src/crypto/rsa/pkcs1v15.go - go - Git at Google

 // Copyright 2009 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 rsa

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

 	"crypto/internal/randutil"
 )

 // This file implements encryption and decryption using PKCS #1 v1.5 padding.

 // PKCS1v15DecrypterOpts is for passing options to PKCS #1 v1.5 decryption using
 // the crypto.Decrypter interface.
 type PKCS1v15DecryptOptions struct {
 	// SessionKeyLen is the length of the session key that is being
 	// decrypted. If not zero, then a padding error during decryption will
 	// cause a random plaintext of this length to be returned rather than
 	// an error. These alternatives happen in constant time.
 	SessionKeyLen int
 }

 // EncryptPKCS1v15 encrypts the given message with RSA and the padding
 // scheme from PKCS #1 v1.5.  The message must be no longer than the
 // length of the public modulus minus 11 bytes.
 //
 // The rand parameter is used as a source of entropy to ensure that
 // encrypting the same message twice doesn't result in the same
 // ciphertext.
 //
 // WARNING: use of this function to encrypt plaintexts other than
 // session keys is dangerous. Use RSA OAEP in new protocols.
 func EncryptPKCS1v15(rand io.Reader, pub *PublicKey, msg []byte) ([]byte, error) {
 	randutil.MaybeReadByte(rand)

 	if err := checkPub(pub); err != nil {
 		return nil, err
 	}
 	k := pub.Size()
 	if len(msg) > k-11 {
 		return nil, ErrMessageTooLong
 	}

 	// EM = 0x00 || 0x02 || PS || 0x00 || M
 	em := make([]byte, k)
 	em[1] = 2
 	ps, mm := em[2:len(em)-len(msg)-1], em[len(em)-len(msg):]
 	err := nonZeroRandomBytes(ps, rand)
 	if err != nil {
 		return nil, err
 	}
 	em[len(em)-len(msg)-1] = 0
 	copy(mm, msg)

 	m := new(big.Int).SetBytes(em)
 	c := encrypt(new(big.Int), pub, m)

 	return c.FillBytes(em), nil
 }

 // DecryptPKCS1v15 decrypts a plaintext using RSA and the padding scheme from PKCS #1 v1.5.
 // If rand != nil, it uses RSA blinding to avoid timing side-channel attacks.
 //
 // Note that whether this function returns an error or not discloses secret
 // information. If an attacker can cause this function to run repeatedly and
 // learn whether each instance returned an error then they can decrypt and
 // forge signatures as if they had the private key. See
 // DecryptPKCS1v15SessionKey for a way of solving this problem.
 func DecryptPKCS1v15(rand io.Reader, priv *PrivateKey, ciphertext []byte) ([]byte, error) {
 	if err := checkPub(&priv.PublicKey); err != nil {
 		return nil, err
 	}
 	valid, out, index, err := decryptPKCS1v15(rand, priv, ciphertext)
 	if err != nil {
 		return nil, err
 	}
 	if valid == 0 {
 		return nil, ErrDecryption
 	}
 	return out[index:], nil
 }

 // DecryptPKCS1v15SessionKey decrypts a session key using RSA and the padding scheme from PKCS #1 v1.5.
 // If rand != nil, it uses RSA blinding to avoid timing side-channel attacks.
 // It returns an error if the ciphertext is the wrong length or if the
 // ciphertext is greater than the public modulus. Otherwise, no error is
 // returned. If the padding is valid, the resulting plaintext message is copied
 // into key. Otherwise, key is unchanged. These alternatives occur in constant
 // time. It is intended that the user of this function generate a random
 // session key beforehand and continue the protocol with the resulting value.
 // This will remove any possibility that an attacker can learn any information
 // about the plaintext.
 // See “Chosen Ciphertext Attacks Against Protocols Based on the RSA
 // Encryption Standard PKCS #1”, Daniel Bleichenbacher, Advances in Cryptology
 // (Crypto '98).
 //
 // Note that if the session key is too small then it may be possible for an
 // attacker to brute-force it. If they can do that then they can learn whether
 // a random value was used (because it'll be different for the same ciphertext)
 // and thus whether the padding was correct. This defeats the point of this
 // function. Using at least a 16-byte key will protect against this attack.
 func DecryptPKCS1v15SessionKey(rand io.Reader, priv *PrivateKey, ciphertext []byte, key []byte) error {
 	if err := checkPub(&priv.PublicKey); err != nil {
 		return err
 	}
 	k := priv.Size()
 	if k-(len(key)+3+8) < 0 {
 		return ErrDecryption
 	}

 	valid, em, index, err := decryptPKCS1v15(rand, priv, ciphertext)
 	if err != nil {
 		return err
 	}

 	if len(em) != k {
 		// This should be impossible because decryptPKCS1v15 always
 		// returns the full slice.
 		return ErrDecryption
 	}

 	valid &= subtle.ConstantTimeEq(int32(len(em)-index), int32(len(key)))
 	subtle.ConstantTimeCopy(valid, key, em[len(em)-len(key):])
 	return nil
 }

