ecdsa.go

Documentation: crypto/ecdsa

  // 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 ecdsa implements the Elliptic Curve Digital Signature Algorithm, as
  // defined in FIPS 186-3.
  //
  // This implementation  derives the nonce from an AES-CTR CSPRNG keyed by
  // ChopMD(256, SHA2-512(priv.D || entropy || hash)). The CSPRNG key is IRO by
  // a result of Coron; the AES-CTR stream is IRO under standard assumptions.
  package ecdsa
  
  // References:
  //   [NSA]: Suite B implementer's guide to FIPS 186-3,
  //     http://www.nsa.gov/ia/_files/ecdsa.pdf
  //   [SECG]: SECG, SEC1
  //     http://www.secg.org/sec1-v2.pdf
  
  import (
  	"crypto"
  	"crypto/aes"
  	"crypto/cipher"
  	"crypto/elliptic"
  	"crypto/sha512"
  	"encoding/asn1"
  	"errors"
  	"io"
  	"math/big"
  )
  
  // A invertible implements fast inverse mod Curve.Params().N
  type invertible interface {
  	// Inverse returns the inverse of k in GF(P)
  	Inverse(k *big.Int) *big.Int
  }
  
  // combinedMult implements fast multiplication S1*g + S2*p (g - generator, p - arbitrary point)
  type combinedMult interface {
  	CombinedMult(bigX, bigY *big.Int, baseScalar, scalar []byte) (x, y *big.Int)
  }
  
  const (
  	aesIV = "IV for ECDSA CTR"
  )
  
  // PublicKey represents an ECDSA public key.
  type PublicKey struct {
  	elliptic.Curve
  	X, Y *big.Int
  }
  
  // PrivateKey represents an ECDSA private key.
  type PrivateKey struct {
  	PublicKey
  	D *big.Int
  }
  
  type ecdsaSignature struct {
  	R, S *big.Int
  }
  
  // Public returns the public key corresponding to priv.
  func (priv *PrivateKey) Public() crypto.PublicKey {
  	return &priv.PublicKey
  }
  
  // Sign signs digest with priv, reading randomness from rand. The opts argument
  // is not currently used but, in keeping with the crypto.Signer interface,
  // should be the hash function used to digest the message.
  //
  // This method implements crypto.Signer, which is an interface to support keys
  // where the private part is kept in, for example, a hardware module. Common
  // uses should use the Sign function in this package directly.
  func (priv *PrivateKey) Sign(rand io.Reader, digest []byte, opts crypto.SignerOpts) ([]byte, error) {
  	r, s, err := Sign(rand, priv, digest)
  	if err != nil {
  		return nil, err
  	}
  
  	return asn1.Marshal(ecdsaSignature{r, s})
  }
  
  var one = new(big.Int).SetInt64(1)
  
  // randFieldElement returns a random element of the field underlying the given
  // curve using the procedure given in [NSA] A.2.1.
  func randFieldElement(c elliptic.Curve, rand io.Reader) (k *big.Int, err error) {
  	params := c.Params()
  	b := make([]byte, params.BitSize/8+8)
  	_, err = io.ReadFull(rand, b)
  	if err != nil {
  		return
  	}
  
  	k = new(big.Int).SetBytes(b)
  	n := new(big.Int).Sub(params.N, one)
  	k.Mod(k, n)
  	k.Add(k, one)
  	return
  }
  
  // GenerateKey generates a public and private key pair.
  func GenerateKey(c elliptic.Curve, rand io.Reader) (*PrivateKey, error) {
  	k, err := randFieldElement(c, rand)
  	if err != nil {
  		return nil, err
  	}
  
  	priv := new(PrivateKey)
  	priv.PublicKey.Curve = c
  	priv.D = k
  	priv.PublicKey.X, priv.PublicKey.Y = c.ScalarBaseMult(k.Bytes())
  	return priv, nil
  }
  
  // hashToInt converts a hash value to an integer. There is some disagreement
  // about how this is done. [NSA] suggests that this is done in the obvious
  // manner, but [SECG] truncates the hash to the bit-length of the curve order
  // first. We follow [SECG] because that's what OpenSSL does. Additionally,
  // OpenSSL right shifts excess bits from the number if the hash is too large
  // and we mirror that too.
  func hashToInt(hash []byte, c elliptic.Curve) *big.Int {
  	orderBits := c.Params().N.BitLen()
  	orderBytes := (orderBits + 7) / 8
  	if len(hash) > orderBytes {
  		hash = hash[:orderBytes]
  	}
  
  	ret := new(big.Int).SetBytes(hash)
  	excess := len(hash)*8 - orderBits
  	if excess > 0 {
  		ret.Rsh(ret, uint(excess))
  	}
  	return ret
  }
  
