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Source file src/crypto/rsa/rsa.go

Documentation: crypto/rsa

     1  // Copyright 2009 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 rsa implements RSA encryption as specified in PKCS #1 and RFC 8017.
     6  //
     7  // RSA is a single, fundamental operation that is used in this package to
     8  // implement either public-key encryption or public-key signatures.
     9  //
    10  // The original specification for encryption and signatures with RSA is PKCS #1
    11  // and the terms "RSA encryption" and "RSA signatures" by default refer to
    12  // PKCS #1 version 1.5. However, that specification has flaws and new designs
    13  // should use version 2, usually called by just OAEP and PSS, where
    14  // possible.
    15  //
    16  // Two sets of interfaces are included in this package. When a more abstract
    17  // interface isn't necessary, there are functions for encrypting/decrypting
    18  // with v1.5/OAEP and signing/verifying with v1.5/PSS. If one needs to abstract
    19  // over the public key primitive, the PrivateKey type implements the
    20  // Decrypter and Signer interfaces from the crypto package.
    21  //
    22  // The RSA operations in this package are not implemented using constant-time algorithms.
    23  package rsa
    24  
    25  import (
    26  	"crypto"
    27  	"crypto/rand"
    28  	"crypto/subtle"
    29  	"errors"
    30  	"hash"
    31  	"io"
    32  	"math"
    33  	"math/big"
    34  
    35  	"crypto/internal/randutil"
    36  )
    37  
    38  var bigZero = big.NewInt(0)
    39  var bigOne = big.NewInt(1)
    40  
    41  // A PublicKey represents the public part of an RSA key.
    42  type PublicKey struct {
    43  	N *big.Int // modulus
    44  	E int      // public exponent
    45  }
    46  
    47  // Any methods implemented on PublicKey might need to also be implemented on
    48  // PrivateKey, as the latter embeds the former and will expose its methods.
    49  
    50  // Size returns the modulus size in bytes. Raw signatures and ciphertexts
    51  // for or by this public key will have the same size.
    52  func (pub *PublicKey) Size() int {
    53  	return (pub.N.BitLen() + 7) / 8
    54  }
    55  
    56  // Equal reports whether pub and x have the same value.
    57  func (pub *PublicKey) Equal(x crypto.PublicKey) bool {
    58  	xx, ok := x.(*PublicKey)
    59  	if !ok {
    60  		return false
    61  	}
    62  	return pub.N.Cmp(xx.N) == 0 && pub.E == xx.E
    63  }
    64  
    65  // OAEPOptions is an interface for passing options to OAEP decryption using the
    66  // crypto.Decrypter interface.
    67  type OAEPOptions struct {
    68  	// Hash is the hash function that will be used when generating the mask.
    69  	Hash crypto.Hash
    70  	// Label is an arbitrary byte string that must be equal to the value
    71  	// used when encrypting.
    72  	Label []byte
    73  }
    74  
    75  var (
    76  	errPublicModulus       = errors.New("crypto/rsa: missing public modulus")
    77  	errPublicExponentSmall = errors.New("crypto/rsa: public exponent too small")
    78  	errPublicExponentLarge = errors.New("crypto/rsa: public exponent too large")
    79  )
    80  
    81  // checkPub sanity checks the public key before we use it.
    82  // We require pub.E to fit into a 32-bit integer so that we
    83  // do not have different behavior depending on whether
    84  // int is 32 or 64 bits. See also
    85  // https://www.imperialviolet.org/2012/03/16/rsae.html.
    86  func checkPub(pub *PublicKey) error {
    87  	if pub.N == nil {
    88  		return errPublicModulus
    89  	}
    90  	if pub.E < 2 {
    91  		return errPublicExponentSmall
    92  	}
    93  	if pub.E > 1<<31-1 {
    94  		return errPublicExponentLarge
    95  	}
    96  	return nil
    97  }
    98  
    99  // A PrivateKey represents an RSA key
   100  type PrivateKey struct {
   101  	PublicKey            // public part.
   102  	D         *big.Int   // private exponent
   103  	Primes    []*big.Int // prime factors of N, has >= 2 elements.
   104  
   105  	// Precomputed contains precomputed values that speed up private
   106  	// operations, if available.
