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+// 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:
+//
+// SHA2-512(priv.D || entropy || hash)[:32]
+//
+// The CSPRNG key is indifferentiable from a random oracle as shown in
+// [Coron], the AES-CTR stream is indifferentiable from a random oracle
+// under standard cryptographic assumptions (see [Larsson] for examples).
+//
+// References:
+// [Coron]
+// https://cs.nyu.edu/~dodis/ps/merkle.pdf
+// [Larsson]
+// https://web.archive.org/web/20040719170906/https://www.nada.kth.se/kurser/kth/2D1441/semteo03/lecturenotes/assump.pdf
+package ecdsa
+
+// Further references:
+// [NSA]: Suite B implementer's guide to FIPS 186-3
+// https://apps.nsa.gov/iaarchive/library/ia-guidance/ia-solutions-for-classified/algorithm-guidance/suite-b-implementers-guide-to-fips-186-3-ecdsa.cfm
+// [SECG]: SECG, SEC1
+// http://www.secg.org/sec1-v2.pdf
+
+import (
+ "crypto"
+ "crypto/aes"
+ "crypto/cipher"
+ "crypto/elliptic"
+ "crypto/internal/randutil"
+ "crypto/sha512"
+ "errors"
+ "io"
+ "math/big"
+
+ "golang.org/x/crypto/cryptobyte"
+ "golang.org/x/crypto/cryptobyte/asn1"
+)
+
+// 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
+}
+
+// Any methods implemented on PublicKey might need to also be implemented on
+// PrivateKey, as the latter embeds the former and will expose its methods.
+
+// Equal reports whether pub and x have the same value.
+//
+// Two keys are only considered to have the same value if they have the same Curve value.
+// Note that for example elliptic.P256() and elliptic.P256().Params() are different
+// values, as the latter is a generic not constant time implementation.
+func (pub *PublicKey) Equal(x crypto.PublicKey) bool {
+ xx, ok := x.(*PublicKey)
+ if !ok {
+ return false
+ }
+ return pub.X.Cmp(xx.X) == 0 && pub.Y.Cmp(xx.Y) == 0 &&
+ // Standard library Curve implementations are singletons, so this check
+ // will work for those. Other Curves might be equivalent even if not
+ // singletons, but there is no definitive way to check for that, and
+ // better to err on the side of safety.
+ pub.Curve == xx.Curve
+}
+
+// PrivateKey represents an ECDSA private key.
+type PrivateKey struct {
+ PublicKey
+ D *big.Int
+}
+
+// Public returns the public key corresponding to priv.
+func (priv *PrivateKey) Public() crypto.PublicKey {
+ return &priv.PublicKey
+}
+
+// Equal reports whether priv and x have the same value.
+//
+// See PublicKey.Equal for details on how Curve is compared.
+func (priv *PrivateKey) Equal(x crypto.PrivateKey) bool {
+ xx, ok := x.(*PrivateKey)
+ if !ok {
+ return false
+ }
+ return priv.PublicKey.Equal(&xx.PublicKey) && priv.D.Cmp(xx.D) == 0
+}
+
+// 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
+ }
+
+ var b cryptobyte.Builder
+ b.AddASN1(asn1.SEQUENCE, func(b *cryptobyte.Builder) {
+ b.AddASN1BigInt(r)
+ b.AddASN1BigInt(s)
+ })
+ return b.Bytes()
+}
+
+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) {
+ randutil.MaybeReadByte(rand)
+
+ // 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
+ return sign(priv, &csprng, c, hash)
+}
+
+func signGeneric(priv *PrivateKey, csprng *cipher.StreamReader, c elliptic.Curve, hash []byte) (r, s *big.Int, err error) {
+ 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
+}
+
+// SignASN1 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 ASN.1 encoded signature. The security of the private key
+// depends on the entropy of rand.
+func SignASN1(rand io.Reader, priv *PrivateKey, hash []byte) ([]byte, error) {
+ return priv.Sign(rand, hash, nil)
+}
+
+// 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
+ }
+ return verify(pub, c, hash, r, s)
+}
+
+func verifyGeneric(pub *PublicKey, c elliptic.Curve, hash []byte, r, s *big.Int) bool {
+ e := hashToInt(hash, c)
+ var w *big.Int
+ N := c.Params().N
+ 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
+}
+
+// VerifyASN1 verifies the ASN.1 encoded signature, sig, of hash using the
+// public key, pub. Its return value records whether the signature is valid.
+func VerifyASN1(pub *PublicKey, hash, sig []byte) bool {
+ var (
+ r, s = &big.Int{}, &big.Int{}
+ inner cryptobyte.String
+ )
+ input := cryptobyte.String(sig)
+ if !input.ReadASN1(&inner, asn1.SEQUENCE) ||
+ !input.Empty() ||
+ !inner.ReadASN1Integer(r) ||
+ !inner.ReadASN1Integer(s) ||
+ !inner.Empty() {
+ return false
+ }
+ return Verify(pub, hash, r, s)
+}
+
+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{}