src/crypto/dsa/dsa.go - go - Git at Google

 // 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 dsa implements the Digital Signature Algorithm, as defined in FIPS 186-3.
 //
 // The DSA operations in this package are not implemented using constant-time algorithms.
 package dsa

 import (
 	"errors"
 	"io"
 	"math/big"

 	"crypto/internal/randutil"
 )

 // Parameters represents the domain parameters for a key. These parameters can
 // be shared across many keys. The bit length of Q must be a multiple of 8.
 type Parameters struct {
 	P, Q, G *big.Int
 }

 // PublicKey represents a DSA public key.
 type PublicKey struct {
 	Parameters
 	Y *big.Int
 }

 // PrivateKey represents a DSA private key.
 type PrivateKey struct {
 	PublicKey
 	X *big.Int
 }

 // ErrInvalidPublicKey results when a public key is not usable by this code.
 // FIPS is quite strict about the format of DSA keys, but other code may be
 // less so. Thus, when using keys which may have been generated by other code,
 // this error must be handled.
 var ErrInvalidPublicKey = errors.New("crypto/dsa: invalid public key")

 // ParameterSizes is an enumeration of the acceptable bit lengths of the primes
 // in a set of DSA parameters. See FIPS 186-3, section 4.2.
 type ParameterSizes int

 const (
 	L1024N160 ParameterSizes = iota
 	L2048N224
 	L2048N256
 	L3072N256
 )

 // numMRTests is the number of Miller-Rabin primality tests that we perform. We
 // pick the largest recommended number from table C.1 of FIPS 186-3.
 const numMRTests = 64

 // GenerateParameters puts a random, valid set of DSA parameters into params.
 // This function can take many seconds, even on fast machines.
 func GenerateParameters(params *Parameters, rand io.Reader, sizes ParameterSizes) error {
 	// This function doesn't follow FIPS 186-3 exactly in that it doesn't
 	// use a verification seed to generate the primes. The verification
 	// seed doesn't appear to be exported or used by other code and
 	// omitting it makes the code cleaner.

 	var L, N int
 	switch sizes {
 	case L1024N160:
 		L = 1024
 		N = 160
 	case L2048N224:
 		L = 2048
 		N = 224
 	case L2048N256:
 		L = 2048
 		N = 256
 	case L3072N256:
 		L = 3072
 		N = 256
 	default:
 		return errors.New("crypto/dsa: invalid ParameterSizes")
 	}

 	qBytes := make([]byte, N/8)
 	pBytes := make([]byte, L/8)

 	q := new(big.Int)
 	p := new(big.Int)
 	rem := new(big.Int)
 	one := new(big.Int)
 	one.SetInt64(1)

 GeneratePrimes:
 	for {
 		if _, err := io.ReadFull(rand, qBytes); err != nil {
 			return err
 		}

 		qBytes[len(qBytes)-1] |= 1
 		qBytes[0] |= 0x80
 		q.SetBytes(qBytes)

 		if !q.ProbablyPrime(numMRTests) {
 			continue
 		}

 		for i := 0; i < 4*L; i++ {
 			if _, err := io.ReadFull(rand, pBytes); err != nil {
 				return err
 			}

 			pBytes[len(pBytes)-1] |= 1
 			pBytes[0] |= 0x80

 			p.SetBytes(pBytes)
 			rem.Mod(p, q)
 			rem.Sub(rem, one)
 			p.Sub(p, rem)
 			if p.BitLen() < L {
 				continue
 			}

 			if !p.ProbablyPrime(numMRTests) {
 				continue
 			}

 			params.P = p
 			params.Q = q
 			break GeneratePrimes
 		}
 	}

 	h := new(big.Int)
 	h.SetInt64(2)
 	g := new(big.Int)

 	pm1 := new(big.Int).Sub(p, one)
 	e := new(big.Int).Div(pm1, q)

 	for {
 		g.Exp(h, e, p)
 		if g.Cmp(one) == 0 {
 			h.Add(h, one)
 			continue
 		}

 		params.G = g
 		return nil
 	}
 }

 // GenerateKey generates a public&private key pair. The Parameters of the
 // PrivateKey must already be valid (see GenerateParameters).
 func GenerateKey(priv *PrivateKey, rand io.Reader) error {
 	if priv.P == nil || priv.Q == nil || priv.G == nil {
 		return errors.New("crypto/dsa: parameters not set up before generating key")
 	}

 	x := new(big.Int)
 	xBytes := make([]byte, priv.Q.BitLen()/8)

 	for {
 		_, err := io.ReadFull(rand, xBytes)
 		if err != nil {
 			return err
 		}
 		x.SetBytes(xBytes)
 		if x.Sign() != 0 && x.Cmp(priv.Q) < 0 {
 			break
 		}
 	}

 	priv.X = x
 	priv.Y = new(big.Int)
 	priv.Y.Exp(priv.G, x, priv.P)
 	return nil
 }