 // decryptPKCS1v15 decrypts ciphertext using priv and blinds the operation if
 // rand is not nil. It returns one or zero in valid that indicates whether the
 // plaintext was correctly structured. In either case, the plaintext is
 // returned in em so that it may be read independently of whether it was valid
 // in order to maintain constant memory access patterns. If the plaintext was
 // valid then index contains the index of the original message in em.
 func decryptPKCS1v15(rand io.Reader, priv *PrivateKey, ciphertext []byte) (valid int, em []byte, index int, err error) {
 	k := priv.Size()
 	if k < 11 {
 		err = ErrDecryption
 		return
 	}

 	c := new(big.Int).SetBytes(ciphertext)
 	m, err := decrypt(rand, priv, c)
 	if err != nil {
 		return
 	}

 	em = m.FillBytes(make([]byte, k))
 	firstByteIsZero := subtle.ConstantTimeByteEq(em[0], 0)
 	secondByteIsTwo := subtle.ConstantTimeByteEq(em[1], 2)

 	// The remainder of the plaintext must be a string of non-zero random
 	// octets, followed by a 0, followed by the message.
 	//   lookingForIndex: 1 iff we are still looking for the zero.
 	//   index: the offset of the first zero byte.
 	lookingForIndex := 1

 	for i := 2; i < len(em); i++ {
 		equals0 := subtle.ConstantTimeByteEq(em[i], 0)
 		index = subtle.ConstantTimeSelect(lookingForIndex&equals0, i, index)
 		lookingForIndex = subtle.ConstantTimeSelect(equals0, 0, lookingForIndex)
 	}

 	// The PS padding must be at least 8 bytes long, and it starts two
 	// bytes into em.
 	validPS := subtle.ConstantTimeLessOrEq(2+8, index)

 	valid = firstByteIsZero & secondByteIsTwo & (^lookingForIndex & 1) & validPS
 	index = subtle.ConstantTimeSelect(valid, index+1, 0)
 	return valid, em, index, nil
 }

 // nonZeroRandomBytes fills the given slice with non-zero random octets.
 func nonZeroRandomBytes(s []byte, rand io.Reader) (err error) {
 	_, err = io.ReadFull(rand, s)
 	if err != nil {
 		return
 	}

 	for i := 0; i < len(s); i++ {
 		for s[i] == 0 {
 			_, err = io.ReadFull(rand, s[i:i+1])
 			if err != nil {
 				return
 			}
 			// In tests, the PRNG may return all zeros so we do
 			// this to break the loop.
 			s[i] ^= 0x42
 		}
 	}

 	return
 }

 // These are ASN1 DER structures:
 //
 //	DigestInfo ::= SEQUENCE {
 //	  digestAlgorithm AlgorithmIdentifier,
 //	  digest OCTET STRING
 //	}
 //
 // For performance, we don't use the generic ASN1 encoder. Rather, we
 // precompute a prefix of the digest value that makes a valid ASN1 DER string
 // with the correct contents.
 var hashPrefixes = map[crypto.Hash][]byte{
 	crypto.MD5:       {0x30, 0x20, 0x30, 0x0c, 0x06, 0x08, 0x2a, 0x86, 0x48, 0x86, 0xf7, 0x0d, 0x02, 0x05, 0x05, 0x00, 0x04, 0x10},
 	crypto.SHA1:      {0x30, 0x21, 0x30, 0x09, 0x06, 0x05, 0x2b, 0x0e, 0x03, 0x02, 0x1a, 0x05, 0x00, 0x04, 0x14},
 	crypto.SHA224:    {0x30, 0x2d, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x04, 0x05, 0x00, 0x04, 0x1c},
 	crypto.SHA256:    {0x30, 0x31, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x01, 0x05, 0x00, 0x04, 0x20},
 	crypto.SHA384:    {0x30, 0x41, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x02, 0x05, 0x00, 0x04, 0x30},
 	crypto.SHA512:    {0x30, 0x51, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x03, 0x05, 0x00, 0x04, 0x40},
 	crypto.MD5SHA1:   {}, // A special TLS case which doesn't use an ASN1 prefix.
 	crypto.RIPEMD160: {0x30, 0x20, 0x30, 0x08, 0x06, 0x06, 0x28, 0xcf, 0x06, 0x03, 0x00, 0x31, 0x04, 0x14},
 }

