text: // 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 elgamal implements ElGamal encryption, suitable for OpenPGP,
  // as specified in "A Public-Key Cryptosystem and a Signature Scheme Based on
  // Discrete Logarithms," IEEE Transactions on Information Theory, v. IT-31,
  // n. 4, 1985, pp. 469-472.
  //
  // This form of ElGamal embeds PKCS#1 v1.5 padding, which may make it
  // unsuitable for other protocols. RSA should be used in preference in any
  // case.
  package elgamal // import "golang.org/x/crypto/openpgp/elgamal"
  
  import (
  	"crypto/rand"
  	"crypto/subtle"
  	"errors"
  	"io"
  	"math/big"
  )
  
  // PublicKey represents an ElGamal public key.
  type PublicKey struct {
  	G, P, Y *big.Int
  }
  
  // PrivateKey represents an ElGamal private key.
  type PrivateKey struct {
  	PublicKey
  	X *big.Int
  }
  
  // Encrypt encrypts the given message to the given public key. The result is a
  // pair of integers. Errors can result from reading random, or because msg is
  // too large to be encrypted to the public key.
  func Encrypt(random io.Reader, pub *PublicKey, msg []byte) (c1, c2 *big.Int, err error) {
  	pLen := (pub.P.BitLen() + 7) / 8
  	if len(msg) > pLen-11 {
  		err = errors.New("elgamal: message too long")
  		return
  	}
  
  	// EM = 0x02 || PS || 0x00 || M
  	em := make([]byte, pLen-1)
  	em[0] = 2
  	ps, mm := em[1:len(em)-len(msg)-1], em[len(em)-len(msg):]
  	err = nonZeroRandomBytes(ps, random)
  	if err != nil {
  		return
  	}
  	em[len(em)-len(msg)-1] = 0
  	copy(mm, msg)
  
  	m := new(big.Int).SetBytes(em)
  
  	k, err := rand.Int(random, pub.P)
  	if err != nil {
  		return
  	}
  
  	c1 = new(big.Int).Exp(pub.G, k, pub.P)
  	s := new(big.Int).Exp(pub.Y, k, pub.P)
  	c2 = s.Mul(s, m)
  	c2.Mod(c2, pub.P)
  
  	return
  }
  
  // Decrypt takes two integers, resulting from an ElGamal encryption, and
  // returns the plaintext of the message. An error can result only if the
  // ciphertext is invalid. Users should keep in mind that this is a padding
  // oracle and thus, if exposed to an adaptive chosen ciphertext attack, can
  // be used to break the cryptosystem.  See ``Chosen Ciphertext Attacks
  // Against Protocols Based on the RSA Encryption Standard PKCS #1'', Daniel
  // Bleichenbacher, Advances in Cryptology (Crypto '98),
  func Decrypt(priv *PrivateKey, c1, c2 *big.Int) (msg []byte, err error) {
  	s := new(big.Int).Exp(c1, priv.X, priv.P)
  	s.ModInverse(s, priv.P)
  	s.Mul(s, c2)
  	s.Mod(s, priv.P)
  	em := s.Bytes()
  
  	firstByteIsTwo := subtle.ConstantTimeByteEq(em[0], 2)
  
  	// The remainder of the plaintext must be a string of non-zero random
  	// octets, followed by a 0, followed by the message.
  	//   lookingForIndex: 1 iff we are still looking for the zero.
  	//   index: the offset of the first zero byte.
  	var lookingForIndex, index int
  	lookingForIndex = 1
  
  	for i := 1; i < len(em); i++ {
  		equals0 := subtle.ConstantTimeByteEq(em[i], 0)
  		index = subtle.ConstantTimeSelect(lookingForIndex&equals0, i, index)
  		lookingForIndex = subtle.ConstantTimeSelect(equals0, 0, lookingForIndex)
  	}
  
  	if firstByteIsTwo != 1 || lookingForIndex != 0 || index < 9 {
  		return nil, errors.New("elgamal: decryption error")
  	}
  	return em[index+1:], nil
  }
  
  // nonZeroRandomBytes fills the given slice with non-zero random octets.
  func nonZeroRandomBytes(s []byte, rand io.Reader) (err error) {
  	_, err = io.ReadFull(rand, s)
  	if err != nil {
  		return
  	}
  
  	for i := 0; i < len(s); i++ {
  		for s[i] == 0 {
  			_, err = io.ReadFull(rand, s[i:i+1])
  			if err != nil {
  				return
  			}
  		}
  	}
  
  	return
  }
  