 // 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, P *big.Int) *big.Int {
 	two := big.NewInt(2)
 	pMinus2 := new(big.Int).Sub(P, two)
 	return new(big.Int).Exp(k, pMinus2, P)
 }

 // Sign signs an arbitrary length hash (which should be the result of hashing a
 // larger message) using the private key, priv. It returns the signature as a
 // pair of integers. The security of the private key depends on the entropy of
 // rand.
 //
 // Note that FIPS 186-3 section 4.6 specifies that the hash should be truncated
 // to the byte-length of the subgroup. This function does not perform that
 // truncation itself.
 //
 // Be aware that calling Sign with an attacker-controlled PrivateKey may
 // require an arbitrary amount of CPU.
 func Sign(rand io.Reader, priv *PrivateKey, hash []byte) (r, s *big.Int, err error) {
 	randutil.MaybeReadByte(rand)

 	// FIPS 186-3, section 4.6

 	n := priv.Q.BitLen()
 	if priv.Q.Sign() <= 0 || priv.P.Sign() <= 0 || priv.G.Sign() <= 0 || priv.X.Sign() <= 0 || n%8 != 0 {
 		err = ErrInvalidPublicKey
 		return
 	}
 	n >>= 3

 	var attempts int
 	for attempts = 10; attempts > 0; attempts-- {
 		k := new(big.Int)
 		buf := make([]byte, n)
 		for {
 			_, err = io.ReadFull(rand, buf)
 			if err != nil {
 				return
 			}
 			k.SetBytes(buf)
 			// priv.Q must be >= 128 because the test above
 			// requires it to be > 0 and that
 			//    ceil(log_2(Q)) mod 8 = 0
 			// Thus this loop will quickly terminate.
 			if k.Sign() > 0 && k.Cmp(priv.Q) < 0 {
 				break
 			}
 		}

 		kInv := fermatInverse(k, priv.Q)

 		r = new(big.Int).Exp(priv.G, k, priv.P)
 		r.Mod(r, priv.Q)

 		if r.Sign() == 0 {
 			continue
 		}

 		z := k.SetBytes(hash)

 		s = new(big.Int).Mul(priv.X, r)
 		s.Add(s, z)
 		s.Mod(s, priv.Q)
 		s.Mul(s, kInv)
 		s.Mod(s, priv.Q)

 		if s.Sign() != 0 {
 			break
 		}
 	}

 	// Only degenerate private keys will require more than a handful of
 	// attempts.
 	if attempts == 0 {
 		return nil, nil, ErrInvalidPublicKey
 	}

 	return
 }

 // Verify verifies the signature in r, s of hash using the public key, pub. It
 // reports whether the signature is valid.
 //
 // Note that FIPS 186-3 section 4.6 specifies that the hash should be truncated
 // to the byte-length of the subgroup. This function does not perform that
 // truncation itself.
 func Verify(pub *PublicKey, hash []byte, r, s *big.Int) bool {
 	// FIPS 186-3, section 4.7

 	if pub.P.Sign() == 0 {
 		return false
 	}

 	if r.Sign() < 1 || r.Cmp(pub.Q) >= 0 {
 		return false
 	}
 	if s.Sign() < 1 || s.Cmp(pub.Q) >= 0 {
 		return false
 	}

 	w := new(big.Int).ModInverse(s, pub.Q)
 	if w == nil {
 		return false
 	}

 	n := pub.Q.BitLen()
 	if n%8 != 0 {
 		return false
 	}
 	z := new(big.Int).SetBytes(hash)

 	u1 := new(big.Int).Mul(z, w)
 	u1.Mod(u1, pub.Q)
 	u2 := w.Mul(r, w)
 	u2.Mod(u2, pub.Q)
 	v := u1.Exp(pub.G, u1, pub.P)
 	u2.Exp(pub.Y, u2, pub.P)
 	v.Mul(v, u2)
 	v.Mod(v, pub.P)
 	v.Mod(v, pub.Q)

 	return v.Cmp(r) == 0
 }
	// 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 dsa implements the Digital Signature Algorithm, as defined in FIPS 186-3.
	//
	// The DSA operations in this package are not implemented using constant-time algorithms.
	package dsa

	import (
	"errors"
	"io"
	"math/big"