 // SignPKCS1v15 calculates the signature of hashed using
 // RSASSA-PKCS1-V1_5-SIGN from RSA PKCS #1 v1.5.  Note that hashed must
 // be the result of hashing the input message using the given hash
 // function. If hash is zero, hashed is signed directly. This isn't
 // advisable except for interoperability.
 //
 // If rand is not nil then RSA blinding will be used to avoid timing
 // side-channel attacks.
 //
 // This function is deterministic. Thus, if the set of possible
 // messages is small, an attacker may be able to build a map from
 // messages to signatures and identify the signed messages. As ever,
 // signatures provide authenticity, not confidentiality.
 func SignPKCS1v15(rand io.Reader, priv *PrivateKey, hash crypto.Hash, hashed []byte) ([]byte, error) {
 	hashLen, prefix, err := pkcs1v15HashInfo(hash, len(hashed))
 	if err != nil {
 		return nil, err
 	}

 	tLen := len(prefix) + hashLen
 	k := priv.Size()
 	if k < tLen+11 {
 		return nil, ErrMessageTooLong
 	}

 	// EM = 0x00 || 0x01 || PS || 0x00 || T
 	em := make([]byte, k)
 	em[1] = 1
 	for i := 2; i < k-tLen-1; i++ {
 		em[i] = 0xff
 	}
 	copy(em[k-tLen:k-hashLen], prefix)
 	copy(em[k-hashLen:k], hashed)

 	m := new(big.Int).SetBytes(em)
 	c, err := decryptAndCheck(rand, priv, m)
 	if err != nil {
 		return nil, err
 	}

 	return c.FillBytes(em), nil
 }

 // VerifyPKCS1v15 verifies an RSA PKCS #1 v1.5 signature.
 // hashed is the result of hashing the input message using the given hash
 // function and sig is the signature. A valid signature is indicated by
 // returning a nil error. If hash is zero then hashed is used directly. This
 // isn't advisable except for interoperability.
 func VerifyPKCS1v15(pub *PublicKey, hash crypto.Hash, hashed []byte, sig []byte) error {
 	hashLen, prefix, err := pkcs1v15HashInfo(hash, len(hashed))
 	if err != nil {
 		return err
 	}

 	tLen := len(prefix) + hashLen
 	k := pub.Size()
 	if k < tLen+11 {
 		return ErrVerification
 	}

 	// RFC 8017 Section 8.2.2: If the length of the signature S is not k
 	// octets (where k is the length in octets of the RSA modulus n), output
 	// "invalid signature" and stop.
 	if k != len(sig) {
 		return ErrVerification
 	}

 	c := new(big.Int).SetBytes(sig)
 	m := encrypt(new(big.Int), pub, c)
 	em := m.FillBytes(make([]byte, k))
 	// EM = 0x00 || 0x01 || PS || 0x00 || T

 	ok := subtle.ConstantTimeByteEq(em[0], 0)
 	ok &= subtle.ConstantTimeByteEq(em[1], 1)
 	ok &= subtle.ConstantTimeCompare(em[k-hashLen:k], hashed)
 	ok &= subtle.ConstantTimeCompare(em[k-tLen:k-hashLen], prefix)
 	ok &= subtle.ConstantTimeByteEq(em[k-tLen-1], 0)

 	for i := 2; i < k-tLen-1; i++ {
 		ok &= subtle.ConstantTimeByteEq(em[i], 0xff)
 	}

 	if ok != 1 {
 		return ErrVerification
 	}

 	return nil
 }

 func pkcs1v15HashInfo(hash crypto.Hash, inLen int) (hashLen int, prefix []byte, err error) {
 	// Special case: crypto.Hash(0) is used to indicate that the data is
 	// signed directly.
 	if hash == 0 {
 		return inLen, nil, nil
 	}

 	hashLen = hash.Size()
 	if inLen != hashLen {
 		return 0, nil, errors.New("crypto/rsa: input must be hashed message")
 	}
 	prefix, ok := hashPrefixes[hash]
 	if !ok {
 		return 0, nil, errors.New("crypto/rsa: unsupported hash function")
 	}
 	return
 }
	// Copyright 2009 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 rsa

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

	"crypto/internal/randutil"
	)

	// This file implements encryption and decryption using PKCS #1 v1.5 padding.

