ceilSqrt(order)
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}
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table := make(map[string]*big.Int)
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for j := big.NewInt(1); j.Cmp(m) <= 0; j.Add(j, big.NewInt(1)) {
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a := new(big.Int).Exp(b, j, n)
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table[a.String()] = new(big.Int).Set(j)
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}
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// p = b^-m modulo n
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p := new(big.Int).Neg(m)
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p.Exp(b, p, n)
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gamma := new(big.Int).Set(x)
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for i := big.NewInt(0); i.Cmp(m) == -1; i.Add(i, big.NewInt(1)) {
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j, ok := table[gamma.String()]
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if ok {
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i.Mul(i, m)
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i.Add(i, j)
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return i, nil
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}
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gamma.Mul(gamma, p)
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gamma.Mod(gamma, n)
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}
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return nil, errors.New("no solution")
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}
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func discreteLog(cmd *cobra.Command, args []string) {
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m, ok := new(big.Int).SetString(discreteLogModulus, 10)
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if !ok {
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cobra.CheckErr("invalid modulus " + discreteLogModulus)
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}
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b, ok := new(big.Int).SetString(discreteLogBase, 10)
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if !ok {
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cobra.CheckErr("invalid base " + discreteLogBase)
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}
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x, ok := new(big.Int).SetString(discreteLogElement, 10)
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if !ok {
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cobra.CheckErr("invalid element " + discreteLogElement)
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}
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var order *big.Int
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if discreteLogOrder != "" {
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order, ok = new(big.Int).SetString(discreteLogOrder, 10)
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if !ok {
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cobra.CheckErr("invalid order " + discreteLogOrder)
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}
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}
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k, err := babyStepGiantStep(m, b, x, order)
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if err != nil {
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cobra.CheckErr(err)
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}
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fmt.Println(k)
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}
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// discreteLogCmd represents the discreteLog command
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var discreteLogCmd = &cobra.Command{
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Use: "discrete-log",
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Short: "Compute the discrete logarithm",
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Long: `Compute the discrete logarithm.`,
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Run: discreteLog,
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}
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func init() {
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rootCmd.AddCommand(discreteLogCmd)
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// Here you will define your flags and configuration settings.
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// Cobra supports Persistent Flags which will work for this command
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// and all subcommands, e.g.:
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// discreteLogCmd.PersistentFlags().String("foo", "", "A help for foo")
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// Cobra supports local flags which will only run when this command
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// is called directly, e.g.:
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// discreteLogCmd.Flags().BoolP("toggle", "t", false, "Help message for toggle")
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discreteLogCmd.Flags().StringVarP(&discreteLogModulus, "modulus", "m", "", "modulus of the cyclic group")
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discreteLogCmd.MarkFlagRequired("modulus")
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discreteLogCmd.Flags().StringVarP(&discreteLogBase, "base", "b", "", "logarithmic base")
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discreteLogCmd.MarkFlagRequired("base")
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discreteLogCmd.Flags().StringVarP(&discreteLogElement, "element", "e", "", "element of the cyclic group to compute logarithm of")
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discreteLogCmd.MarkFlagRequired("element")
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discreteLogCmd.Flags().StringVar(&discreteLogOrder, "order", "", "order of the cyclic group")
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}
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