rsa.go

     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  // Operations involving private keys are implemented using constant-time
    23  // algorithms, except for [GenerateKey], [PrivateKey.Precompute], and
    24  // [PrivateKey.Validate].
    25  package rsa
    26  
    27  import (
    28  	"crypto"
    29  	"crypto/internal/bigmod"
    30  	"crypto/internal/boring"
    31  	"crypto/internal/boring/bbig"
    32  	"crypto/internal/randutil"
    33  	"crypto/rand"
    34  	"crypto/subtle"
    35  	"errors"
    36  	"hash"
    37  	"io"
    38  	"math"
    39  	"math/big"
    40  )
    41  
    42  var bigOne = big.NewInt(1)
    43  
    44  // A PublicKey represents the public part of an RSA key.
    45  //
    46  // The value of the modulus N is considered secret by this library and protected
    47  // from leaking through timing side-channels. However, neither the value of the
    48  // exponent E nor the precise bit size of N are similarly protected.
    49  type PublicKey struct {
    50  	N *big.Int // modulus
    51  	E int      // public exponent
    52  }
    53  
    54  // Any methods implemented on PublicKey might need to also be implemented on
    55  // PrivateKey, as the latter embeds the former and will expose its methods.
    56  
    57  // Size returns the modulus size in bytes. Raw signatures and ciphertexts
    58  // for or by this public key will have the same size.
    59  func (pub *PublicKey) Size() int {
    60  	return (pub.N.BitLen() + 7) / 8
    61  }
    62  
    63  // Equal reports whether pub and x have the same value.
    64  func (pub *PublicKey) Equal(x crypto.PublicKey) bool {
    65  	xx, ok := x.(*PublicKey)
    66  	if !ok {
    67  		return false
    68  	}
    69  	return bigIntEqual(pub.N, xx.N) && pub.E == xx.E
    70  }
    71  
    72  // OAEPOptions is an interface for passing options to OAEP decryption using the
    73  // crypto.Decrypter interface.
    74  type OAEPOptions struct {
    75  	// Hash is the hash function that will be used when generating the mask.
    76  	Hash crypto.Hash
    77  
    78  	// MGFHash is the hash function used for MGF1.
    79  	// If zero, Hash is used instead.
    80  	MGFHash crypto.Hash
    81  
    82  	// Label is an arbitrary byte string that must be equal to the value
    83  	// used when encrypting.
    84  	Label []byte
    85  }
    86  
    87  var (
    88  	errPublicModulus       = errors.New("crypto/rsa: missing public modulus")
    89  	errPublicExponentSmall = errors.New("crypto/rsa: public exponent too small")
    90  	errPublicExponentLarge = errors.New("crypto/rsa: public exponent too large")
    91  )
    92  
    93  // checkPub sanity checks the public key before we use it.
    94  // We require pub.E to fit into a 32-bit integer so that we
    95  // do not have different behavior depending on whether
    96  // int is 32 or 64 bits. See also
    97  // https://www.imperialviolet.org/2012/03/16/rsae.html.
    98  func checkPub(pub *PublicKey) error {
    99  	if pub.N == nil {
   100  		return errPublicModulus
   101  	}
   102  	if pub.E < 2 {
   103  		return errPublicExponentSmall
   104  	}
   105  	if pub.E > 1<<31-1 {
   106  		return errPublicExponentLarge
   107  	}
   108  	return nil
   109  }
   110  
   111  // A PrivateKey represents an RSA key
   112  type PrivateKey struct {
   113  	PublicKey            // public part.
   114  	D         *big.Int   // private exponent
   115  	Primes    []*big.Int // prime factors of N, has >= 2 elements.
   116  
   117  	// Precomputed contains precomputed values that speed up RSA operations,
   118  	// if available. It must be generated by calling PrivateKey.Precompute and
   119  	// must not be modified.
   120  	Precomputed PrecomputedValues
   121  }
   122  
   123  // Public returns the public key corresponding to priv.