   107  	Precomputed PrecomputedValues
   108  }
   109  
   110  // Public returns the public key corresponding to priv.
   111  func (priv *PrivateKey) Public() crypto.PublicKey {
   112  	return &priv.PublicKey
   113  }
   114  
   115  // Equal reports whether priv and x have equivalent values. It ignores
   116  // Precomputed values.
   117  func (priv *PrivateKey) Equal(x crypto.PrivateKey) bool {
   118  	xx, ok := x.(*PrivateKey)
   119  	if !ok {
   120  		return false
   121  	}
   122  	if !priv.PublicKey.Equal(&xx.PublicKey) || priv.D.Cmp(xx.D) != 0 {
   123  		return false
   124  	}
   125  	if len(priv.Primes) != len(xx.Primes) {
   126  		return false
   127  	}
   128  	for i := range priv.Primes {
   129  		if priv.Primes[i].Cmp(xx.Primes[i]) != 0 {
   130  			return false
   131  		}
   132  	}
   133  	return true
   134  }
   135  
   136  // Sign signs digest with priv, reading randomness from rand. If opts is a
   137  // *PSSOptions then the PSS algorithm will be used, otherwise PKCS #1 v1.5 will
   138  // be used. digest must be the result of hashing the input message using
   139  // opts.HashFunc().
   140  //
   141  // This method implements crypto.Signer, which is an interface to support keys
   142  // where the private part is kept in, for example, a hardware module. Common
   143  // uses should use the Sign* functions in this package directly.
   144  func (priv *PrivateKey) Sign(rand io.Reader, digest []byte, opts crypto.SignerOpts) ([]byte, error) {
   145  	if pssOpts, ok := opts.(*PSSOptions); ok {
   146  		return SignPSS(rand, priv, pssOpts.Hash, digest, pssOpts)
   147  	}
   148  
   149  	return SignPKCS1v15(rand, priv, opts.HashFunc(), digest)
   150  }
   151  
   152  // Decrypt decrypts ciphertext with priv. If opts is nil or of type
   153  // *PKCS1v15DecryptOptions then PKCS #1 v1.5 decryption is performed. Otherwise
   154  // opts must have type *OAEPOptions and OAEP decryption is done.
   155  func (priv *PrivateKey) Decrypt(rand io.Reader, ciphertext []byte, opts crypto.DecrypterOpts) (plaintext []byte, err error) {
   156  	if opts == nil {
   157  		return DecryptPKCS1v15(rand, priv, ciphertext)
   158  	}
   159  
   160  	switch opts := opts.(type) {
   161  	case *OAEPOptions:
   162  		return DecryptOAEP(opts.Hash.New(), rand, priv, ciphertext, opts.Label)
   163  
   164  	case *PKCS1v15DecryptOptions:
   165  		if l := opts.SessionKeyLen; l > 0 {
   166  			plaintext = make([]byte, l)
   167  			if _, err := io.ReadFull(rand, plaintext); err != nil {
   168  				return nil, err
   169  			}
   170  			if err := DecryptPKCS1v15SessionKey(rand, priv, ciphertext, plaintext); err != nil {
   171  				return nil, err
   172  			}
   173  			return plaintext, nil
   174  		} else {
   175  			return DecryptPKCS1v15(rand, priv, ciphertext)
   176  		}
   177  
   178  	default:
   179  		return nil, errors.New("crypto/rsa: invalid options for Decrypt")
   180  	}
   181  }
   182  
   183  type PrecomputedValues struct {
   184  	Dp, Dq *big.Int // D mod (P-1) (or mod Q-1)
   185  	Qinv   *big.Int // Q^-1 mod P
   186  
   187  	// CRTValues is used for the 3rd and subsequent primes. Due to a
   188  	// historical accident, the CRT for the first two primes is handled
   189  	// differently in PKCS #1 and interoperability is sufficiently
   190  	// important that we mirror this.
