src/crypto/rand/util.go

// Copyright 2011 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

import (
	"crypto/internal/randutil"
	"errors"
	"io"
	"math/big"
)

// Prime returns a number of the given bit length that 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) (*big.Int, error) {
	if bits < 2 {
		return nil, errors.New("crypto/rand: prime size must be at least 2-bit")
	}

	randutil.MaybeReadByte(rand)

	b := uint(bits % 8)
	if b == 0 {
		b = 8
	}

	bytes := make([]byte, (bits+7)/8)
	p := new(big.Int)

	for {
		if _, err := io.ReadFull(rand, bytes); 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)
		// 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
			}
		}
		// Make the value odd since an even number this large certainly isn't prime.
		bytes[len(bytes)-1] |= 1

		p.SetBytes(bytes)
		if p.ProbablyPrime(20) {
			return p, nil
		}
	}
}

// Int returns a uniform random value in [0, max). It panics if max <= 0.
func Int(rand io.Reader, max *big.Int) (n *big.Int, err error) {
	if max.Sign() <= 0 {
		panic("crypto/rand: argument to Int is <= 0")
	}
	n = new(big.Int)
	n.Sub(max, n.SetUint64(1))
	// bitLen is the maximum bit length needed to encode a value < max.
	bitLen := n.BitLen()
	if bitLen == 0 {
		// the only valid result is 0
		return
	}
	// k is the maximum byte length needed to encode a value < max.
	k := (bitLen + 7) / 8
	// b is the number of bits in the most significant byte of max-1.
	b := uint(bitLen % 8)
	if b == 0 {
		b = 8
	}

	bytes := make([]byte, k)

	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
		}
	}
}