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math/big: handle negative moduli in ModInverse 

Currently, there is no check for a negative modulus in ModInverse.
Negative moduli are passed internally to GCD, which returns 0 for
negative arguments. Mod is symmetric with respect to negative moduli,
so the calculation can be done by just negating the modulus before
passing the arguments to GCD.

Fixes #24949

Change-Id: Ifd1e64c9b2343f0489c04ab65504e73a623378c7
Reviewed-on: https://go-review.googlesource.com/108115
Reviewed-by: Robert Griesemer <gri@golang.org>
Run-TryBot: Robert Griesemer <gri@golang.org>
This commit is contained in:
Brian Kessler 2018-04-19 09:08:24 -06:00 committed by Robert Griesemer
parent 4d44a87243
commit 6f7ec484f6
2 changed files with 9 additions and 3 deletions
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6
src/math/big/int.go
View File

@ -663,8 +663,12 @@ func (z *Int) Rand(rnd *rand.Rand, n *Int) *Int {
// inverse in the ring ℤ/nℤ. In this case, z is unchanged and the return value // inverse in the ring ℤ/nℤ. In this case, z is unchanged and the return value
// is nil. // is nil.
func (z *Int) ModInverse(g, n *Int) *Int { func (z *Int) ModInverse(g, n *Int) *Int {
// GCD expects parameters a and b to be > 0.
if n.neg {
var n2 Int
n = n2.Neg(n)
}
if g.neg { if g.neg {
// GCD expects parameters a and b to be > 0.
var g2 Int var g2 Int
g = g2.Mod(g, n) g = g2.Mod(g, n)
} }

6
src/math/big/int_test.go
View File

@ -1409,19 +1409,21 @@ var modInverseTests = []struct {
{"1234567", "458948883992"}, {"1234567", "458948883992"},
{"239487239847", "2410312426921032588552076022197566074856950548502459942654116941958108831682612228890093858261341614673227141477904012196503648957050582631942730706805009223062734745341073406696246014589361659774041027169249453200378729434170325843778659198143763193776859869524088940195577346119843545301547043747207749969763750084308926339295559968882457872412993810129130294592999947926365264059284647209730384947211681434464714438488520940127459844288859336526896320919633919"}, {"239487239847", "2410312426921032588552076022197566074856950548502459942654116941958108831682612228890093858261341614673227141477904012196503648957050582631942730706805009223062734745341073406696246014589361659774041027169249453200378729434170325843778659198143763193776859869524088940195577346119843545301547043747207749969763750084308926339295559968882457872412993810129130294592999947926365264059284647209730384947211681434464714438488520940127459844288859336526896320919633919"},
{"-10", "13"}, // issue #16984 {"-10", "13"}, // issue #16984
{"10", "-13"},
{"-17", "-13"},
} }
func TestModInverse(t *testing.T) { func TestModInverse(t *testing.T) {
var element, modulus, gcd, inverse Int var element, modulus, gcd, inverse Int
one := NewInt(1) one := NewInt(1)
for i, test := range modInverseTests { for _, test := range modInverseTests {
(&element).SetString(test.element, 10) (&element).SetString(test.element, 10)
(&modulus).SetString(test.modulus, 10) (&modulus).SetString(test.modulus, 10)
(&inverse).ModInverse(&element, &modulus) (&inverse).ModInverse(&element, &modulus)
(&inverse).Mul(&inverse, &element) (&inverse).Mul(&inverse, &element)
(&inverse).Mod(&inverse, &modulus) (&inverse).Mod(&inverse, &modulus)
if (&inverse).Cmp(one) != 0 { if (&inverse).Cmp(one) != 0 {
t.Errorf("#%d: failed (e·e^(-1)=%s)", i, &inverse) t.Errorf("ModInverse(%d,%d)*%d%%%d=%d, not 1", &element, &modulus, &element, &modulus, &inverse)
} }
} }
// exhaustive test for small values // exhaustive test for small values