add modular square root command

cmd/modSqrt.go

@@ -0,0 +1,88 @@
+/*
+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 modSqrtQ string
+var modSqrtN string
+
+func modSqrt(cmd *cobra.Command, args []string) {
+	q, ok := new(big.Int).SetString(modSqrtQ, 10)
+	if !ok {
+		cobra.CheckErr("invalid input " + modSqrtQ)
+	}
+
+	n, ok := new(big.Int).SetString(modSqrtN, 10)
+	if !ok {
+		cobra.CheckErr("invalid input " + modSqrtN)
+	}
+
+	// TODO: support moduli that are not odd primes
+	// can use Hansel's lemma for prime powers
+	// can use CRT for constructing answers for composite moduli
+	// see https://en.wikipedia.org/wiki/Quadratic_residue#Complexity_of_finding_square_roots
+
+	rounds := 10
+	z := new(big.Int).Mod(n, big.NewInt(2))
+	if z.Cmp(big.NewInt(0)) == 0 || !n.ProbablyPrime(rounds) {
+		cobra.CheckErr(modSqrtN + " is not an odd prime")
+	}
+
+	res := z.ModSqrt(q, n)
+	if res == nil {
+		cobra.CheckErr("cannot find a modular square root: " + modSqrtQ + " is not a quadratic residue modulo " + modSqrtN)
+	} else {
+		fmt.Println(z)
+	}
+}
+
+// modSqrtCmd represents the modSqrt command
+var modSqrtCmd = &cobra.Command{
+	Use:   "mod-sqrt -q Q -m M",
+	Short: "Compute a modular square root",
+	Long: `Compute a modular square root.
+
+Given an integer q and a modulus m, this will compute a value x such that
+x^2 = q (mod n)`,
+	Run: modSqrt,
+}
+
+func init() {
+	rootCmd.AddCommand(modSqrtCmd)
+
+	// Here you will define your flags and configuration settings.
+
+	// Cobra supports Persistent Flags which will work for this command
+	// and all subcommands, e.g.:
+	// modSqrtCmd.PersistentFlags().String("foo", "", "A help for foo")
+
+	// Cobra supports local flags which will only run when this command
+	// is called directly, e.g.:
+	// modSqrtCmd.Flags().BoolP("toggle", "t", false, "Help message for toggle")
+
+	modSqrtCmd.Flags().StringVarP(&modSqrtQ, "residue", "q", "", "candidate to test")
+	modSqrtCmd.MarkFlagRequired("residue")
+
+	modSqrtCmd.Flags().StringVarP(&modSqrtN, "modulus", "m", "", "modulus")
+	modSqrtCmd.MarkFlagRequired("modulus")
+}