	// PKCS1v15DecrypterOpts is for passing options to PKCS #1 v1.5 decryption using
	// the crypto.Decrypter interface.
	type PKCS1v15DecryptOptions struct {
	// SessionKeyLen is the length of the session key that is being
	// decrypted. If not zero, then a padding error during decryption will
	// cause a random plaintext of this length to be returned rather than
	// an error. These alternatives happen in constant time.
	SessionKeyLen int
	}

	// EncryptPKCS1v15 encrypts the given message with RSA and the padding
	// scheme from PKCS #1 v1.5. The message must be no longer than the
	// length of the public modulus minus 11 bytes.
	//
	// The rand parameter is used as a source of entropy to ensure that
	// encrypting the same message twice doesn't result in the same
	// ciphertext.
	//
	// WARNING: use of this function to encrypt plaintexts other than
	// session keys is dangerous. Use RSA OAEP in new protocols.
	func EncryptPKCS1v15(rand io.Reader, pub *PublicKey, msg []byte) ([]byte, error) {
	randutil.MaybeReadByte(rand)

	if err := checkPub(pub); err != nil {
	return nil, err
	}
	k := pub.Size()
	if len(msg) > k-11 {
	return nil, ErrMessageTooLong
	}

	// EM = 0x00 \|\| 0x02 \|\| PS \|\| 0x00 \|\| M
	em := make([]byte, k)
	em[1] = 2
	ps, mm := em[2:len(em)-len(msg)-1], em[len(em)-len(msg):]
	err := nonZeroRandomBytes(ps, rand)
	if err != nil {
	return nil, err
	}
	em[len(em)-len(msg)-1] = 0
	copy(mm, msg)

	m := new(big.Int).SetBytes(em)
	c := encrypt(new(big.Int), pub, m)

	return c.FillBytes(em), nil
	}

	// DecryptPKCS1v15 decrypts a plaintext using RSA and the padding scheme from PKCS #1 v1.5.
	// If rand != nil, it uses RSA blinding to avoid timing side-channel attacks.
	//
	// Note that whether this function returns an error or not discloses secret
	// information. If an attacker can cause this function to run repeatedly and
	// learn whether each instance returned an error then they can decrypt and
	// forge signatures as if they had the private key. See
	// DecryptPKCS1v15SessionKey for a way of solving this problem.
	func DecryptPKCS1v15(rand io.Reader, priv *PrivateKey, ciphertext []byte) ([]byte, error) {
	if err := checkPub(&priv.PublicKey); err != nil {
	return nil, err
	}
	valid, out, index, err := decryptPKCS1v15(rand, priv, ciphertext)
	if err != nil {
	return nil, err
	}
	if valid == 0 {
	return nil, ErrDecryption
	}
	return out[index:], nil
	}

	// DecryptPKCS1v15SessionKey decrypts a session key using RSA and the padding scheme from PKCS #1 v1.5.
	// If rand != nil, it uses RSA blinding to avoid timing side-channel attacks.
	// It returns an error if the ciphertext is the wrong length or if the
	// ciphertext is greater than the public modulus. Otherwise, no error is
	// returned. If the padding is valid, the resulting plaintext message is copied
	// into key. Otherwise, key is unchanged. These alternatives occur in constant
	// time. It is intended that the user of this function generate a random
	// session key beforehand and continue the protocol with the resulting value.
	// This will remove any possibility that an attacker can learn any information
	// about the plaintext.
	// See “Chosen Ciphertext Attacks Against Protocols Based on the RSA
	// Encryption Standard PKCS #1”, Daniel Bleichenbacher, Advances in Cryptology
	// (Crypto '98).
	//
	// Note that if the session key is too small then it may be possible for an
	// attacker to brute-force it. If they can do that then they can learn whether
	// a random value was used (because it'll be different for the same ciphertext)
	// and thus whether the padding was correct. This defeats the point of this
	// function. Using at least a 16-byte key will protect against this attack.
	func DecryptPKCS1v15SessionKey(rand io.Reader, priv *PrivateKey, ciphertext []byte, key []byte) error {
	if err := checkPub(&priv.PublicKey); err != nil {
	return err
	}
	k := priv.Size()
	if k-(len(key)+3+8) < 0 {
	return ErrDecryption
	}

	valid, em, index, err := decryptPKCS1v15(rand, priv, ciphertext)
	if err != nil {
	return err
	}

	if len(em) != k {
	// This should be impossible because decryptPKCS1v15 always
	// returns the full slice.
	return ErrDecryption
	}

	valid &= subtle.ConstantTimeEq(int32(len(em)-index), int32(len(key)))
	subtle.ConstantTimeCopy(valid, key, em[len(em)-len(key):])
	return nil
	}

