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big: fix mistakes with probablyPrime

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probablyPrime would return false negatives in some cases.

This code has now been tested against GMP for several million iterations without issues.

Fixes #638.

R=rsc
CC=golang-dev
https://golang.org/cl/252041
This commit is contained in:
Adam Langley 2010-03-05 15:55:26 -05:00
parent 0ac5ef70db
commit 308064fc59
2 changed files with 12 additions and 4 deletions
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7
src/pkg/big/int_test.go
View File

@ -480,6 +480,9 @@ var primes = []string{
"10953742525620032441",
"17908251027575790097",
// http://code.google.com/p/go/issues/detail?id=638
"18699199384836356663",
"98920366548084643601728869055592650835572950932266967461790948584315647051443",
"94560208308847015747498523884063394671606671904944666360068158221458669711639",
@ -503,14 +506,14 @@ func TestProbablyPrime(t *testing.T) {
for i, s := range primes {
p, _ := new(Int).SetString(s, 10)
if !ProbablyPrime(p, 20) {
t.Errorf("#%d prime found to be non-prime", i)
t.Errorf("#%d prime found to be non-prime (%s)", i, s)
}
}
for i, s := range composites {
c, _ := new(Int).SetString(s, 10)
if ProbablyPrime(c, 20) {
t.Errorf("#%d composite found to be prime", i)
t.Errorf("#%d composite found to be prime (%s)", i, s)
}
}
}

9
src/pkg/big/nat.go
View File

@ -586,6 +586,7 @@ func powersOfTwoDecompose(n []Word) (q []Word, k Word) {
q = makeN(nil, len(n)-zeroWords, false)
shiftRight(q, n[zeroWords:], x)
q = normN(q)
k = Word(_W*zeroWords + x)
return
@ -705,7 +706,7 @@ const (
var bigOne = []Word{1}
var bigTwo = []Word{2}
// ProbablyPrime performs reps Miller-Rabin tests to check whether n is prime.
// probablyPrime performs reps Miller-Rabin tests to check whether n is prime.
// If it returns true, n is prime with probability 1 - 1/4^reps.
// If it returns false, n is not prime.
func probablyPrime(n []Word, reps int) bool {
@ -714,6 +715,10 @@ func probablyPrime(n []Word, reps int) bool {
}
if len(n) == 1 {
if n[0] < 2 {
return false
}
if n[0]%2 == 0 {
return n[0] == 2
}
@ -761,7 +766,7 @@ func probablyPrime(n []Word, reps int) bool {
NextRandom:
for i := 0; i < reps; i++ {
x = randomN(x, rand, nm3, nm3Len)
addNN(x, x, bigTwo)
x = addNN(x, x, bigTwo)
y = expNNN(y, x, q, n)
if cmpNN(y, bigOne) == 0 || cmpNN(y, nm1) == 0 {
continue