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Source file src/crypto/ecdsa/ecdsa.go

Documentation: crypto/ecdsa

     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  //
     8  // This implementation  derives the nonce from an AES-CTR CSPRNG keyed by
     9  // ChopMD(256, SHA2-512(priv.D || entropy || hash)). The CSPRNG key is IRO by
    10  // a result of Coron; the AES-CTR stream is IRO under standard assumptions.
    11  package ecdsa
    12  
    13  // References:
    14  //   [NSA]: Suite B implementer's guide to FIPS 186-3,
    15  //     http://www.nsa.gov/ia/_files/ecdsa.pdf
    16  //   [SECG]: SECG, SEC1
    17  //     http://www.secg.org/sec1-v2.pdf
    18  
    19  import (
    20  	"crypto"
    21  	"crypto/aes"
    22  	"crypto/cipher"
    23  	"crypto/elliptic"
    24  	"crypto/sha512"
    25  	"encoding/asn1"
    26  	"errors"
    27  	"io"
    28  	"math/big"
    29  )
    30  
    31  // A invertible implements fast inverse mod Curve.Params().N
    32  type invertible interface {
    33  	// Inverse returns the inverse of k in GF(P)
    34  	Inverse(k *big.Int) *big.Int
    35  }
    36  
    37  // combinedMult implements fast multiplication S1*g + S2*p (g - generator, p - arbitrary point)
    38  type combinedMult interface {
    39  	CombinedMult(bigX, bigY *big.Int, baseScalar, scalar []byte) (x, y *big.Int)
    40  }
    41  
    42  const (
    43  	aesIV = "IV for ECDSA CTR"
    44  )
    45  
    46  // PublicKey represents an ECDSA public key.
    47  type PublicKey struct {
    48  	elliptic.Curve
    49  	X, Y *big.Int
    50  }
    51  
    52  // PrivateKey represents an ECDSA private key.
    53  type PrivateKey struct {
    54  	PublicKey
    55  	D *big.Int
    56  }
    57  
    58  type ecdsaSignature struct {
    59  	R, S *big.Int
    60  }
    61  
    62  // Public returns the public key corresponding to priv.
    63  func (priv *PrivateKey) Public() crypto.PublicKey {
    64  	return &priv.PublicKey
    65  }
    66  
    67  // Sign signs digest with priv, reading randomness from rand. The opts argument
    68  // is not currently used but, in keeping with the crypto.Signer interface,
    69  // should be the hash function used to digest the message.
    70  //
    71  // This method implements crypto.Signer, which is an interface to support keys
    72  // where the private part is kept in, for example, a hardware module. Common
    73  // uses should use the Sign function in this package directly.
    74  func (priv *PrivateKey) Sign(rand io.Reader, digest []byte, opts crypto.SignerOpts) ([]byte, error) {
    75  	r, s, err := Sign(rand, priv, digest)
    76  	if err != nil {
    77  		return nil, err
    78  	}
    79  
    80  	return asn1.Marshal(ecdsaSignature{r, s})
    81  }
    82  
    83  var one = new(big.Int).SetInt64(1)
    84  
    85  // randFieldElement returns a random element of the field underlying the given
    86  // curve using the procedure given in [NSA] A.2.1.
    87  func randFieldElement(c elliptic.Curve, rand io.Reader) (k *big.Int, err error) {
    88  	params := c.Params()
    89  	b := make([]byte, params.BitSize/8+8)
    90  	_, err = io.ReadFull(rand, b)
    91  	if err != nil {
    92  		return
    93  	}
    94  
    95  	k = new(big.Int).SetBytes(b)
    96  	n := new(big.Int).Sub(params.N, one)
    97  	k.Mod(k, n)
    98  	k.Add(k, one)
    99  	return
   100  }
   101  
   102  // GenerateKey generates a public and private key pair.
   103  func GenerateKey(c elliptic.Curve, rand io.Reader) (*PrivateKey, error) {
   104  	k, err := randFieldElement(c, rand)
   105  	if err != nil {
   106  		return nil, err
   107  	}
   108  
   109  	priv := new(PrivateKey)
   110  	priv.PublicKey.Curve = c
   111  	priv.D = k
   112  	priv.PublicKey.X, priv.PublicKey.Y = c.ScalarBaseMult(k.Bytes())
   113  	return priv, nil
   114  }
   115  
   116  // hashToInt converts a hash value to an integer. There is some disagreement
   117  // about how this is done. [NSA] suggests that this is done in the obvious
   118  // manner, but [SECG] truncates the hash to the bit-length of the curve order
   119  // first. We follow [SECG] because that's what OpenSSL does. Additionally,
   120  // OpenSSL right shifts excess bits from the number if the hash is too large
   121  // and we mirror that too.
   122  func hashToInt(hash []byte, c elliptic.Curve) *big.Int {
   123  	orderBits := c.Params().N.BitLen()
   124  	orderBytes := (orderBits + 7) / 8
   125  	if len(hash) > orderBytes {
   126  		hash = hash[:orderBytes]
   127  	}
   128  
   129  	ret := new(big.Int).SetBytes(hash)
   130  	excess := len(hash)*8 - orderBits
   131  	if excess > 0 {
   132  		ret.Rsh(ret, uint(excess))
   133  	}
   134  	return ret
   135  }
   136  
