369 lines
11 KiB
Go
369 lines
11 KiB
Go
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// Copyright 2011 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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// Package ecdsa implements the Elliptic Curve Digital Signature Algorithm, as
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// defined in FIPS 186-4 and SEC 1, Version 2.0.
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//
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// Signatures generated by this package are not deterministic, but entropy is
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// mixed with the private key and the message, achieving the same level of
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// security in case of randomness source failure.
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package ecdsa
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// [FIPS 186-4] references ANSI X9.62-2005 for the bulk of the ECDSA algorithm.
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// That standard is not freely available, which is a problem in an open source
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// implementation, because not only the implementer, but also any maintainer,
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// contributor, reviewer, auditor, and learner needs access to it. Instead, this
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// package references and follows the equivalent [SEC 1, Version 2.0].
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//
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// [FIPS 186-4]: https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf
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// [SEC 1, Version 2.0]: https://www.secg.org/sec1-v2.pdf
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import (
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"crypto"
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"crypto/aes"
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"crypto/cipher"
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"crypto/elliptic"
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"crypto/internal/randutil"
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"crypto/sha512"
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"errors"
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"io"
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"math/big"
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"golang.org/x/crypto/cryptobyte"
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"golang.org/x/crypto/cryptobyte/asn1"
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)
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// A invertible implements fast inverse in GF(N).
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type invertible interface {
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// Inverse returns the inverse of k mod Params().N.
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Inverse(k *big.Int) *big.Int
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}
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// A combinedMult implements fast combined multiplication for verification.
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type combinedMult interface {
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// CombinedMult returns [s1]G + [s2]P where G is the generator.
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CombinedMult(Px, Py *big.Int, s1, s2 []byte) (x, y *big.Int)
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}
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const (
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aesIV = "IV for ECDSA CTR"
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)
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// PublicKey represents an ECDSA public key.
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type PublicKey struct {
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elliptic.Curve
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X, Y *big.Int
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}
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// Any methods implemented on PublicKey might need to also be implemented on
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// PrivateKey, as the latter embeds the former and will expose its methods.
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// Equal reports whether pub and x have the same value.
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//
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// Two keys are only considered to have the same value if they have the same Curve value.
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// Note that for example elliptic.P256() and elliptic.P256().Params() are different
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// values, as the latter is a generic not constant time implementation.
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func (pub *PublicKey) Equal(x crypto.PublicKey) bool {
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xx, ok := x.(*PublicKey)
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if !ok {
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return false
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}
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return pub.X.Cmp(xx.X) == 0 && pub.Y.Cmp(xx.Y) == 0 &&
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// Standard library Curve implementations are singletons, so this check
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// will work for those. Other Curves might be equivalent even if not
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// singletons, but there is no definitive way to check for that, and
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// better to err on the side of safety.
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pub.Curve == xx.Curve
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}
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// PrivateKey represents an ECDSA private key.
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type PrivateKey struct {
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PublicKey
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D *big.Int
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}
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// Public returns the public key corresponding to priv.
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func (priv *PrivateKey) Public() crypto.PublicKey {
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return &priv.PublicKey
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}
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// Equal reports whether priv and x have the same value.
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//
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// See PublicKey.Equal for details on how Curve is compared.
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func (priv *PrivateKey) Equal(x crypto.PrivateKey) bool {
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xx, ok := x.(*PrivateKey)
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if !ok {
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return false
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}
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return priv.PublicKey.Equal(&xx.PublicKey) && priv.D.Cmp(xx.D) == 0
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}
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// Sign signs digest with priv, reading randomness from rand. The opts argument
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// is not currently used but, in keeping with the crypto.Signer interface,
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// should be the hash function used to digest the message.
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//
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// This method implements crypto.Signer, which is an interface to support keys
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// where the private part is kept in, for example, a hardware module. Common
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// uses can use the SignASN1 function in this package directly.
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func (priv *PrivateKey) Sign(rand io.Reader, digest []byte, opts crypto.SignerOpts) ([]byte, error) {
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r, s, err := Sign(rand, priv, digest)
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if err != nil {
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return nil, err
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}
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var b cryptobyte.Builder
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b.AddASN1(asn1.SEQUENCE, func(b *cryptobyte.Builder) {
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b.AddASN1BigInt(r)
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b.AddASN1BigInt(s)
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})
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return b.Bytes()
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}
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var one = new(big.Int).SetInt64(1)
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// randFieldElement returns a random element of the order of the given
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// curve using the procedure given in FIPS 186-4, Appendix B.5.1.
