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	//
     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	//     https://apps.nsa.gov/iaarchive/library/ia-guidance/ia-solutions-for-classified/algorithm-guidance/suite-b-implementers-guide-to-fips-186-3-ecdsa.cfm
    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/internal/randutil"
    25		"crypto/sha512"
    26		"encoding/asn1"
    27		"errors"
    28		"io"
    29		"math/big"
    30	)
    31	
    32	// A invertible implements fast inverse mod Curve.Params().N
    33	type invertible interface {
    34		// Inverse returns the inverse of k in GF(P)
    35		Inverse(k *big.Int) *big.Int
    36	}
    37	
    38	// combinedMult implements fast multiplication S1*g + S2*p (g - generator, p - arbitrary point)
    39	type combinedMult interface {
    40		CombinedMult(bigX, bigY *big.Int, baseScalar, scalar []byte) (x, y *big.Int)
    41	}
    42	
    43	const (
    44		aesIV = "IV for ECDSA CTR"
    45	)
    46	
    47	// PublicKey represents an ECDSA public key.
    48	type PublicKey struct {
    49		elliptic.Curve
    50		X, Y *big.Int
    51	}
    52	
    53	// PrivateKey represents an ECDSA private key.
    54	type PrivateKey struct {
    55		PublicKey
    56		D *big.Int
    57	}
    58	
    59	type ecdsaSignature struct {
    60		R, S *big.Int
    61	}
    62	
    63	// Public returns the public key corresponding to priv.
    64	func (priv *PrivateKey) Public() crypto.PublicKey {
    65		return &priv.PublicKey
    66	}
    67	
    68	// Sign signs digest with priv, reading randomness from rand. The opts argument
    69	// is not currently used but, in keeping with the crypto.Signer interface,
    70	// should be the hash function used to digest the message.
    71	//
    72	// This method implements crypto.Signer, which is an interface to support keys
    73	// where the private part is kept in, for example, a hardware module. Common
    74	// uses should use the Sign function in this package directly.
    75	func (priv *PrivateKey) Sign(rand io.Reader, digest []byte, opts crypto.SignerOpts) ([]byte, error) {
    76		r, s, err := Sign(rand, priv, digest)
    77		if err != nil {
    78			return nil, err
    79		}
    80	
    81		return asn1.Marshal(ecdsaSignature{r, s})
    82	}
    83	
    84	var one = new(big.Int).SetInt64(1)
    85	
    86	// randFieldElement returns a random element of the field underlying the given
    87	// curve using the procedure given in [NSA] A.2.1.
    88	func randFieldElement(c elliptic.Curve, rand io.Reader) (k *big.Int, err error) {
    89		params := c.Params()
    90		b := make([]byte, params.BitSize/8+8)
    91		_, err = io.ReadFull(rand, b)
    92		if err != nil {
    93			return
    94		}
    95	
    96		k = new(big.Int).SetBytes(b)
    97		n := new(big.Int).Sub(params.N, one)
    98		k.Mod(k, n)
    99		k.Add(k, one)
   100		return
   101	}
   102	
   103	// GenerateKey generates a public and private key pair.
   104	func GenerateKey(c elliptic.Curve, rand io.Reader) (*PrivateKey, error) {
   105		k, err := randFieldElement(c, rand)
   106		if err != nil {
   107			return nil, err
   108		}
   109	
   110		priv := new(PrivateKey)
   111		priv.PublicKey.Curve = c
   112		priv.D = k
   113		priv.PublicKey.X, priv.PublicKey.Y = c.ScalarBaseMult(k.Bytes())
   114		return priv, nil
   115	}
   116	
   117	// hashToInt converts a hash value to an integer. There is some disagreement
   118	// about how this is done. [NSA] suggests that this is done in the obvious
   119	// manner, but [SECG] truncates the hash to the bit-length of the curve order
   120	// first. We follow [SECG] because that's what OpenSSL does. Additionally,
   121	// OpenSSL right shifts excess bits from the number if the hash is too large
   122	// and we mirror that too.
   123	func hashToInt(hash []byte, c elliptic.Curve) *big.Int {
   124		orderBits := c.Params().N.BitLen()
   125		orderBytes := (orderBits + 7) / 8
   126		if len(hash) > orderBytes {
   127			hash = hash[:orderBytes]
   128		}
   129	
   130		ret := new(big.Int).SetBytes(hash)
   131		excess := len(hash)*8 - orderBits
   132		if excess > 0 {
   133			ret.Rsh(ret, uint(excess))
   134		}
   135		return ret
   136	}
   137	
   138	// fermatInverse calculates the inverse of k in GF(P) using Fermat's method.
   139	// This has better constant-time properties than Euclid's method (implemented
   140	// in math/big.Int.ModInverse) although math/big itself isn't strictly
   141	// constant-time so it's not perfect.