   124  func (priv *PrivateKey) Public() crypto.PublicKey {
   125  	return &priv.PublicKey
   126  }
   127  
   128  // Equal reports whether priv and x have equivalent values. It ignores
   129  // Precomputed values.
   130  func (priv *PrivateKey) Equal(x crypto.PrivateKey) bool {
   131  	xx, ok := x.(*PrivateKey)
   132  	if !ok {
   133  		return false
   134  	}
   135  	if !priv.PublicKey.Equal(&xx.PublicKey) || !bigIntEqual(priv.D, xx.D) {
   136  		return false
   137  	}
   138  	if len(priv.Primes) != len(xx.Primes) {
   139  		return false
   140  	}
   141  	for i := range priv.Primes {
   142  		if !bigIntEqual(priv.Primes[i], xx.Primes[i]) {
   143  			return false
   144  		}
   145  	}
   146  	return true
   147  }
   148  
   149  // bigIntEqual reports whether a and b are equal leaking only their bit length
   150  // through timing side-channels.
   151  func bigIntEqual(a, b *big.Int) bool {
   152  	return subtle.ConstantTimeCompare(a.Bytes(), b.Bytes()) == 1
   153  }
   154  
   155  // Sign signs digest with priv, reading randomness from rand. If opts is a
   156  // *[PSSOptions] then the PSS algorithm will be used, otherwise PKCS #1 v1.5 will
   157  // be used. digest must be the result of hashing the input message using
   158  // opts.HashFunc().
   159  //
   160  // This method implements [crypto.Signer], which is an interface to support keys
   161  // where the private part is kept in, for example, a hardware module. Common
   162  // uses should use the Sign* functions in this package directly.
   163  func (priv *PrivateKey) Sign(rand io.Reader, digest []byte, opts crypto.SignerOpts) ([]byte, error) {
   164  	if pssOpts, ok := opts.(*PSSOptions); ok {
   165  		return SignPSS(rand, priv, pssOpts.Hash, digest, pssOpts)
   166  	}
   167  
   168  	return SignPKCS1v15(rand, priv, opts.HashFunc(), digest)
   169  }
   170  
   171  // Decrypt decrypts ciphertext with priv. If opts is nil or of type
   172  // *[PKCS1v15DecryptOptions] then PKCS #1 v1.5 decryption is performed. Otherwise
   173  // opts must have type *[OAEPOptions] and OAEP decryption is done.
   174  func (priv *PrivateKey) Decrypt(rand io.Reader, ciphertext []byte, opts crypto.DecrypterOpts) (plaintext []byte, err error) {
   175  	if opts == nil {
   176  		return DecryptPKCS1v15(rand, priv, ciphertext)
   177  	}
   178  
   179  	switch opts := opts.(type) {
   180  	case *OAEPOptions:
   181  		if opts.MGFHash == 0 {
   182  			return decryptOAEP(opts.Hash.New(), opts.Hash.New(), rand, priv, ciphertext, opts.Label)
   183  		} else {
   184  			return decryptOAEP(opts.Hash.New(), opts.MGFHash.New(), rand, priv, ciphertext, opts.Label)
   185  		}
   186  
   187  	case *PKCS1v15DecryptOptions:
   188  		if l := opts.SessionKeyLen; l > 0 {
   189  			plaintext = make([]byte, l)
   190  			if _, err := io.ReadFull(rand, plaintext); err != nil {
   191  				return nil, err
   192  			}
   193  			if err := DecryptPKCS1v15SessionKey(rand, priv, ciphertext, plaintext); err != nil {
   194  				return nil, err
   195  			}
   196  			return plaintext, nil
   197  		} else {
   198  			return DecryptPKCS1v15(rand, priv, ciphertext)
   199  		}
   200  
   201  	default:
   202  		return nil, errors.New("crypto/rsa: invalid options for Decrypt")
   203  	}
   204  }
   205  
   206  type PrecomputedValues struct {
   207  	Dp, Dq *big.Int // D mod (P-1) (or mod Q-1)
   208  	Qinv   *big.Int // Q^-1 mod P
   209  
   210  	// CRTValues is used for the 3rd and subsequent primes. Due to a
   211  	// historical accident, the CRT for the first two primes is handled
   212  	// differently in PKCS #1 and interoperability is sufficiently
   213  	// important that we mirror this.
