2017-10-07 00:16:47 +00:00
|
|
|
// Copyright 2011 The Go Authors. All rights reserved.
|
2012-03-27 23:13:14 +00:00
|
|
|
// Use of this source code is governed by a BSD-style
|
|
|
|
// license that can be found in the LICENSE file.
|
|
|
|
|
|
|
|
package rand
|
|
|
|
|
|
|
|
import (
|
|
|
|
"errors"
|
|
|
|
"io"
|
|
|
|
"math/big"
|
|
|
|
)
|
|
|
|
|
2014-09-21 17:33:12 +00:00
|
|
|
// smallPrimes is a list of small, prime numbers that allows us to rapidly
|
|
|
|
// exclude some fraction of composite candidates when searching for a random
|
|
|
|
// prime. This list is truncated at the point where smallPrimesProduct exceeds
|
|
|
|
// a uint64. It does not include two because we ensure that the candidates are
|
|
|
|
// odd by construction.
|
|
|
|
var smallPrimes = []uint8{
|
|
|
|
3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53,
|
|
|
|
}
|
|
|
|
|
|
|
|
// smallPrimesProduct is the product of the values in smallPrimes and allows us
|
|
|
|
// to reduce a candidate prime by this number and then determine whether it's
|
|
|
|
// coprime to all the elements of smallPrimes without further big.Int
|
|
|
|
// operations.
|
|
|
|
var smallPrimesProduct = new(big.Int).SetUint64(16294579238595022365)
|
|
|
|
|
2012-03-27 23:13:14 +00:00
|
|
|
// Prime returns a number, p, of the given size, such that p is prime
|
|
|
|
// with high probability.
|
2015-08-28 15:33:40 +00:00
|
|
|
// Prime will return error for any error returned by rand.Read or if bits < 2.
|
2012-03-27 23:13:14 +00:00
|
|
|
func Prime(rand io.Reader, bits int) (p *big.Int, err error) {
|
2015-08-28 15:33:40 +00:00
|
|
|
if bits < 2 {
|
|
|
|
err = errors.New("crypto/rand: prime size must be at least 2-bit")
|
|
|
|
return
|
2012-03-27 23:13:14 +00:00
|
|
|
}
|
|
|
|
|
|
|
|
b := uint(bits % 8)
|
|
|
|
if b == 0 {
|
|
|
|
b = 8
|
|
|
|
}
|
|
|
|
|
|
|
|
bytes := make([]byte, (bits+7)/8)
|
|
|
|
p = new(big.Int)
|
|
|
|
|
2014-09-21 17:33:12 +00:00
|
|
|
bigMod := new(big.Int)
|
|
|
|
|
2012-03-27 23:13:14 +00:00
|
|
|
for {
|
|
|
|
_, err = io.ReadFull(rand, bytes)
|
|
|
|
if err != nil {
|
|
|
|
return nil, err
|
|
|
|
}
|
|
|
|
|
|
|
|
// Clear bits in the first byte to make sure the candidate has a size <= bits.
|
|
|
|
bytes[0] &= uint8(int(1<<b) - 1)
|
2014-09-21 17:33:12 +00:00
|
|
|
// Don't let the value be too small, i.e, set the most significant two bits.
|
|
|
|
// Setting the top two bits, rather than just the top bit,
|
|
|
|
// means that when two of these values are multiplied together,
|
|
|
|
// the result isn't ever one bit short.
|
|
|
|
if b >= 2 {
|
|
|
|
bytes[0] |= 3 << (b - 2)
|
|
|
|
} else {
|
|
|
|
// Here b==1, because b cannot be zero.
|
|
|
|
bytes[0] |= 1
|
|
|
|
if len(bytes) > 1 {
|
|
|
|
bytes[1] |= 0x80
|
|
|
|
}
|
|
|
|
}
|
2012-03-27 23:13:14 +00:00
|
|
|
// Make the value odd since an even number this large certainly isn't prime.
|
|
|
|
bytes[len(bytes)-1] |= 1
|
|
|
|
|
|
|
|
p.SetBytes(bytes)
|
2014-09-21 17:33:12 +00:00
|
|
|
|
2017-10-07 00:16:47 +00:00
|
|
|
// Calculate the value mod the product of smallPrimes. If it's
|
2014-09-21 17:33:12 +00:00
|
|
|
// a multiple of any of these primes we add two until it isn't.
|
|
|
|
// The probability of overflowing is minimal and can be ignored
|
|
|
|
// because we still perform Miller-Rabin tests on the result.
|
|
|
|
bigMod.Mod(p, smallPrimesProduct)
|
|
|
|
mod := bigMod.Uint64()
|
|
|
|
|
|
|
|
NextDelta:
|
|
|
|
for delta := uint64(0); delta < 1<<20; delta += 2 {
|
|
|
|
m := mod + delta
|
|
|
|
for _, prime := range smallPrimes {
|
2015-08-28 15:33:40 +00:00
|
|
|
if m%uint64(prime) == 0 && (bits > 6 || m != uint64(prime)) {
|
2014-09-21 17:33:12 +00:00
|
|
|
continue NextDelta
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
if delta > 0 {
|
|
|
|
bigMod.SetUint64(delta)
|
|
|
|
p.Add(p, bigMod)
|
|
|
|
}
|
|
|
|
break
|
|
|
|
}
|
|
|
|
|
|
|
|
// There is a tiny possibility that, by adding delta, we caused
|
|
|
|
// the number to be one bit too long. Thus we check BitLen
|
|
|
|
// here.
|
|
|
|
if p.ProbablyPrime(20) && p.BitLen() == bits {
|
2012-03-27 23:13:14 +00:00
|
|
|
return
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
2014-09-21 17:33:12 +00:00
|
|
|
// Int returns a uniform random value in [0, max). It panics if max <= 0.
|
2012-03-27 23:13:14 +00:00
|
|
|
func Int(rand io.Reader, max *big.Int) (n *big.Int, err error) {
|
2014-09-21 17:33:12 +00:00
|
|
|
if max.Sign() <= 0 {
|
|
|
|
panic("crypto/rand: argument to Int is <= 0")
|
|
|
|
}
|
2012-03-27 23:13:14 +00:00
|
|
|
k := (max.BitLen() + 7) / 8
|
|
|
|
|
|
|
|
// b is the number of bits in the most significant byte of max.
|
|
|
|
b := uint(max.BitLen() % 8)
|
|
|
|
if b == 0 {
|
|
|
|
b = 8
|
|
|
|
}
|
|
|
|
|
|
|
|
bytes := make([]byte, k)
|
|
|
|
n = new(big.Int)
|
|
|
|
|
|
|
|
for {
|
|
|
|
_, err = io.ReadFull(rand, bytes)
|
|
|
|
if err != nil {
|
|
|
|
return nil, err
|
|
|
|
}
|
|
|
|
|
|
|
|
// Clear bits in the first byte to increase the probability
|
|
|
|
// that the candidate is < max.
|
|
|
|
bytes[0] &= uint8(int(1<<b) - 1)
|
|
|
|
|
|
|
|
n.SetBytes(bytes)
|
|
|
|
if n.Cmp(max) < 0 {
|
|
|
|
return
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|