	// decryptPKCS1v15 decrypts ciphertext using priv and blinds the operation if
	// rand is not nil. It returns one or zero in valid that indicates whether the
	// plaintext was correctly structured. In either case, the plaintext is
	// returned in em so that it may be read independently of whether it was valid
	// in order to maintain constant memory access patterns. If the plaintext was
	// valid then index contains the index of the original message in em.
	func decryptPKCS1v15(rand io.Reader, priv *PrivateKey, ciphertext []byte) (valid int, em []byte, index int, err error) {
	k := priv.Size()
	if k < 11 {
	err = ErrDecryption
	return
	}

	c := new(big.Int).SetBytes(ciphertext)
	m, err := decrypt(rand, priv, c)
	if err != nil {
	return
	}

	em = m.FillBytes(make([]byte, k))
	firstByteIsZero := subtle.ConstantTimeByteEq(em[0], 0)
	secondByteIsTwo := subtle.ConstantTimeByteEq(em[1], 2)

	// The remainder of the plaintext must be a string of non-zero random
	// octets, followed by a 0, followed by the message.
	// lookingForIndex: 1 iff we are still looking for the zero.
	// index: the offset of the first zero byte.
	lookingForIndex := 1

	for i := 2; i < len(em); i++ {
	equals0 := subtle.ConstantTimeByteEq(em[i], 0)
	index = subtle.ConstantTimeSelect(lookingForIndex&equals0, i, index)
	lookingForIndex = subtle.ConstantTimeSelect(equals0, 0, lookingForIndex)
	}

	// The PS padding must be at least 8 bytes long, and it starts two
	// bytes into em.
	validPS := subtle.ConstantTimeLessOrEq(2+8, index)

	valid = firstByteIsZero & secondByteIsTwo & (^lookingForIndex & 1) & validPS
	index = subtle.ConstantTimeSelect(valid, index+1, 0)
	return valid, em, index, nil
	}

	// nonZeroRandomBytes fills the given slice with non-zero random octets.
	func nonZeroRandomBytes(s []byte, rand io.Reader) (err error) {
	_, err = io.ReadFull(rand, s)
	if err != nil {
	return
	}

	for i := 0; i < len(s); i++ {
	for s[i] == 0 {
	_, err = io.ReadFull(rand, s[i:i+1])
	if err != nil {
	return
	}
	// In tests, the PRNG may return all zeros so we do
	// this to break the loop.
	s[i] ^= 0x42
	}
	}

	return
	}

	// These are ASN1 DER structures:
	//
	// DigestInfo ::= SEQUENCE {
	// digestAlgorithm AlgorithmIdentifier,
	// digest OCTET STRING
	// }
	//
	// For performance, we don't use the generic ASN1 encoder. Rather, we
	// precompute a prefix of the digest value that makes a valid ASN1 DER string
	// with the correct contents.
	var hashPrefixes = map[crypto.Hash][]byte{
	crypto.MD5: {0x30, 0x20, 0x30, 0x0c, 0x06, 0x08, 0x2a, 0x86, 0x48, 0x86, 0xf7, 0x0d, 0x02, 0x05, 0x05, 0x00, 0x04, 0x10},
	crypto.SHA1: {0x30, 0x21, 0x30, 0x09, 0x06, 0x05, 0x2b, 0x0e, 0x03, 0x02, 0x1a, 0x05, 0x00, 0x04, 0x14},
	crypto.SHA224: {0x30, 0x2d, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x04, 0x05, 0x00, 0x04, 0x1c},
	crypto.SHA256: {0x30, 0x31, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x01, 0x05, 0x00, 0x04, 0x20},
	crypto.SHA384: {0x30, 0x41, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x02, 0x05, 0x00, 0x04, 0x30},
	crypto.SHA512: {0x30, 0x51, 0x30, 0x0d, 0x06, 0x09, 0x60, 0x86, 0x48, 0x01, 0x65, 0x03, 0x04, 0x02, 0x03, 0x05, 0x00, 0x04, 0x40},
	crypto.MD5SHA1: {}, // A special TLS case which doesn't use an ASN1 prefix.
	crypto.RIPEMD160: {0x30, 0x20, 0x30, 0x08, 0x06, 0x06, 0x28, 0xcf, 0x06, 0x03, 0x00, 0x31, 0x04, 0x14},
	}