   142	func fermatInverse(k, N *big.Int) *big.Int {
   143		two := big.NewInt(2)
   144		nMinus2 := new(big.Int).Sub(N, two)
   145		return new(big.Int).Exp(k, nMinus2, N)
   146	}
   147	
   148	var errZeroParam = errors.New("zero parameter")
   149	
   150	// Sign signs a hash (which should be the result of hashing a larger message)
   151	// using the private key, priv. If the hash is longer than the bit-length of the
   152	// private key's curve order, the hash will be truncated to that length.  It
   153	// returns the signature as a pair of integers. The security of the private key
   154	// depends on the entropy of rand.
   155	func Sign(rand io.Reader, priv *PrivateKey, hash []byte) (r, s *big.Int, err error) {
   156		randutil.MaybeReadByte(rand)
   157	
   158		// Get min(log2(q) / 2, 256) bits of entropy from rand.
   159		entropylen := (priv.Curve.Params().BitSize + 7) / 16
   160		if entropylen > 32 {
   161			entropylen = 32
   162		}
   163		entropy := make([]byte, entropylen)
   164		_, err = io.ReadFull(rand, entropy)
   165		if err != nil {
   166			return
   167		}
   168	
   169		// Initialize an SHA-512 hash context; digest ...
   170		md := sha512.New()
   171		md.Write(priv.D.Bytes()) // the private key,
   172		md.Write(entropy)        // the entropy,
   173		md.Write(hash)           // and the input hash;
   174		key := md.Sum(nil)[:32]  // and compute ChopMD-256(SHA-512),
   175		// which is an indifferentiable MAC.
   176	
   177		// Create an AES-CTR instance to use as a CSPRNG.
   178		block, err := aes.NewCipher(key)
   179		if err != nil {
   180			return nil, nil, err
   181		}
   182	
   183		// Create a CSPRNG that xors a stream of zeros with
   184		// the output of the AES-CTR instance.
   185		csprng := cipher.StreamReader{
   186			R: zeroReader,
   187			S: cipher.NewCTR(block, []byte(aesIV)),
   188		}
   189	
   190		// See [NSA] 3.4.1
   191		c := priv.PublicKey.Curve
   192		N := c.Params().N
   193		if N.Sign() == 0 {
   194			return nil, nil, errZeroParam
   195		}
   196		var k, kInv *big.Int
   197		for {
   198			for {
   199				k, err = randFieldElement(c, csprng)
   200				if err != nil {
   201					r = nil
   202					return
   203				}
   204	
   205				if in, ok := priv.Curve.(invertible); ok {
   206					kInv = in.Inverse(k)
   207				} else {
   208					kInv = fermatInverse(k, N) // N != 0
   209				}
   210	
   211				r, _ = priv.Curve.ScalarBaseMult(k.Bytes())
   212				r.Mod(r, N)
   213				if r.Sign() != 0 {
   214					break
   215				}
   216			}
   217	
   218			e := hashToInt(hash, c)
   219			s = new(big.Int).Mul(priv.D, r)
   220			s.Add(s, e)
   221			s.Mul(s, kInv)
   222			s.Mod(s, N) // N != 0
   223			if s.Sign() != 0 {
   224				break
   225			}
   226		}
   227	
   228		return
   229	}
   230	
   231	// Verify verifies the signature in r, s of hash using the public key, pub. Its
   232	// return value records whether the signature is valid.
   233	func Verify(pub *PublicKey, hash []byte, r, s *big.Int) bool {
   234		// See [NSA] 3.4.2
   235		c := pub.Curve
   236		N := c.Params().N
   237	
   238		if r.Sign() <= 0 || s.Sign() <= 0 {
   239			return false
   240		}
   241		if r.Cmp(N) >= 0 || s.Cmp(N) >= 0 {
   242			return false
   243		}
   244		e := hashToInt(hash, c)
   245	
   246		var w *big.Int
   247		if in, ok := c.(invertible); ok {
   248			w = in.Inverse(s)
   249		} else {
   250			w = new(big.Int).ModInverse(s, N)
   251		}
   252	
   253		u1 := e.Mul(e, w)
   254		u1.Mod(u1, N)
   255		u2 := w.Mul(r, w)
   256		u2.Mod(u2, N)
   257	
   258		// Check if implements S1*g + S2*p
   259		var x, y *big.Int
   260		if opt, ok := c.(combinedMult); ok {
   261			x, y = opt.CombinedMult(pub.X, pub.Y, u1.Bytes(), u2.Bytes())
   262		} else {
   263			x1, y1 := c.ScalarBaseMult(u1.Bytes())
   264			x2, y2 := c.ScalarMult(pub.X, pub.Y, u2.Bytes())
   265			x, y = c.Add(x1, y1, x2, y2)
   266		}
   267	
   268		if x.Sign() == 0 && y.Sign() == 0 {
   269			return false
   270		}
   271		x.Mod(x, N)
   272		return x.Cmp(r) == 0
   273	}
   274	
   275	type zr struct {
   276		io.Reader
   277	}
   278	
   279	// Read replaces the contents of dst with zeros.
   280	func (z *zr) Read(dst []byte) (n int, err error) {
   281		for i := range dst {
   282			dst[i] = 0
   283		}
   284		return len(dst), nil
   285	}
   286	
   287	var zeroReader = &zr{}
   288	

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