   214  	//
   215  	// Deprecated: These values are still filled in by Precompute for
   216  	// backwards compatibility but are not used. Multi-prime RSA is very rare,
   217  	// and is implemented by this package without CRT optimizations to limit
   218  	// complexity.
   219  	CRTValues []CRTValue
   220  
   221  	n, p, q *bigmod.Modulus // moduli for CRT with Montgomery precomputed constants
   222  }
   223  
   224  // CRTValue contains the precomputed Chinese remainder theorem values.
   225  type CRTValue struct {
   226  	Exp   *big.Int // D mod (prime-1).
   227  	Coeff *big.Int // R·Coeff ≡ 1 mod Prime.
   228  	R     *big.Int // product of primes prior to this (inc p and q).
   229  }
   230  
   231  // Validate performs basic sanity checks on the key.
   232  // It returns nil if the key is valid, or else an error describing a problem.
   233  func (priv *PrivateKey) Validate() error {
   234  	if err := checkPub(&priv.PublicKey); err != nil {
   235  		return err
   236  	}
   237  
   238  	// Check that Πprimes == n.
   239  	modulus := new(big.Int).Set(bigOne)
   240  	for _, prime := range priv.Primes {
   241  		// Any primes ≤ 1 will cause divide-by-zero panics later.
   242  		if prime.Cmp(bigOne) <= 0 {
   243  			return errors.New("crypto/rsa: invalid prime value")
   244  		}
   245  		modulus.Mul(modulus, prime)
   246  	}
   247  	if modulus.Cmp(priv.N) != 0 {
   248  		return errors.New("crypto/rsa: invalid modulus")
   249  	}
   250  
   251  	// Check that de ≡ 1 mod p-1, for each prime.
   252  	// This implies that e is coprime to each p-1 as e has a multiplicative
   253  	// inverse. Therefore e is coprime to lcm(p-1,q-1,r-1,...) =
   254  	// exponent(ℤ/nℤ). It also implies that a^de ≡ a mod p as a^(p-1) ≡ 1
   255  	// mod p. Thus a^de ≡ a mod n for all a coprime to n, as required.
   256  	congruence := new(big.Int)
   257  	de := new(big.Int).SetInt64(int64(priv.E))
   258  	de.Mul(de, priv.D)
   259  	for _, prime := range priv.Primes {
   260  		pminus1 := new(big.Int).Sub(prime, bigOne)
   261  		congruence.Mod(de, pminus1)
   262  		if congruence.Cmp(bigOne) != 0 {
   263  			return errors.New("crypto/rsa: invalid exponents")
   264  		}
   265  	}
   266  	return nil
   267  }
   268  
   269  // GenerateKey generates a random RSA private key of the given bit size.
   270  //
   271  // Most applications should use [crypto/rand.Reader] as rand. Note that the
   272  // returned key does not depend deterministically on the bytes read from rand,
   273  // and may change between calls and/or between versions.
   274  func GenerateKey(random io.Reader, bits int) (*PrivateKey, error) {
   275  	return GenerateMultiPrimeKey(random, 2, bits)
   276  }
   277  
   278  // GenerateMultiPrimeKey generates a multi-prime RSA keypair of the given bit
   279  // size and the given random source.
   280  //
   281  // Table 1 in "[On the Security of Multi-prime RSA]" suggests maximum numbers of
   282  // primes for a given bit size.
   283  //
   284  // Although the public keys are compatible (actually, indistinguishable) from
   285  // the 2-prime case, the private keys are not. Thus it may not be possible to
   286  // export multi-prime private keys in certain formats or to subsequently import
   287  // them into other code.
   288  //
   289  // This package does not implement CRT optimizations for multi-prime RSA, so the
   290  // keys with more than two primes will have worse performance.
