move primitive root functions to lib
This commit is contained in:
filifa
parent
4661e2d974
commit
0fdb60275f
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@ -17,121 +17,17 @@ along with this program. If not, see <http://www.gnu.org/licenses/>.
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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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"log"
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"math/big"
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"github.com/spf13/cobra"
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"scm.dairydemon.net/filifa/mathtools/internal/lib"
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)
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var modulus string
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var tpf []string
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func totient(n *big.Int) *big.Int {
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N := new(big.Int).Set(n)
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phi := new(big.Int).Set(N)
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sqrtn := new(big.Int).Sqrt(N)
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for i := big.NewInt(2); i.Cmp(sqrtn) != 1; i.Add(i, big.NewInt(1)) {
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mod := new(big.Int).Mod(N, i)
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if mod.Cmp(big.NewInt(0)) != 0 {
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continue
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}
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// phi -= phi // i
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tmp := new(big.Int).Div(phi, i)
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phi.Sub(phi, tmp)
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for mod.Cmp(big.NewInt(0)) == 0 {
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N.Div(N, i)
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mod.Mod(N, i)
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}
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}
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if N.Cmp(big.NewInt(1)) == 1 {
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// phi -= phi // N
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tmp := new(big.Int).Div(phi, N)
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phi.Sub(phi, tmp)
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}
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return phi
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}
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func multiplicativeOrder(g *big.Int, modulus *big.Int) *big.Int {
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e := new(big.Int).Set(g)
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var k *big.Int
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for k = big.NewInt(1); e.Cmp(big.NewInt(1)) != 0; k.Add(k, big.NewInt(1)) {
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e.Mul(e, g)
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e.Mod(e, modulus)
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}
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return k
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}
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func computeNaive(modulus *big.Int) (*big.Int, error) {
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if modulus.Cmp(big.NewInt(1)) == 0 {
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return big.NewInt(0), nil
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}
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phi := totient(modulus)
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for g := big.NewInt(1); g.Cmp(modulus) == -1; g.Add(g, big.NewInt(1)) {
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gcd := new(big.Int).GCD(nil, nil, g, modulus)
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if gcd.Cmp(big.NewInt(1)) != 0 {
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continue
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}
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order := multiplicativeOrder(g, modulus)
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if order.Cmp(phi) == 0 {
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return g, nil
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}
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}
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return nil, errors.New("no primitive root")
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}
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func computeFromFactors(modulus *big.Int, tpf []string) (*big.Int, error) {
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phi := big.NewInt(1)
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factors := make(map[string]bool)
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for _, s := range tpf {
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p, ok := new(big.Int).SetString(s, 10)
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if !ok {
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return nil, errors.New("invalid input " + s)
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}
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phi.Mul(phi, p)
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factors[p.Text(10)] = true
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}
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for g := big.NewInt(1); g.Cmp(modulus) == -1; g.Add(g, big.NewInt(1)) {
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gcd := new(big.Int).GCD(nil, nil, g, modulus)
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if gcd.Cmp(big.NewInt(1)) != 0 {
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continue
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}
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isPrimitive := true
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for p := range factors {
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e := new(big.Int)
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f, _ := new(big.Int).SetString(p, 10)
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k := new(big.Int).Div(phi, f)
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e.Exp(g, k, modulus)
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if e.Cmp(big.NewInt(1)) == 0 {
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isPrimitive = false
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break
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}
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}
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if isPrimitive {
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return g, nil
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}
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}
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return nil, errors.New("no primitive root")
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}
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func primitiveRoot(cmd *cobra.Command, args []string) {
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m, ok := new(big.Int).SetString(modulus, 10)
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if !ok {
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@ -141,12 +37,12 @@ func primitiveRoot(cmd *cobra.Command, args []string) {
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root := new(big.Int)
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var err error
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if len(tpf) == 0 {
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root, err = computeNaive(m)
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root, err = lib.PrimitiveRoot(m)
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if err != nil {
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log.Fatal(err)
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}
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} else {
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root, err = computeFromFactors(m, tpf)
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root, err = lib.PrimitiveRootFast(m, tpf)
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if err != nil {
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log.Fatal(err)
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}
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@ -76,3 +76,107 @@ func ArePairwiseCoprime(moduli []*big.Int) bool {
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return true
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}
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func Totient(n *big.Int) *big.Int {
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N := new(big.Int).Set(n)
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phi := new(big.Int).Set(N)
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sqrtn := new(big.Int).Sqrt(N)
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for i := big.NewInt(2); i.Cmp(sqrtn) != 1; i.Add(i, big.NewInt(1)) {
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mod := new(big.Int).Mod(N, i)
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if mod.Cmp(big.NewInt(0)) != 0 {
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continue
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}
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// phi -= phi // i
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tmp := new(big.Int).Div(phi, i)
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phi.Sub(phi, tmp)
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for mod.Cmp(big.NewInt(0)) == 0 {
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N.Div(N, i)
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mod.Mod(N, i)
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}
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}
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if N.Cmp(big.NewInt(1)) == 1 {
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// phi -= phi // N
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tmp := new(big.Int).Div(phi, N)
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phi.Sub(phi, tmp)
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}
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return phi
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}
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func MultiplicativeOrder(g *big.Int, modulus *big.Int) *big.Int {
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e := new(big.Int).Set(g)
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var k *big.Int
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for k = big.NewInt(1); e.Cmp(big.NewInt(1)) != 0; k.Add(k, big.NewInt(1)) {
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e.Mul(e, g)
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e.Mod(e, modulus)
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}
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return k
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}
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func PrimitiveRoot(modulus *big.Int) (*big.Int, error) {
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if modulus.Cmp(big.NewInt(1)) == 0 {
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return big.NewInt(0), nil
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}
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phi := Totient(modulus)
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for g := big.NewInt(1); g.Cmp(modulus) == -1; g.Add(g, big.NewInt(1)) {
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gcd := new(big.Int).GCD(nil, nil, g, modulus)
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if gcd.Cmp(big.NewInt(1)) != 0 {
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continue
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}
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order := MultiplicativeOrder(g, modulus)
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if order.Cmp(phi) == 0 {
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return g, nil
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}
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}
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return nil, errors.New("no primitive root")
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}
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func PrimitiveRootFast(modulus *big.Int, tpf []string) (*big.Int, error) {
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phi := big.NewInt(1)
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factors := make(map[string]bool)
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for _, s := range tpf {
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p, ok := new(big.Int).SetString(s, 10)
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if !ok {
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return nil, errors.New("invalid input " + s)
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}
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phi.Mul(phi, p)
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factors[p.Text(10)] = true
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}
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for g := big.NewInt(1); g.Cmp(modulus) == -1; g.Add(g, big.NewInt(1)) {
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gcd := new(big.Int).GCD(nil, nil, g, modulus)
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if gcd.Cmp(big.NewInt(1)) != 0 {
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continue
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}
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isPrimitive := true
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for p := range factors {
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e := new(big.Int)
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f, _ := new(big.Int).SetString(p, 10)
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k := new(big.Int).Div(phi, f)
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e.Exp(g, k, modulus)
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if e.Cmp(big.NewInt(1)) == 0 {
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isPrimitive = false
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break
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}
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}
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if isPrimitive {
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return g, nil
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}
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}
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return nil, errors.New("no primitive root")
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}
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