  // fermatInverse calculates the inverse of k in GF(P) using Fermat's method.
  // This has better constant-time properties than Euclid's method (implemented
  // in math/big.Int.ModInverse) although math/big itself isn't strictly
  // constant-time so it's not perfect.
  func fermatInverse(k, N *big.Int) *big.Int {
  	two := big.NewInt(2)
  	nMinus2 := new(big.Int).Sub(N, two)
  	return new(big.Int).Exp(k, nMinus2, N)
  }
  
  var errZeroParam = errors.New("zero parameter")
  
  // Sign signs a hash (which should be the result of hashing a larger message)
  // using the private key, priv. If the hash is longer than the bit-length of the
  // private key's curve order, the hash will be truncated to that length.  It
  // returns the signature as a pair of integers. The security of the private key
  // depends on the entropy of rand.
  func Sign(rand io.Reader, priv *PrivateKey, hash []byte) (r, s *big.Int, err error) {
  	// Get min(log2(q) / 2, 256) bits of entropy from rand.
  	entropylen := (priv.Curve.Params().BitSize + 7) / 16
  	if entropylen > 32 {
  		entropylen = 32
  	}
  	entropy := make([]byte, entropylen)
  	_, err = io.ReadFull(rand, entropy)
  	if err != nil {
  		return
  	}
  
  	// Initialize an SHA-512 hash context; digest ...
  	md := sha512.New()
  	md.Write(priv.D.Bytes()) // the private key,
  	md.Write(entropy)        // the entropy,
  	md.Write(hash)           // and the input hash;
  	key := md.Sum(nil)[:32]  // and compute ChopMD-256(SHA-512),
  	// which is an indifferentiable MAC.
  
  	// Create an AES-CTR instance to use as a CSPRNG.
  	block, err := aes.NewCipher(key)
  	if err != nil {
  		return nil, nil, err
  	}
  
  	// Create a CSPRNG that xors a stream of zeros with
  	// the output of the AES-CTR instance.
  	csprng := cipher.StreamReader{
  		R: zeroReader,
  		S: cipher.NewCTR(block, []byte(aesIV)),
  	}
  
  	// See [NSA] 3.4.1
  	c := priv.PublicKey.Curve
  	N := c.Params().N
  	if N.Sign() == 0 {
  		return nil, nil, errZeroParam
  	}
  	var k, kInv *big.Int
  	for {
  		for {
  			k, err = randFieldElement(c, csprng)
  			if err != nil {
  				r = nil
  				return
  			}
  
  			if in, ok := priv.Curve.(invertible); ok {
  				kInv = in.Inverse(k)
  			} else {
  				kInv = fermatInverse(k, N) // N != 0
  			}
  
  			r, _ = priv.Curve.ScalarBaseMult(k.Bytes())
  			r.Mod(r, N)
  			if r.Sign() != 0 {
  				break
  			}
  		}
  
  		e := hashToInt(hash, c)
  		s = new(big.Int).Mul(priv.D, r)
  		s.Add(s, e)
  		s.Mul(s, kInv)
  		s.Mod(s, N) // N != 0
  		if s.Sign() != 0 {
  			break
  		}
  	}
  
  	return
  }
  
  // Verify verifies the signature in r, s of hash using the public key, pub. Its
  // return value records whether the signature is valid.
  func Verify(pub *PublicKey, hash []byte, r, s *big.Int) bool {
  	// See [NSA] 3.4.2
  	c := pub.Curve
  	N := c.Params().N
  
  	if r.Sign() <= 0 || s.Sign() <= 0 {
  		return false
  	}
  	if r.Cmp(N) >= 0 || s.Cmp(N) >= 0 {
  		return false
  	}
  	e := hashToInt(hash, c)
  
  	var w *big.Int
  	if in, ok := c.(invertible); ok {
  		w = in.Inverse(s)
  	} else {
  		w = new(big.Int).ModInverse(s, N)
  	}
  
  	u1 := e.Mul(e, w)
  	u1.Mod(u1, N)
  	u2 := w.Mul(r, w)
  	u2.Mod(u2, N)
  
  	// Check if implements S1*g + S2*p
  	var x, y *big.Int
  	if opt, ok := c.(combinedMult); ok {
  		x, y = opt.CombinedMult(pub.X, pub.Y, u1.Bytes(), u2.Bytes())
  	} else {
  		x1, y1 := c.ScalarBaseMult(u1.Bytes())
  		x2, y2 := c.ScalarMult(pub.X, pub.Y, u2.Bytes())
  		x, y = c.Add(x1, y1, x2, y2)
  	}
  
  	if x.Sign() == 0 && y.Sign() == 0 {
  		return false
  	}
  	x.Mod(x, N)
  	return x.Cmp(r) == 0
  }
  
  type zr struct {
  	io.Reader
  }
  
  // Read replaces the contents of dst with zeros.
  func (z *zr) Read(dst []byte) (n int, err error) {
  	for i := range dst {
  		dst[i] = 0
  	}
  	return len(dst), nil
  }
  
  var zeroReader = &zr{}
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