1// Copyright 2022 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
5package ecdsa
6
7import (
8	"crypto/elliptic"
9	"errors"
10	"io"
11	"math/big"
12
13	"golang.org/x/crypto/cryptobyte"
14	"golang.org/x/crypto/cryptobyte/asn1"
15)
16
17// This file contains a math/big implementation of ECDSA that is only used for
18// deprecated custom curves.
19
20func generateLegacy(c elliptic.Curve, rand io.Reader) (*PrivateKey, error) {
21	k, err := randFieldElement(c, rand)
22	if err != nil {
23		return nil, err
24	}
25
26	priv := new(PrivateKey)
27	priv.PublicKey.Curve = c
28	priv.D = k
29	priv.PublicKey.X, priv.PublicKey.Y = c.ScalarBaseMult(k.Bytes())
30	return priv, nil
31}
32
33// hashToInt converts a hash value to an integer. Per FIPS 186-4, Section 6.4,
34// we use the left-most bits of the hash to match the bit-length of the order of
35// the curve. This also performs Step 5 of SEC 1, Version 2.0, Section 4.1.3.
36func hashToInt(hash []byte, c elliptic.Curve) *big.Int {
37	orderBits := c.Params().N.BitLen()
38	orderBytes := (orderBits + 7) / 8
39	if len(hash) > orderBytes {
40		hash = hash[:orderBytes]
41	}
42
43	ret := new(big.Int).SetBytes(hash)
44	excess := len(hash)*8 - orderBits
45	if excess > 0 {
46		ret.Rsh(ret, uint(excess))
47	}
48	return ret
49}
50
51var errZeroParam = errors.New("zero parameter")
52
53// Sign signs a hash (which should be the result of hashing a larger message)
54// using the private key, priv. If the hash is longer than the bit-length of the
55// private key's curve order, the hash will be truncated to that length. It
56// returns the signature as a pair of integers. Most applications should use
57// [SignASN1] instead of dealing directly with r, s.
58func Sign(rand io.Reader, priv *PrivateKey, hash []byte) (r, s *big.Int, err error) {
59	sig, err := SignASN1(rand, priv, hash)
60	if err != nil {
61		return nil, nil, err
62	}
63
64	r, s = new(big.Int), new(big.Int)
65	var inner cryptobyte.String
66	input := cryptobyte.String(sig)
67	if !input.ReadASN1(&inner, asn1.SEQUENCE) ||
68		!input.Empty() ||
69		!inner.ReadASN1Integer(r) ||
70		!inner.ReadASN1Integer(s) ||
71		!inner.Empty() {
72		return nil, nil, errors.New("invalid ASN.1 from SignASN1")
73	}
74	return r, s, nil
75}
76
77func signLegacy(priv *PrivateKey, csprng io.Reader, hash []byte) (sig []byte, err error) {
78	c := priv.Curve
79
80	// SEC 1, Version 2.0, Section 4.1.3
81	N := c.Params().N
82	if N.Sign() == 0 {
83		return nil, errZeroParam
84	}
85	var k, kInv, r, s *big.Int
86	for {
87		for {
88			k, err = randFieldElement(c, csprng)
89			if err != nil {
90				return nil, err
91			}
92
93			kInv = new(big.Int).ModInverse(k, N)
94
95			r, _ = c.ScalarBaseMult(k.Bytes())
96			r.Mod(r, N)
97			if r.Sign() != 0 {
98				break
99			}
100		}
101
102		e := hashToInt(hash, c)
103		s = new(big.Int).Mul(priv.D, r)
104		s.Add(s, e)
105		s.Mul(s, kInv)
106		s.Mod(s, N) // N != 0
107		if s.Sign() != 0 {
108			break
109		}
110	}
111
112	return encodeSignature(r.Bytes(), s.Bytes())
113}
114
115// Verify verifies the signature in r, s of hash using the public key, pub. Its
116// return value records whether the signature is valid. Most applications should
117// use VerifyASN1 instead of dealing directly with r, s.
118//
119// The inputs are not considered confidential, and may leak through timing side
120// channels, or if an attacker has control of part of the inputs.
121func Verify(pub *PublicKey, hash []byte, r, s *big.Int) bool {
122	if r.Sign() <= 0 || s.Sign() <= 0 {
123		return false
124	}
125	sig, err := encodeSignature(r.Bytes(), s.Bytes())
126	if err != nil {
127		return false
128	}
129	return VerifyASN1(pub, hash, sig)
130}
131
132func verifyLegacy(pub *PublicKey, hash []byte, sig []byte) bool {
133	rBytes, sBytes, err := parseSignature(sig)
134	if err != nil {
135		return false
136	}
137	r, s := new(big.Int).SetBytes(rBytes), new(big.Int).SetBytes(sBytes)
138
139	c := pub.Curve
140	N := c.Params().N
141
142	if r.Sign() <= 0 || s.Sign() <= 0 {
143		return false
144	}
145	if r.Cmp(N) >= 0 || s.Cmp(N) >= 0 {
146		return false
147	}
148
149	// SEC 1, Version 2.0, Section 4.1.4
150	e := hashToInt(hash, c)
151	w := new(big.Int).ModInverse(s, N)
152
153	u1 := e.Mul(e, w)
154	u1.Mod(u1, N)
155	u2 := w.Mul(r, w)
156	u2.Mod(u2, N)
157
158	x1, y1 := c.ScalarBaseMult(u1.Bytes())
159	x2, y2 := c.ScalarMult(pub.X, pub.Y, u2.Bytes())
160	x, y := c.Add(x1, y1, x2, y2)
161
162	if x.Sign() == 0 && y.Sign() == 0 {
163		return false
164	}
165	x.Mod(x, N)
166	return x.Cmp(r) == 0
167}
168
169var one = new(big.Int).SetInt64(1)
170
171// randFieldElement returns a random element of the order of the given
172// curve using the procedure given in FIPS 186-4, Appendix B.5.2.
173func randFieldElement(c elliptic.Curve, rand io.Reader) (k *big.Int, err error) {
174	// See randomPoint for notes on the algorithm. This has to match, or s390x
175	// signatures will come out different from other architectures, which will
176	// break TLS recorded tests.
177	for {
178		N := c.Params().N
179		b := make([]byte, (N.BitLen()+7)/8)
180		if _, err = io.ReadFull(rand, b); err != nil {
181			return
182		}
183		if excess := len(b)*8 - N.BitLen(); excess > 0 {
184			b[0] >>= excess
185		}
186		k = new(big.Int).SetBytes(b)
187		if k.Sign() != 0 && k.Cmp(N) < 0 {
188			return
189		}
190	}
191}
192