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func randFieldElement(c elliptic.Curve, rand io.Reader) (k *big.Int, err error) {
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params := c.Params()
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// Note that for P-521 this will actually be 63 bits more than the order, as
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// division rounds down, but the extra bit is inconsequential.
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b := make([]byte, params.BitSize/8+8) // TODO: use params.N.BitLen()
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_, err = io.ReadFull(rand, b)
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if err != nil {
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return
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}
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k = new(big.Int).SetBytes(b)
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n := new(big.Int).Sub(params.N, one)
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k.Mod(k, n)
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k.Add(k, one)
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return
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}
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// GenerateKey generates a public and private key pair.
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func GenerateKey(c elliptic.Curve, rand io.Reader) (*PrivateKey, error) {
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k, err := randFieldElement(c, rand)
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if err != nil {
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return nil, err
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}
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priv := new(PrivateKey)
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priv.PublicKey.Curve = c
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priv.D = k
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priv.PublicKey.X, priv.PublicKey.Y = c.ScalarBaseMult(k.Bytes())
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return priv, nil
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}
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// hashToInt converts a hash value to an integer. Per FIPS 186-4, Section 6.4,
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// we use the left-most bits of the hash to match the bit-length of the order of
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// the curve. This also performs Step 5 of SEC 1, Version 2.0, Section 4.1.3.
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func hashToInt(hash []byte, c elliptic.Curve) *big.Int {
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orderBits := c.Params().N.BitLen()
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orderBytes := (orderBits + 7) / 8
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if len(hash) > orderBytes {
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hash = hash[:orderBytes]
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}
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ret := new(big.Int).SetBytes(hash)
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excess := len(hash)*8 - orderBits
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if excess > 0 {
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ret.Rsh(ret, uint(excess))
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}
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return ret
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}
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// fermatInverse calculates the inverse of k in GF(P) using Fermat's method
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// (exponentiation modulo P - 2, per Euler's theorem). This has better
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// constant-time properties than Euclid's method (implemented in
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// math/big.Int.ModInverse and FIPS 186-4, Appendix C.1) although math/big
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// itself isn't strictly constant-time so it's not perfect.
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func fermatInverse(k, N *big.Int) *big.Int {
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two := big.NewInt(2)
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nMinus2 := new(big.Int).Sub(N, two)
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return new(big.Int).Exp(k, nMinus2, N)
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}
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var errZeroParam = errors.New("zero parameter")
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// Sign signs a hash (which should be the result of hashing a larger message)
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// using the private key, priv. If the hash is longer than the bit-length of the
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// private key's curve order, the hash will be truncated to that length. It
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// returns the signature as a pair of integers. Most applications should use
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// SignASN1 instead of dealing directly with r, s.
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func Sign(rand io.Reader, priv *PrivateKey, hash []byte) (r, s *big.Int, err error) {
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randutil.MaybeReadByte(rand)
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// This implementation derives the nonce from an AES-CTR CSPRNG keyed by:
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//
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// SHA2-512(priv.D || entropy || hash)[:32]
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//
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// The CSPRNG key is indifferentiable from a random oracle as shown in
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// [Coron], the AES-CTR stream is indifferentiable from a random oracle
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// under standard cryptographic assumptions (see [Larsson] for examples).
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//
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// [Coron]: https://cs.nyu.edu/~dodis/ps/merkle.pdf
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// [Larsson]: https://web.archive.org/web/20040719170906/https://www.nada.kth.se/kurser/kth/2D1441/semteo03/lecturenotes/assump.pdf
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// Get 256 bits of entropy from rand.
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entropy := make([]byte, 32)
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_, err = io.ReadFull(rand, entropy)
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if err != nil {
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return
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}
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// Initialize an SHA-512 hash context; digest...
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md := sha512.New()
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md.Write(priv.D.Bytes()) // the private key,
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md.Write(entropy) // the entropy,
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md.Write(hash) // and the input hash;
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key := md.Sum(nil)[:32] // and compute ChopMD-256(SHA-512),
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// which is an indifferentiable MAC.
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// Create an AES-CTR instance to use as a CSPRNG.