	// SignPKCS1v15 calculates the signature of hashed using
	// RSASSA-PKCS1-V1_5-SIGN from RSA PKCS #1 v1.5. Note that hashed must
	// be the result of hashing the input message using the given hash
	// function. If hash is zero, hashed is signed directly. This isn't
	// advisable except for interoperability.
	//
	// If rand is not nil then RSA blinding will be used to avoid timing
	// side-channel attacks.
	//
	// This function is deterministic. Thus, if the set of possible
	// messages is small, an attacker may be able to build a map from
	// messages to signatures and identify the signed messages. As ever,
	// signatures provide authenticity, not confidentiality.
	func SignPKCS1v15(rand io.Reader, priv *PrivateKey, hash crypto.Hash, hashed []byte) ([]byte, error) {
	hashLen, prefix, err := pkcs1v15HashInfo(hash, len(hashed))
	if err != nil {
	return nil, err
	}

	tLen := len(prefix) + hashLen
	k := priv.Size()
	if k < tLen+11 {
	return nil, ErrMessageTooLong
	}

	// EM = 0x00 \|\| 0x01 \|\| PS \|\| 0x00 \|\| T
	em := make([]byte, k)
	em[1] = 1
	for i := 2; i < k-tLen-1; i++ {
	em[i] = 0xff
	}
	copy(em[k-tLen:k-hashLen], prefix)
	copy(em[k-hashLen:k], hashed)

	m := new(big.Int).SetBytes(em)
	c, err := decryptAndCheck(rand, priv, m)
	if err != nil {
	return nil, err
	}

	return c.FillBytes(em), nil
	}

	// VerifyPKCS1v15 verifies an RSA PKCS #1 v1.5 signature.
	// hashed is the result of hashing the input message using the given hash
	// function and sig is the signature. A valid signature is indicated by
	// returning a nil error. If hash is zero then hashed is used directly. This
	// isn't advisable except for interoperability.
	func VerifyPKCS1v15(pub *PublicKey, hash crypto.Hash, hashed []byte, sig []byte) error {
	hashLen, prefix, err := pkcs1v15HashInfo(hash, len(hashed))
	if err != nil {
	return err
	}

	tLen := len(prefix) + hashLen
	k := pub.Size()
	if k < tLen+11 {
	return ErrVerification
	}

	// RFC 8017 Section 8.2.2: If the length of the signature S is not k
	// octets (where k is the length in octets of the RSA modulus n), output
	// "invalid signature" and stop.
	if k != len(sig) {
	return ErrVerification
	}

	c := new(big.Int).SetBytes(sig)
	m := encrypt(new(big.Int), pub, c)
	em := m.FillBytes(make([]byte, k))
	// EM = 0x00 \|\| 0x01 \|\| PS \|\| 0x00 \|\| T

	ok := subtle.ConstantTimeByteEq(em[0], 0)
	ok &= subtle.ConstantTimeByteEq(em[1], 1)
	ok &= subtle.ConstantTimeCompare(em[k-hashLen:k], hashed)
	ok &= subtle.ConstantTimeCompare(em[k-tLen:k-hashLen], prefix)
	ok &= subtle.ConstantTimeByteEq(em[k-tLen-1], 0)

	for i := 2; i < k-tLen-1; i++ {
	ok &= subtle.ConstantTimeByteEq(em[i], 0xff)
	}

	if ok != 1 {
	return ErrVerification
	}

	return nil
	}

	func pkcs1v15HashInfo(hash crypto.Hash, inLen int) (hashLen int, prefix []byte, err error) {
	// Special case: crypto.Hash(0) is used to indicate that the data is
	// signed directly.
	if hash == 0 {
	return inLen, nil, nil
	}

	hashLen = hash.Size()
	if inLen != hashLen {
	return 0, nil, errors.New("crypto/rsa: input must be hashed message")
	}
	prefix, ok := hashPrefixes[hash]
	if !ok {
	return 0, nil, errors.New("crypto/rsa: unsupported hash function")
	}
	return
	}