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