   191  	CRTValues []CRTValue
   192  }
   193  
   194  // CRTValue contains the precomputed Chinese remainder theorem values.
   195  type CRTValue struct {
   196  	Exp   *big.Int // D mod (prime-1).
   197  	Coeff *big.Int // R·Coeff ≡ 1 mod Prime.
   198  	R     *big.Int // product of primes prior to this (inc p and q).
   199  }
   200  
   201  // Validate performs basic sanity checks on the key.
   202  // It returns nil if the key is valid, or else an error describing a problem.
   203  func (priv *PrivateKey) Validate() error {
   204  	if err := checkPub(&priv.PublicKey); err != nil {
   205  		return err
   206  	}
   207  
   208  	// Check that Πprimes == n.
   209  	modulus := new(big.Int).Set(bigOne)
   210  	for _, prime := range priv.Primes {
   211  		// Any primes ≤ 1 will cause divide-by-zero panics later.
   212  		if prime.Cmp(bigOne) <= 0 {
   213  			return errors.New("crypto/rsa: invalid prime value")
   214  		}
   215  		modulus.Mul(modulus, prime)
   216  	}
   217  	if modulus.Cmp(priv.N) != 0 {
   218  		return errors.New("crypto/rsa: invalid modulus")
   219  	}
   220  
   221  	// Check that de ≡ 1 mod p-1, for each prime.
   222  	// This implies that e is coprime to each p-1 as e has a multiplicative
   223  	// inverse. Therefore e is coprime to lcm(p-1,q-1,r-1,...) =
   224  	// exponent(ℤ/nℤ). It also implies that a^de ≡ a mod p as a^(p-1) ≡ 1
   225  	// mod p. Thus a^de ≡ a mod n for all a coprime to n, as required.
   226  	congruence := new(big.Int)
   227  	de := new(big.Int).SetInt64(int64(priv.E))
   228  	de.Mul(de, priv.D)
   229  	for _, prime := range priv.Primes {
   230  		pminus1 := new(big.Int).Sub(prime, bigOne)
   231  		congruence.Mod(de, pminus1)
   232  		if congruence.Cmp(bigOne) != 0 {
   233  			return errors.New("crypto/rsa: invalid exponents")
   234  		}
   235  	}
   236  	return nil
   237  }
   238  
   239  // GenerateKey generates an RSA keypair of the given bit size using the
   240  // random source random (for example, crypto/rand.Reader).
   241  func GenerateKey(random io.Reader, bits int) (*PrivateKey, error) {
   242  	return GenerateMultiPrimeKey(random, 2, bits)
   243  }
   244  
   245  // GenerateMultiPrimeKey generates a multi-prime RSA keypair of the given bit
   246  // size and the given random source, as suggested in [1]. Although the public
   247  // keys are compatible (actually, indistinguishable) from the 2-prime case,
   248  // the private keys are not. Thus it may not be possible to export multi-prime
   249  // private keys in certain formats or to subsequently import them into other
   250  // code.
   251  //
   252  // Table 1 in [2] suggests maximum numbers of primes for a given size.
   253  //
   254  // [1] US patent 4405829 (1972, expired)
   255  // [2] http://www.cacr.math.uwaterloo.ca/techreports/2006/cacr2006-16.pdf
   256  func GenerateMultiPrimeKey(random io.Reader, nprimes int, bits int) (*PrivateKey, error) {
   257  	randutil.MaybeReadByte(random)
   258  
   259  	priv := new(PrivateKey)
   260  	priv.E = 65537
   261  
   262  	if nprimes < 2 {
   263  		return nil, errors.New("crypto/rsa: GenerateMultiPrimeKey: nprimes must be >= 2")
   264  	}
   265  
   266  	if bits < 64 {
   267  		primeLimit := float64(uint64(1) << uint(bits/nprimes))
   268  		// pi approximates the number of primes less than primeLimit
   269  		pi := primeLimit / (math.Log(primeLimit) - 1)
   270  		// Generated primes start with 11 (in binary) so we can only
   271  		// use a quarter of them.
