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1 | // Copyright 2011 The Go Authors. All rights reserved. |
2 | // Use of this source code is governed by a BSD-style | |
3 | // license that can be found in the LICENSE file. | |
4 | ||
5 | // Package elgamal implements ElGamal encryption, suitable for OpenPGP, | |
6 | // as specified in "A Public-Key Cryptosystem and a Signature Scheme Based on | |
7 | // Discrete Logarithms," IEEE Transactions on Information Theory, v. IT-31, | |
8 | // n. 4, 1985, pp. 469-472. | |
9 | // | |
10 | // This form of ElGamal embeds PKCS#1 v1.5 padding, which may make it | |
11 | // unsuitable for other protocols. RSA should be used in preference in any | |
12 | // case. | |
13 | package elgamal // import "golang.org/x/crypto/openpgp/elgamal" | |
14 | ||
15 | import ( | |
16 | "crypto/rand" | |
17 | "crypto/subtle" | |
18 | "errors" | |
19 | "io" | |
20 | "math/big" | |
21 | ) | |
22 | ||
23 | // PublicKey represents an ElGamal public key. | |
24 | type PublicKey struct { | |
25 | G, P, Y *big.Int | |
26 | } | |
27 | ||
28 | // PrivateKey represents an ElGamal private key. | |
29 | type PrivateKey struct { | |
30 | PublicKey | |
31 | X *big.Int | |
32 | } | |
33 | ||
34 | // Encrypt encrypts the given message to the given public key. The result is a | |
35 | // pair of integers. Errors can result from reading random, or because msg is | |
36 | // too large to be encrypted to the public key. | |
37 | func Encrypt(random io.Reader, pub *PublicKey, msg []byte) (c1, c2 *big.Int, err error) { | |
38 | pLen := (pub.P.BitLen() + 7) / 8 | |
39 | if len(msg) > pLen-11 { | |
40 | err = errors.New("elgamal: message too long") | |
41 | return | |
42 | } | |
43 | ||
44 | // EM = 0x02 || PS || 0x00 || M | |
45 | em := make([]byte, pLen-1) | |
46 | em[0] = 2 | |
47 | ps, mm := em[1:len(em)-len(msg)-1], em[len(em)-len(msg):] | |
48 | err = nonZeroRandomBytes(ps, random) | |
49 | if err != nil { | |
50 | return | |
51 | } | |
52 | em[len(em)-len(msg)-1] = 0 | |
53 | copy(mm, msg) | |
54 | ||
55 | m := new(big.Int).SetBytes(em) | |
56 | ||
57 | k, err := rand.Int(random, pub.P) | |
58 | if err != nil { | |
59 | return | |
60 | } | |
61 | ||
62 | c1 = new(big.Int).Exp(pub.G, k, pub.P) | |
63 | s := new(big.Int).Exp(pub.Y, k, pub.P) | |
64 | c2 = s.Mul(s, m) | |
65 | c2.Mod(c2, pub.P) | |
66 | ||
67 | return | |
68 | } | |
69 | ||
70 | // Decrypt takes two integers, resulting from an ElGamal encryption, and | |
71 | // returns the plaintext of the message. An error can result only if the | |
72 | // ciphertext is invalid. Users should keep in mind that this is a padding | |
73 | // oracle and thus, if exposed to an adaptive chosen ciphertext attack, can | |
74 | // be used to break the cryptosystem. See ``Chosen Ciphertext Attacks | |
75 | // Against Protocols Based on the RSA Encryption Standard PKCS #1'', Daniel | |
76 | // Bleichenbacher, Advances in Cryptology (Crypto '98), | |
77 | func Decrypt(priv *PrivateKey, c1, c2 *big.Int) (msg []byte, err error) { | |
78 | s := new(big.Int).Exp(c1, priv.X, priv.P) | |
79 | s.ModInverse(s, priv.P) | |
80 | s.Mul(s, c2) | |
81 | s.Mod(s, priv.P) | |
82 | em := s.Bytes() | |
83 | ||
84 | firstByteIsTwo := subtle.ConstantTimeByteEq(em[0], 2) | |
85 | ||
86 | // The remainder of the plaintext must be a string of non-zero random | |
87 | // octets, followed by a 0, followed by the message. | |
88 | // lookingForIndex: 1 iff we are still looking for the zero. | |
89 | // index: the offset of the first zero byte. | |
90 | var lookingForIndex, index int | |
91 | lookingForIndex = 1 | |
92 | ||
93 | for i := 1; i < len(em); i++ { | |
94 | equals0 := subtle.ConstantTimeByteEq(em[i], 0) | |
95 | index = subtle.ConstantTimeSelect(lookingForIndex&equals0, i, index) | |
96 | lookingForIndex = subtle.ConstantTimeSelect(equals0, 0, lookingForIndex) | |
97 | } | |
98 | ||
99 | if firstByteIsTwo != 1 || lookingForIndex != 0 || index < 9 { | |
100 | return nil, errors.New("elgamal: decryption error") | |
101 | } | |
102 | return em[index+1:], nil | |
103 | } | |
104 | ||
105 | // nonZeroRandomBytes fills the given slice with non-zero random octets. | |
106 | func nonZeroRandomBytes(s []byte, rand io.Reader) (err error) { | |
107 | _, err = io.ReadFull(rand, s) | |
108 | if err != nil { | |
109 | return | |
110 | } | |
111 | ||
112 | for i := 0; i < len(s); i++ { | |
113 | for s[i] == 0 { | |
114 | _, err = io.ReadFull(rand, s[i:i+1]) | |
115 | if err != nil { | |
116 | return | |
117 | } | |
118 | } | |
119 | } | |
120 | ||
121 | return | |
122 | } |