crypto/rand: support generation of 2-5 bit primes, also document the error return for Prime

Fixes #6849.
Fixes #6867.

R=golang-dev, agl
CC=golang-dev
https://golang.org/cl/35870043

src/pkg/crypto/rand/util.go

@@ -27,9 +27,11 @@ var smallPrimesProduct = new(big.Int).SetUint64(16294579238595022365)
 
 // Prime returns a number, p, of the given size, such that p is prime
 // with high probability.
+// Prime will return error for any error returned by rand.Read or if bits < 2.
 func Prime(rand io.Reader, bits int) (p *big.Int, err error) {
-	if bits < 1 {
-		err = errors.New("crypto/rand: prime size must be positive")
+	if bits < 2 {
+		err = errors.New("crypto/rand: prime size must be at least 2-bit")
+		return
 	}
 
 	b := uint(bits % 8)
@@ -79,7 +81,7 @@ func Prime(rand io.Reader, bits int) (p *big.Int, err error) {
 		for delta := uint64(0); delta < 1<<20; delta += 2 {
 			m := mod + delta
 			for _, prime := range smallPrimes {
-				if m%uint64(prime) == 0 {
+				if m%uint64(prime) == 0 && (bits > 6 || m != uint64(prime)) {
 					continue NextDelta
 				}
 			}

src/pkg/crypto/rand/util_test.go

+// Copyright 2013 The Go Authors.  All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package rand_test
+
+import (
+	"crypto/rand"
+	"testing"
+)
+
+// http://golang.org/issue/6849.
+func TestPrimeSmall(t *testing.T) {
+	for n := 2; n < 10; n++ {
+		p, err := rand.Prime(rand.Reader, n)
+		if err != nil {
+			t.Fatalf("Can't generate %d-bit prime: %v", n, err)
+		}
+		if p.BitLen() != n {
+			t.Fatalf("%v is not %d-bit", p, n)
+		}
+		if !p.ProbablyPrime(32) {
+			t.Fatalf("%v is not prime", p)
+		}
+	}
+}