   272  		pi /= 4
   273  		// Use a factor of two to ensure that key generation terminates
   274  		// in a reasonable amount of time.
   275  		pi /= 2
   276  		if pi <= float64(nprimes) {
   277  			return nil, errors.New("crypto/rsa: too few primes of given length to generate an RSA key")
   278  		}
   279  	}
   280  
   281  	primes := make([]*big.Int, nprimes)
   282  
   283  NextSetOfPrimes:
   284  	for {
   285  		todo := bits
   286  		// crypto/rand should set the top two bits in each prime.
   287  		// Thus each prime has the form
   288  		//   p_i = 2^bitlen(p_i) × 0.11... (in base 2).
   289  		// And the product is:
   290  		//   P = 2^todo × α
   291  		// where α is the product of nprimes numbers of the form 0.11...
   292  		//
   293  		// If α < 1/2 (which can happen for nprimes > 2), we need to
   294  		// shift todo to compensate for lost bits: the mean value of 0.11...
   295  		// is 7/8, so todo + shift - nprimes * log2(7/8) ~= bits - 1/2
   296  		// will give good results.
   297  		if nprimes >= 7 {
   298  			todo += (nprimes - 2) / 5
   299  		}
   300  		for i := 0; i < nprimes; i++ {
   301  			var err error
   302  			primes[i], err = rand.Prime(random, todo/(nprimes-i))
   303  			if err != nil {
   304  				return nil, err
   305  			}
   306  			todo -= primes[i].BitLen()
   307  		}
   308  
   309  		// Make sure that primes is pairwise unequal.
   310  		for i, prime := range primes {
   311  			for j := 0; j < i; j++ {
   312  				if prime.Cmp(primes[j]) == 0 {
   313  					continue NextSetOfPrimes
   314  				}
   315  			}
   316  		}
   317  
   318  		n := new(big.Int).Set(bigOne)
   319  		totient := new(big.Int).Set(bigOne)
   320  		pminus1 := new(big.Int)
   321  		for _, prime := range primes {
   322  			n.Mul(n, prime)
   323  			pminus1.Sub(prime, bigOne)
   324  			totient.Mul(totient, pminus1)
   325  		}
   326  		if n.BitLen() != bits {
   327  			// This should never happen for nprimes == 2 because
   328  			// crypto/rand should set the top two bits in each prime.
   329  			// For nprimes > 2 we hope it does not happen often.
   330  			continue NextSetOfPrimes
   331  		}
   332  
   333  		priv.D = new(big.Int)
   334  		e := big.NewInt(int64(priv.E))
   335  		ok := priv.D.ModInverse(e, totient)
   336  
   337  		if ok != nil {
   338  			priv.Primes = primes
   339  			priv.N = n
   340  			break
   341  		}
   342  	}
   343  
   344  	priv.Precompute()
   345  	return priv, nil
   346  }
   347  
   348  // incCounter increments a four byte, big-endian counter.
   349  func incCounter(c *[4]byte) {
   350  	if c[3]++; c[3] != 0 {
   351  		return
   352  	}
   353  	if c[2]++; c[2] != 0 {
   354  		return
   355  	}
   356  	if c[1]++; c[1] != 0 {
   357  		return
   358  	}
   359  	c[0]++
   360  }
   361  
   362  // mgf1XOR XORs the bytes in out with a mask generated using the MGF1 function
   363  // specified in PKCS #1 v2.1.
   364  func mgf1XOR(out []byte, hash hash.Hash, seed []byte) {
   365  	var counter [4]byte
   366  	var digest []byte
   367  
   368  	done := 0
   369  	for done < len(out) {
   370  		hash.Write(seed)
   371  		hash.Write(counter[0:4])
   372  		digest = hash.Sum(digest[:0])
   373  		hash.Reset()
   374  
   375  		for i := 0; i < len(digest) && done < len(out); i++ {
   376  			out[done] ^= digest[i]
   377  			done++
   378  		}
   379  		incCounter(&counter)
   380  	}
   381  }
   382  
   383  // ErrMessageTooLong is returned when attempting to encrypt a message which is
   384  // too large for the size of the public key.
