Source file src/pkg/crypto/ecdsa/ecdsa.go

     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 ecdsa implements the Elliptic Curve Digital Signature Algorithm, as
     6	// defined in FIPS 186-3.
     7	package ecdsa
     8	
     9	// References:
    10	//   [NSA]: Suite B implementer's guide to FIPS 186-3,
    11	//     http://www.nsa.gov/ia/_files/ecdsa.pdf
    12	//   [SECG]: SECG, SEC1
    13	//     http://www.secg.org/download/aid-780/sec1-v2.pdf
    14	
    15	import (
    16		"crypto/elliptic"
    17		"io"
    18		"math/big"
    19	)
    20	
    21	// PublicKey represents an ECDSA public key.
    22	type PublicKey struct {
    23		elliptic.Curve
    24		X, Y *big.Int
    25	}
    26	
    27	// PrivateKey represents a ECDSA private key.
    28	type PrivateKey struct {
    29		PublicKey
    30		D *big.Int
    31	}
    32	
    33	var one = new(big.Int).SetInt64(1)
    34	
    35	// randFieldElement returns a random element of the field underlying the given
    36	// curve using the procedure given in [NSA] A.2.1.
    37	func randFieldElement(c elliptic.Curve, rand io.Reader) (k *big.Int, err error) {
    38		params := c.Params()
    39		b := make([]byte, params.BitSize/8+8)
    40		_, err = io.ReadFull(rand, b)
    41		if err != nil {
    42			return
    43		}
    44	
    45		k = new(big.Int).SetBytes(b)
    46		n := new(big.Int).Sub(params.N, one)
    47		k.Mod(k, n)
    48		k.Add(k, one)
    49		return
    50	}
    51	
    52	// GenerateKey generates a public&private key pair.
    53	func GenerateKey(c elliptic.Curve, rand io.Reader) (priv *PrivateKey, err error) {
    54		k, err := randFieldElement(c, rand)
    55		if err != nil {
    56			return
    57		}
    58	
    59		priv = new(PrivateKey)
    60		priv.PublicKey.Curve = c
    61		priv.D = k
    62		priv.PublicKey.X, priv.PublicKey.Y = c.ScalarBaseMult(k.Bytes())
    63		return
    64	}
    65	
    66	// hashToInt converts a hash value to an integer. There is some disagreement
    67	// about how this is done. [NSA] suggests that this is done in the obvious
    68	// manner, but [SECG] truncates the hash to the bit-length of the curve order
    69	// first. We follow [SECG] because that's what OpenSSL does.
    70	func hashToInt(hash []byte, c elliptic.Curve) *big.Int {
    71		orderBits := c.Params().N.BitLen()
    72		orderBytes := (orderBits + 7) / 8
    73		if len(hash) > orderBytes {
    74			hash = hash[:orderBytes]
    75		}
    76	
    77		ret := new(big.Int).SetBytes(hash)
    78		excess := orderBytes*8 - orderBits
    79		if excess > 0 {
    80			ret.Rsh(ret, uint(excess))
    81		}
    82		return ret
    83	}
    84	
    85	// Sign signs an arbitrary length hash (which should be the result of hashing a
    86	// larger message) using the private key, priv. It returns the signature as a
    87	// pair of integers. The security of the private key depends on the entropy of
    88	// rand.
    89	func Sign(rand io.Reader, priv *PrivateKey, hash []byte) (r, s *big.Int, err error) {
    90		// See [NSA] 3.4.1
    91		c := priv.PublicKey.Curve
    92		N := c.Params().N
    93	
    94		var k, kInv *big.Int
    95		for {
    96			for {
    97				k, err = randFieldElement(c, rand)
    98				if err != nil {
    99					r = nil
   100					return
   101				}
   102	
   103				kInv = new(big.Int).ModInverse(k, N)
   104				r, _ = priv.Curve.ScalarBaseMult(k.Bytes())
   105				r.Mod(r, N)
   106				if r.Sign() != 0 {
   107					break
   108				}
   109			}
   110	
   111			e := hashToInt(hash, c)
   112			s = new(big.Int).Mul(priv.D, r)
   113			s.Add(s, e)
   114			s.Mul(s, kInv)
   115			s.Mod(s, N)
   116			if s.Sign() != 0 {
   117				break
   118			}
   119		}
   120	
   121		return
   122	}
   123	
   124	// Verify verifies the signature in r, s of hash using the public key, pub. It
   125	// returns true iff the signature is valid.
   126	func Verify(pub *PublicKey, hash []byte, r, s *big.Int) bool {
   127		// See [NSA] 3.4.2
   128		c := pub.Curve
   129		N := c.Params().N
   130	
   131		if r.Sign() == 0 || s.Sign() == 0 {
   132			return false
   133		}
   134		if r.Cmp(N) >= 0 || s.Cmp(N) >= 0 {
   135			return false
   136		}
   137		e := hashToInt(hash, c)
   138		w := new(big.Int).ModInverse(s, N)
   139	
   140		u1 := e.Mul(e, w)
   141		u2 := w.Mul(r, w)
   142	
   143		x1, y1 := c.ScalarBaseMult(u1.Bytes())
   144		x2, y2 := c.ScalarMult(pub.X, pub.Y, u2.Bytes())
   145		if x1.Cmp(x2) == 0 {
   146			return false
   147		}
   148		x, _ := c.Add(x1, y1, x2, y2)
   149		x.Mod(x, N)
   150		return x.Cmp(r) == 0
   151	}