   137  // fermatInverse calculates the inverse of k in GF(P) using Fermat's method.
   138  // This has better constant-time properties than Euclid's method (implemented
   139  // in math/big.Int.ModInverse) although math/big itself isn't strictly
   140  // constant-time so it's not perfect.
   141  func fermatInverse(k, N *big.Int) *big.Int {
   142  	two := big.NewInt(2)
   143  	nMinus2 := new(big.Int).Sub(N, two)
   144  	return new(big.Int).Exp(k, nMinus2, N)
   145  }
   146  
   147  var errZeroParam = errors.New("zero parameter")
   148  
   149  // Sign signs a hash (which should be the result of hashing a larger message)
   150  // using the private key, priv. If the hash is longer than the bit-length of the
   151  // private key's curve order, the hash will be truncated to that length.  It
   152  // returns the signature as a pair of integers. The security of the private key
   153  // depends on the entropy of rand.
   154  func Sign(rand io.Reader, priv *PrivateKey, hash []byte) (r, s *big.Int, err error) {
   155  	// Get min(log2(q) / 2, 256) bits of entropy from rand.
   156  	entropylen := (priv.Curve.Params().BitSize + 7) / 16
   157  	if entropylen > 32 {
   158  		entropylen = 32
   159  	}
   160  	entropy := make([]byte, entropylen)
   161  	_, err = io.ReadFull(rand, entropy)
   162  	if err != nil {
   163  		return
   164  	}
   165  
   166  	// Initialize an SHA-512 hash context; digest ...
   167  	md := sha512.New()
   168  	md.Write(priv.D.Bytes()) // the private key,
   169  	md.Write(entropy)        // the entropy,
   170  	md.Write(hash)           // and the input hash;
   171  	key := md.Sum(nil)[:32]  // and compute ChopMD-256(SHA-512),
   172  	// which is an indifferentiable MAC.
   173  
   174  	// Create an AES-CTR instance to use as a CSPRNG.
   175  	block, err := aes.NewCipher(key)
   176  	if err != nil {
   177  		return nil, nil, err
   178  	}
   179  
   180  	// Create a CSPRNG that xors a stream of zeros with
   181  	// the output of the AES-CTR instance.
   182  	csprng := cipher.StreamReader{
   183  		R: zeroReader,
   184  		S: cipher.NewCTR(block, []byte(aesIV)),
   185  	}
   186  
   187  	// See [NSA] 3.4.1
   188  	c := priv.PublicKey.Curve
   189  	N := c.Params().N
   190  	if N.Sign() == 0 {
   191  		return nil, nil, errZeroParam
   192  	}
   193  	var k, kInv *big.Int
   194  	for {
   195  		for {
   196  			k, err = randFieldElement(c, csprng)
   197  			if err != nil {
   198  				r = nil
   199  				return
   200  			}
   201  
   202  			if in, ok := priv.Curve.(invertible); ok {
   203  				kInv = in.Inverse(k)
   204  			} else {
   205  				kInv = fermatInverse(k, N) // N != 0
   206  			}
   207  
   208  			r, _ = priv.Curve.ScalarBaseMult(k.Bytes())
   209  			r.Mod(r, N)
   210  			if r.Sign() != 0 {
   211  				break
   212  			}
   213  		}
   214  
   215  		e := hashToInt(hash, c)
   216  		s = new(big.Int).Mul(priv.D, r)
   217  		s.Add(s, e)
   218  		s.Mul(s, kInv)
   219  		s.Mod(s, N) // N != 0
   220  		if s.Sign() != 0 {
   221  			break
   222  		}
   223  	}
   224  
   225  	return
   226  }
   227  
   228  // Verify verifies the signature in r, s of hash using the public key, pub. Its
   229  // return value records whether the signature is valid.
   230  func Verify(pub *PublicKey, hash []byte, r, s *big.Int) bool {
   231  	// See [NSA] 3.4.2
   232  	c := pub.Curve
   233  	N := c.Params().N
   234  
   235  	if r.Sign() <= 0 || s.Sign() <= 0 {
   236  		return false
   237  	}
   238  	if r.Cmp(N) >= 0 || s.Cmp(N) >= 0 {
   239  		return false
   240  	}
   241  	e := hashToInt(hash, c)
   242  
   243  	var w *big.Int
   244  	if in, ok := c.(invertible); ok {
   245  		w = in.Inverse(s)
   246  	} else {
   247  		w = new(big.Int).ModInverse(s, N)
   248  	}
   249  
   250  	u1 := e.Mul(e, w)
   251  	u1.Mod(u1, N)
   252  	u2 := w.Mul(r, w)
   253  	u2.Mod(u2, N)
   254  
   255  	// Check if implements S1*g + S2*p
   256  	var x, y *big.Int
   257  	if opt, ok := c.(combinedMult); ok {
   258  		x, y = opt.CombinedMult(pub.X, pub.Y, u1.Bytes(), u2.Bytes())
   259  	} else {
   260  		x1, y1 := c.ScalarBaseMult(u1.Bytes())
   261  		x2, y2 := c.ScalarMult(pub.X, pub.Y, u2.Bytes())
   262  		x, y = c.Add(x1, y1, x2, y2)
   263  	}
   264  
   265  	if x.Sign() == 0 && y.Sign() == 0 {
   266  		return false
   267  	}
   268  	x.Mod(x, N)
   269  	return x.Cmp(r) == 0
   270  }
   271  
   272  type zr struct {
   273  	io.Reader
   274  }
   275  
   276  // Read replaces the contents of dst with zeros.
   277  func (z *zr) Read(dst []byte) (n int, err error) {
   278  	for i := range dst {
   279  		dst[i] = 0
   280  	}
   281  	return len(dst), nil
   282  }
   283  
   284  var zeroReader = &zr{}
   285  

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