   385  var ErrMessageTooLong = errors.New("crypto/rsa: message too long for RSA public key size")
   386  
   387  func encrypt(c *big.Int, pub *PublicKey, m *big.Int) *big.Int {
   388  	e := big.NewInt(int64(pub.E))
   389  	c.Exp(m, e, pub.N)
   390  	return c
   391  }
   392  
   393  // EncryptOAEP encrypts the given message with RSA-OAEP.
   394  //
   395  // OAEP is parameterised by a hash function that is used as a random oracle.
   396  // Encryption and decryption of a given message must use the same hash function
   397  // and sha256.New() is a reasonable choice.
   398  //
   399  // The random parameter is used as a source of entropy to ensure that
   400  // encrypting the same message twice doesn't result in the same ciphertext.
   401  //
   402  // The label parameter may contain arbitrary data that will not be encrypted,
   403  // but which gives important context to the message. For example, if a given
   404  // public key is used to decrypt two types of messages then distinct label
   405  // values could be used to ensure that a ciphertext for one purpose cannot be
   406  // used for another by an attacker. If not required it can be empty.
   407  //
   408  // The message must be no longer than the length of the public modulus minus
   409  // twice the hash length, minus a further 2.
   410  func EncryptOAEP(hash hash.Hash, random io.Reader, pub *PublicKey, msg []byte, label []byte) ([]byte, error) {
   411  	if err := checkPub(pub); err != nil {
   412  		return nil, err
   413  	}
   414  	hash.Reset()
   415  	k := pub.Size()
   416  	if len(msg) > k-2*hash.Size()-2 {
   417  		return nil, ErrMessageTooLong
   418  	}
   419  
   420  	hash.Write(label)
   421  	lHash := hash.Sum(nil)
   422  	hash.Reset()
   423  
   424  	em := make([]byte, k)
   425  	seed := em[1 : 1+hash.Size()]
   426  	db := em[1+hash.Size():]
   427  
   428  	copy(db[0:hash.Size()], lHash)
   429  	db[len(db)-len(msg)-1] = 1
   430  	copy(db[len(db)-len(msg):], msg)
   431  
   432  	_, err := io.ReadFull(random, seed)
   433  	if err != nil {
   434  		return nil, err
   435  	}
   436  
   437  	mgf1XOR(db, hash, seed)
   438  	mgf1XOR(seed, hash, db)
   439  
   440  	m := new(big.Int)
   441  	m.SetBytes(em)
   442  	c := encrypt(new(big.Int), pub, m)
   443  
   444  	out := make([]byte, k)
   445  	return c.FillBytes(out), nil
   446  }
   447  
   448  // ErrDecryption represents a failure to decrypt a message.
   449  // It is deliberately vague to avoid adaptive attacks.
   450  var ErrDecryption = errors.New("crypto/rsa: decryption error")
   451  
   452  // ErrVerification represents a failure to verify a signature.
   453  // It is deliberately vague to avoid adaptive attacks.
   454  var ErrVerification = errors.New("crypto/rsa: verification error")
   455  
   456  // Precompute performs some calculations that speed up private key operations
   457  // in the future.
   458  func (priv *PrivateKey) Precompute() {
   459  	if priv.Precomputed.Dp != nil {
   460  		return
   461  	}
   462  
   463  	priv.Precomputed.Dp = new(big.Int).Sub(priv.Primes[0], bigOne)
   464  	priv.Precomputed.Dp.Mod(priv.D, priv.Precomputed.Dp)
   465  
   466  	priv.Precomputed.Dq = new(big.Int).Sub(priv.Primes[1], bigOne)
   467  	priv.Precomputed.Dq.Mod(priv.D, priv.Precomputed.Dq)
   468  
   469  	priv.Precomputed.Qinv = new(big.Int).ModInverse(priv.Primes[1], priv.Primes[0])
   470  
   471  	r := new(big.Int).Mul(priv.Primes[0], priv.Primes[1])
   472  	priv.Precomputed.CRTValues = make([]CRTValue, len(priv.Primes)-2)
   473  	for i := 2; i < len(priv.Primes); i++ {
   474  		prime := priv.Primes[i]
   475  		values := &priv.Precomputed.CRTValues[i-2]
   476  
   477  		values.Exp = new(big.Int).Sub(prime, bigOne)
   478  		values.Exp.Mod(priv.D, values.Exp)
   479  
   480  		values.R = new(big.Int).Set(r)
   481  		values.Coeff = new(big.Int).ModInverse(r, prime)
   482  
   483  		r.Mul(r, prime)
   484  	}
   485  }
   486  
   487  // decrypt performs an RSA decryption, resulting in a plaintext integer. If a
   488  // random source is given, RSA blinding is used.