	"crypto/internal/randutil"
	)

	// Parameters represents the domain parameters for a key. These parameters can
	// be shared across many keys. The bit length of Q must be a multiple of 8.
	type Parameters struct {
	P, Q, G *big.Int
	}

	// PublicKey represents a DSA public key.
	type PublicKey struct {
	Parameters
	Y *big.Int
	}

	// PrivateKey represents a DSA private key.
	type PrivateKey struct {
	PublicKey
	X *big.Int
	}

	// ErrInvalidPublicKey results when a public key is not usable by this code.
	// FIPS is quite strict about the format of DSA keys, but other code may be
	// less so. Thus, when using keys which may have been generated by other code,
	// this error must be handled.
	var ErrInvalidPublicKey = errors.New("crypto/dsa: invalid public key")

	// ParameterSizes is an enumeration of the acceptable bit lengths of the primes
	// in a set of DSA parameters. See FIPS 186-3, section 4.2.
	type ParameterSizes int

	const (
	L1024N160 ParameterSizes = iota
	L2048N224
	L2048N256
	L3072N256
	)

	// numMRTests is the number of Miller-Rabin primality tests that we perform. We
	// pick the largest recommended number from table C.1 of FIPS 186-3.
	const numMRTests = 64

	// GenerateParameters puts a random, valid set of DSA parameters into params.
	// This function can take many seconds, even on fast machines.
	func GenerateParameters(params *Parameters, rand io.Reader, sizes ParameterSizes) error {
	// This function doesn't follow FIPS 186-3 exactly in that it doesn't
	// use a verification seed to generate the primes. The verification
	// seed doesn't appear to be exported or used by other code and
	// omitting it makes the code cleaner.

	var L, N int
	switch sizes {
	case L1024N160:
	L = 1024
	N = 160
	case L2048N224:
	L = 2048
	N = 224
	case L2048N256:
	L = 2048
	N = 256
	case L3072N256:
	L = 3072
	N = 256
	default:
	return errors.New("crypto/dsa: invalid ParameterSizes")
	}

	qBytes := make([]byte, N/8)
	pBytes := make([]byte, L/8)

	q := new(big.Int)
	p := new(big.Int)
	rem := new(big.Int)
	one := new(big.Int)
	one.SetInt64(1)

	GeneratePrimes:
	for {
	if _, err := io.ReadFull(rand, qBytes); err != nil {
	return err
	}

	qBytes[len(qBytes)-1] \|= 1
	qBytes[0] \|= 0x80
	q.SetBytes(qBytes)

	if !q.ProbablyPrime(numMRTests) {
	continue
	}

	for i := 0; i < 4*L; i++ {
	if _, err := io.ReadFull(rand, pBytes); err != nil {
	return err
	}

	pBytes[len(pBytes)-1] \|= 1
	pBytes[0] \|= 0x80

	p.SetBytes(pBytes)
	rem.Mod(p, q)
	rem.Sub(rem, one)
	p.Sub(p, rem)
	if p.BitLen() < L {
	continue
	}

	if !p.ProbablyPrime(numMRTests) {
	continue
	}

	params.P = p
	params.Q = q
	break GeneratePrimes
	}
	}

	h := new(big.Int)
	h.SetInt64(2)
	g := new(big.Int)

	pm1 := new(big.Int).Sub(p, one)
	e := new(big.Int).Div(pm1, q)

	for {
	g.Exp(h, e, p)
	if g.Cmp(one) == 0 {
	h.Add(h, one)
	continue
	}

	params.G = g
	return nil
	}
	}

	// GenerateKey generates a public&private key pair. The Parameters of the
	// PrivateKey must already be valid (see GenerateParameters).
	func GenerateKey(priv *PrivateKey, rand io.Reader) error {
	if priv.P == nil \|\| priv.Q == nil \|\| priv.G == nil {
	return errors.New("crypto/dsa: parameters not set up before generating key")
	}

