big: add ModInverse.

ModInverse is just a small wrapper around GcdInt, but it's nice to
have in order to be clear about what one is doing in other code.

R=gri, agl1
CC=golang-dev
https://golang.org/cl/1244045

diff --git a/src/pkg/big/int.go b/src/pkg/big/int.go
index a74028fd745b58fb599dadec3edbab556e1ff7b4..da4e1c83ca1a6202a860c8020a37017b1aefab06 100755 (executable)
--- a/src/pkg/big/int.go
+++ b/src/pkg/big/int.go
@@ -518,6 +518,20 @@ func ProbablyPrime(z *Int, n int) bool {
 }
 
 
+// ModInverse sets z to the multiplicative inverse of g in the group ℤ/pℤ (where
+// p is a prime) and returns z.
+func (z *Int) ModInverse(g, p *Int) *Int {
+       var d Int
+       GcdInt(&d, z, nil, g, p)
+       // x and y are such that g*x + p*y = d. Since p is prime, d = 1. Taking
+       // that modulo p results in g*x = 1, therefore x is the inverse element.
+       if z.neg {
+               z.Add(z, p)
+       }
+       return z
+}
+
+
 // Lsh sets z = x << n and returns z.
 func (z *Int) Lsh(x *Int, n uint) *Int {
        z.abs = z.abs.shl(x.abs, n)

diff --git a/src/pkg/big/int_test.go b/src/pkg/big/int_test.go
index e92ebe508a1002f654a5daba047031e87daf3e93..269c814d46649c8b47c25aad81f8608755ccc83f 100755 (executable)
--- a/src/pkg/big/int_test.go
+++ b/src/pkg/big/int_test.go
@@ -1019,3 +1019,30 @@ func TestNot(t *testing.T) {
                }
        }
 }
+
+
+type modInverseTest struct {
+       element string
+       prime   string
+}
+
+var modInverseTests = []modInverseTest{
+       modInverseTest{"1", "7"},
+       modInverseTest{"1", "13"},
+       modInverseTest{"239487239847", "2410312426921032588552076022197566074856950548502459942654116941958108831682612228890093858261341614673227141477904012196503648957050582631942730706805009223062734745341073406696246014589361659774041027169249453200378729434170325843778659198143763193776859869524088940195577346119843545301547043747207749969763750084308926339295559968882457872412993810129130294592999947926365264059284647209730384947211681434464714438488520940127459844288859336526896320919633919"},
+}
+
+func TestModInverse(t *testing.T) {
+       var element, prime Int
+       one := NewInt(1)
+       for i, test := range modInverseTests {
+               (&element).SetString(test.element, 10)
+               (&prime).SetString(test.prime, 10)
+               inverse := new(Int).ModInverse(&element, &prime)
+               inverse.Mul(inverse, &element)
+               inverse.Mod(inverse, &prime)
+               if inverse.Cmp(one) != 0 {
+                       t.Errorf("#%d: failed (e·e^(-1)=%s)", i, inverse)
+               }
+       }
+}