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block, err := aes.NewCipher(key)
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if err != nil {
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return nil, nil, err
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}
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// Create a CSPRNG that xors a stream of zeros with
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// the output of the AES-CTR instance.
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csprng := cipher.StreamReader{
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R: zeroReader,
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S: cipher.NewCTR(block, []byte(aesIV)),
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}
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c := priv.PublicKey.Curve
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return sign(priv, &csprng, c, hash)
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}
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func signGeneric(priv *PrivateKey, csprng *cipher.StreamReader, c elliptic.Curve, hash []byte) (r, s *big.Int, err error) {
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// SEC 1, Version 2.0, Section 4.1.3
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N := c.Params().N
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if N.Sign() == 0 {
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return nil, nil, errZeroParam
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}
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var k, kInv *big.Int
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for {
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for {
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k, err = randFieldElement(c, *csprng)
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if err != nil {
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r = nil
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return
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}
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if in, ok := priv.Curve.(invertible); ok {
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kInv = in.Inverse(k)
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} else {
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kInv = fermatInverse(k, N) // N != 0
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}
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r, _ = priv.Curve.ScalarBaseMult(k.Bytes())
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r.Mod(r, N)
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if r.Sign() != 0 {
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break
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}
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}
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e := hashToInt(hash, c)
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s = new(big.Int).Mul(priv.D, r)
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s.Add(s, e)
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s.Mul(s, kInv)
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s.Mod(s, N) // N != 0
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if s.Sign() != 0 {
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break
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}
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}
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return
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}
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// SignASN1 signs a hash (which should be the result of hashing a larger message)
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// using the private key, priv. If the hash is longer than the bit-length of the
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// private key's curve order, the hash will be truncated to that length. It
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// returns the ASN.1 encoded signature.
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func SignASN1(rand io.Reader, priv *PrivateKey, hash []byte) ([]byte, error) {
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return priv.Sign(rand, hash, nil)
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}
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// Verify verifies the signature in r, s of hash using the public key, pub. Its
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// return value records whether the signature is valid. Most applications should
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// use VerifyASN1 instead of dealing directly with r, s.
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func Verify(pub *PublicKey, hash []byte, r, s *big.Int) bool {
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c := pub.Curve
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N := c.Params().N
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if r.Sign() <= 0 || s.Sign() <= 0 {
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return false
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}
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if r.Cmp(N) >= 0 || s.Cmp(N) >= 0 {
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return false
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}
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return verify(pub, c, hash, r, s)
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}
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func verifyGeneric(pub *PublicKey, c elliptic.Curve, hash []byte, r, s *big.Int) bool {
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// SEC 1, Version 2.0, Section 4.1.4
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e := hashToInt(hash, c)
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var w *big.Int
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N := c.Params().N
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if in, ok := c.(invertible); ok {
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w = in.Inverse(s)
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} else {
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w = new(big.Int).ModInverse(s, N)
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}
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u1 := e.Mul(e, w)
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u1.Mod(u1, N)
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u2 := w.Mul(r, w)
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u2.Mod(u2, N)
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// Check if implements S1*g + S2*p
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var x, y *big.Int
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if opt, ok := c.(combinedMult); ok {
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x, y = opt.CombinedMult(pub.X, pub.Y, u1.Bytes(), u2.Bytes())
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} else {
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x1, y1 := c.ScalarBaseMult(u1.Bytes())
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x2, y2 := c.ScalarMult(pub.X, pub.Y, u2.Bytes())
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x, y = c.Add(x1, y1, x2, y2)
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}
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if x.Sign() == 0 && y.Sign() == 0 {
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return false
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}
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x.Mod(x, N)
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return x.Cmp(r) == 0
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}
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// VerifyASN1 verifies the ASN.1 encoded signature, sig, of hash using the
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// public key, pub. Its return value records whether the signature is valid.
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func VerifyASN1(pub *PublicKey, hash, sig []byte) bool {
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var (
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r, s = &big.Int{}, &big.Int{}
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inner cryptobyte.String
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)
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input := cryptobyte.String(sig)
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if !input.ReadASN1(&inner, asn1.SEQUENCE) ||
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!input.Empty() ||
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!inner.ReadASN1Integer(r) ||
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!inner.ReadASN1Integer(s) ||
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!inner.Empty() {
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return false
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}
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return Verify(pub, hash, r, s)
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}
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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{}
|