	x := new(big.Int)
	xBytes := make([]byte, priv.Q.BitLen()/8)

	for {
	_, err := io.ReadFull(rand, xBytes)
	if err != nil {
	return err
	}
	x.SetBytes(xBytes)
	if x.Sign() != 0 && x.Cmp(priv.Q) < 0 {
	break
	}
	}

	priv.X = x
	priv.Y = new(big.Int)
	priv.Y.Exp(priv.G, x, priv.P)
	return nil
	}

	// 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, P big.Int) big.Int {
	two := big.NewInt(2)
	pMinus2 := new(big.Int).Sub(P, two)
	return new(big.Int).Exp(k, pMinus2, P)
	}

	// Sign signs an arbitrary length hash (which should be the result of hashing a
	// larger message) using the private key, priv. It returns the signature as a
	// pair of integers. The security of the private key depends on the entropy of
	// rand.
	//
	// Note that FIPS 186-3 section 4.6 specifies that the hash should be truncated
	// to the byte-length of the subgroup. This function does not perform that
	// truncation itself.
	//
	// Be aware that calling Sign with an attacker-controlled PrivateKey may
	// require an arbitrary amount of CPU.
	func Sign(rand io.Reader, priv PrivateKey, hash []byte) (r, s big.Int, err error) {
	randutil.MaybeReadByte(rand)

	// FIPS 186-3, section 4.6

	n := priv.Q.BitLen()
	if priv.Q.Sign() <= 0 \|\| priv.P.Sign() <= 0 \|\| priv.G.Sign() <= 0 \|\| priv.X.Sign() <= 0 \|\| n%8 != 0 {
	err = ErrInvalidPublicKey
	return
	}
	n >>= 3

	var attempts int
	for attempts = 10; attempts > 0; attempts-- {
	k := new(big.Int)
	buf := make([]byte, n)
	for {
	_, err = io.ReadFull(rand, buf)
	if err != nil {
	return
	}
	k.SetBytes(buf)
	// priv.Q must be >= 128 because the test above
	// requires it to be > 0 and that
	// ceil(log_2(Q)) mod 8 = 0
	// Thus this loop will quickly terminate.
	if k.Sign() > 0 && k.Cmp(priv.Q) < 0 {
	break
	}
	}

	kInv := fermatInverse(k, priv.Q)

	r = new(big.Int).Exp(priv.G, k, priv.P)
	r.Mod(r, priv.Q)

	if r.Sign() == 0 {
	continue
	}

	z := k.SetBytes(hash)

	s = new(big.Int).Mul(priv.X, r)
	s.Add(s, z)
	s.Mod(s, priv.Q)
	s.Mul(s, kInv)
	s.Mod(s, priv.Q)

	if s.Sign() != 0 {
	break
	}
	}

	// Only degenerate private keys will require more than a handful of
	// attempts.
	if attempts == 0 {
	return nil, nil, ErrInvalidPublicKey
	}

	return
	}

	// Verify verifies the signature in r, s of hash using the public key, pub. It
	// reports whether the signature is valid.
	//
	// Note that FIPS 186-3 section 4.6 specifies that the hash should be truncated
	// to the byte-length of the subgroup. This function does not perform that
	// truncation itself.
	func Verify(pub PublicKey, hash []byte, r, s big.Int) bool {
	// FIPS 186-3, section 4.7

	if pub.P.Sign() == 0 {
	return false
	}

	if r.Sign() < 1 \|\| r.Cmp(pub.Q) >= 0 {
	return false
	}
	if s.Sign() < 1 \|\| s.Cmp(pub.Q) >= 0 {
	return false
	}

	w := new(big.Int).ModInverse(s, pub.Q)
	if w == nil {
	return false
	}

	n := pub.Q.BitLen()
	if n%8 != 0 {
	return false
	}
	z := new(big.Int).SetBytes(hash)

	u1 := new(big.Int).Mul(z, w)
	u1.Mod(u1, pub.Q)
	u2 := w.Mul(r, w)
	u2.Mod(u2, pub.Q)
	v := u1.Exp(pub.G, u1, pub.P)
	u2.Exp(pub.Y, u2, pub.P)
	v.Mul(v, u2)
	v.Mod(v, pub.P)
	v.Mod(v, pub.Q)

	return v.Cmp(r) == 0
	}