   489  func decrypt(random io.Reader, priv *PrivateKey, c *big.Int) (m *big.Int, err error) {
   490  	// TODO(agl): can we get away with reusing blinds?
   491  	if c.Cmp(priv.N) > 0 {
   492  		err = ErrDecryption
   493  		return
   494  	}
   495  	if priv.N.Sign() == 0 {
   496  		return nil, ErrDecryption
   497  	}
   498  
   499  	var ir *big.Int
   500  	if random != nil {
   501  		randutil.MaybeReadByte(random)
   502  
   503  		// Blinding enabled. Blinding involves multiplying c by r^e.
   504  		// Then the decryption operation performs (m^e * r^e)^d mod n
   505  		// which equals mr mod n. The factor of r can then be removed
   506  		// by multiplying by the multiplicative inverse of r.
   507  
   508  		var r *big.Int
   509  		ir = new(big.Int)
   510  		for {
   511  			r, err = rand.Int(random, priv.N)
   512  			if err != nil {
   513  				return
   514  			}
   515  			if r.Cmp(bigZero) == 0 {
   516  				r = bigOne
   517  			}
   518  			ok := ir.ModInverse(r, priv.N)
   519  			if ok != nil {
   520  				break
   521  			}
   522  		}
   523  		bigE := big.NewInt(int64(priv.E))
   524  		rpowe := new(big.Int).Exp(r, bigE, priv.N) // N != 0
   525  		cCopy := new(big.Int).Set(c)
   526  		cCopy.Mul(cCopy, rpowe)
   527  		cCopy.Mod(cCopy, priv.N)
   528  		c = cCopy
   529  	}
   530  
   531  	if priv.Precomputed.Dp == nil {
   532  		m = new(big.Int).Exp(c, priv.D, priv.N)
   533  	} else {
   534  		// We have the precalculated values needed for the CRT.
   535  		m = new(big.Int).Exp(c, priv.Precomputed.Dp, priv.Primes[0])
   536  		m2 := new(big.Int).Exp(c, priv.Precomputed.Dq, priv.Primes[1])
   537  		m.Sub(m, m2)
   538  		if m.Sign() < 0 {
   539  			m.Add(m, priv.Primes[0])
   540  		}
   541  		m.Mul(m, priv.Precomputed.Qinv)
   542  		m.Mod(m, priv.Primes[0])
   543  		m.Mul(m, priv.Primes[1])
   544  		m.Add(m, m2)
   545  
   546  		for i, values := range priv.Precomputed.CRTValues {
   547  			prime := priv.Primes[2+i]
   548  			m2.Exp(c, values.Exp, prime)
   549  			m2.Sub(m2, m)
   550  			m2.Mul(m2, values.Coeff)
   551  			m2.Mod(m2, prime)
   552  			if m2.Sign() < 0 {
   553  				m2.Add(m2, prime)
   554  			}
   555  			m2.Mul(m2, values.R)
   556  			m.Add(m, m2)
   557  		}
   558  	}
   559  
   560  	if ir != nil {
   561  		// Unblind.
   562  		m.Mul(m, ir)
   563  		m.Mod(m, priv.N)
   564  	}
   565  
   566  	return
   567  }
   568  
   569  func decryptAndCheck(random io.Reader, priv *PrivateKey, c *big.Int) (m *big.Int, err error) {
   570  	m, err = decrypt(random, priv, c)
   571  	if err != nil {
   572  		return nil, err
   573  	}
   574  
   575  	// In order to defend against errors in the CRT computation, m^e is
   576  	// calculated, which should match the original ciphertext.
