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 a74028f..da4e1c8 100755
--- a/src/pkg/big/int.go
+++ b/src/pkg/big/int.go
@@ -518,6 +518,20 @@
}
+// 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 e92ebe5..269c814 100755
--- a/src/pkg/big/int_test.go
+++ b/src/pkg/big/int_test.go
@@ -1019,3 +1019,30 @@
}
}
}
+
+
+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)
+ }
+ }
+}