   577  	check := encrypt(new(big.Int), &priv.PublicKey, m)
   578  	if c.Cmp(check) != 0 {
   579  		return nil, errors.New("rsa: internal error")
   580  	}
   581  	return m, nil
   582  }
   583  
   584  // DecryptOAEP decrypts ciphertext using RSA-OAEP.
   585  //
   586  // OAEP is parameterised by a hash function that is used as a random oracle.
   587  // Encryption and decryption of a given message must use the same hash function
   588  // and sha256.New() is a reasonable choice.
   589  //
   590  // The random parameter, if not nil, is used to blind the private-key operation
   591  // and avoid timing side-channel attacks. Blinding is purely internal to this
   592  // function – the random data need not match that used when encrypting.
   593  //
   594  // The label parameter must match the value given when encrypting. See
   595  // EncryptOAEP for details.
   596  func DecryptOAEP(hash hash.Hash, random io.Reader, priv *PrivateKey, ciphertext []byte, label []byte) ([]byte, error) {
   597  	if err := checkPub(&priv.PublicKey); err != nil {
   598  		return nil, err
   599  	}
   600  	k := priv.Size()
   601  	if len(ciphertext) > k ||
   602  		k < hash.Size()*2+2 {
   603  		return nil, ErrDecryption
   604  	}
   605  
   606  	c := new(big.Int).SetBytes(ciphertext)
   607  
   608  	m, err := decrypt(random, priv, c)
   609  	if err != nil {
   610  		return nil, err
   611  	}
   612  
   613  	hash.Write(label)
   614  	lHash := hash.Sum(nil)
   615  	hash.Reset()
   616  
   617  	// We probably leak the number of leading zeros.
   618  	// It's not clear that we can do anything about this.
   619  	em := m.FillBytes(make([]byte, k))
   620  
   621  	firstByteIsZero := subtle.ConstantTimeByteEq(em[0], 0)
   622  
   623  	seed := em[1 : hash.Size()+1]
   624  	db := em[hash.Size()+1:]
   625  
   626  	mgf1XOR(seed, hash, db)
   627  	mgf1XOR(db, hash, seed)
   628  
   629  	lHash2 := db[0:hash.Size()]
   630  
   631  	// We have to validate the plaintext in constant time in order to avoid
   632  	// attacks like: J. Manger. A Chosen Ciphertext Attack on RSA Optimal
   633  	// Asymmetric Encryption Padding (OAEP) as Standardized in PKCS #1
   634  	// v2.0. In J. Kilian, editor, Advances in Cryptology.
   635  	lHash2Good := subtle.ConstantTimeCompare(lHash, lHash2)
   636  
   637  	// The remainder of the plaintext must be zero or more 0x00, followed
   638  	// by 0x01, followed by the message.
   639  	//   lookingForIndex: 1 iff we are still looking for the 0x01
   640  	//   index: the offset of the first 0x01 byte
   641  	//   invalid: 1 iff we saw a non-zero byte before the 0x01.
   642  	var lookingForIndex, index, invalid int
   643  	lookingForIndex = 1
   644  	rest := db[hash.Size():]
   645  
   646  	for i := 0; i < len(rest); i++ {
   647  		equals0 := subtle.ConstantTimeByteEq(rest[i], 0)
   648  		equals1 := subtle.ConstantTimeByteEq(rest[i], 1)
   649  		index = subtle.ConstantTimeSelect(lookingForIndex&equals1, i, index)
   650  		lookingForIndex = subtle.ConstantTimeSelect(equals1, 0, lookingForIndex)
   651  		invalid = subtle.ConstantTimeSelect(lookingForIndex&^equals0, 1, invalid)
   652  	}
   653  
   654  	if firstByteIsZero&lHash2Good&^invalid&^lookingForIndex != 1 {
   655  		return nil, ErrDecryption
   656  	}
   657  
   658  	return rest[index+1:], nil
   659  }
   660  

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