   291  //
   292  // Deprecated: The use of this function with a number of primes different from
   293  // two is not recommended for the above security, compatibility, and performance
   294  // reasons. Use [GenerateKey] instead.
   295  //
   296  // [On the Security of Multi-prime RSA]: http://www.cacr.math.uwaterloo.ca/techreports/2006/cacr2006-16.pdf
   297  func GenerateMultiPrimeKey(random io.Reader, nprimes int, bits int) (*PrivateKey, error) {
   298  	randutil.MaybeReadByte(random)
   299  
   300  	if boring.Enabled && random == boring.RandReader && nprimes == 2 &&
   301  		(bits == 2048 || bits == 3072 || bits == 4096) {
   302  		bN, bE, bD, bP, bQ, bDp, bDq, bQinv, err := boring.GenerateKeyRSA(bits)
   303  		if err != nil {
   304  			return nil, err
   305  		}
   306  		N := bbig.Dec(bN)
   307  		E := bbig.Dec(bE)
   308  		D := bbig.Dec(bD)
   309  		P := bbig.Dec(bP)
   310  		Q := bbig.Dec(bQ)
   311  		Dp := bbig.Dec(bDp)
   312  		Dq := bbig.Dec(bDq)
   313  		Qinv := bbig.Dec(bQinv)
   314  		e64 := E.Int64()
   315  		if !E.IsInt64() || int64(int(e64)) != e64 {
   316  			return nil, errors.New("crypto/rsa: generated key exponent too large")
   317  		}
   318  
   319  		mn, err := bigmod.NewModulusFromBig(N)
   320  		if err != nil {
   321  			return nil, err
   322  		}
   323  		mp, err := bigmod.NewModulusFromBig(P)
   324  		if err != nil {
   325  			return nil, err
   326  		}
   327  		mq, err := bigmod.NewModulusFromBig(Q)
   328  		if err != nil {
   329  			return nil, err
   330  		}
   331  
   332  		key := &PrivateKey{
   333  			PublicKey: PublicKey{
   334  				N: N,
   335  				E: int(e64),
   336  			},
   337  			D:      D,
   338  			Primes: []*big.Int{P, Q},
   339  			Precomputed: PrecomputedValues{
   340  				Dp:        Dp,
   341  				Dq:        Dq,
   342  				Qinv:      Qinv,
   343  				CRTValues: make([]CRTValue, 0), // non-nil, to match Precompute
   344  				n:         mn,
   345  				p:         mp,
   346  				q:         mq,
   347  			},
   348  		}
   349  		return key, nil
   350  	}
   351  
   352  	priv := new(PrivateKey)
   353  	priv.E = 65537
   354  
   355  	if nprimes < 2 {
   356  		return nil, errors.New("crypto/rsa: GenerateMultiPrimeKey: nprimes must be >= 2")
   357  	}
   358  
   359  	if bits < 64 {
   360  		primeLimit := float64(uint64(1) << uint(bits/nprimes))
   361  		// pi approximates the number of primes less than primeLimit
   362  		pi := primeLimit / (math.Log(primeLimit) - 1)
   363  		// Generated primes start with 11 (in binary) so we can only
   364  		// use a quarter of them.
   365  		pi /= 4
   366  		// Use a factor of two to ensure that key generation terminates
   367  		// in a reasonable amount of time.
   368  		pi /= 2
   369  		if pi <= float64(nprimes) {
   370  			return nil, errors.New("crypto/rsa: too few primes of given length to generate an RSA key")
   371  		}
   372  	}
   373  
   374  	primes := make([]*big.Int, nprimes)
   375  
   376  NextSetOfPrimes:
   377  	for {
   378  		todo := bits
   379  		// crypto/rand should set the top two bits in each prime.
   380  		// Thus each prime has the form
   381  		//   p_i = 2^bitlen(p_i) × 0.11... (in base 2).
   382  		// And the product is:
   383  		//   P = 2^todo × α
   384  		// where α is the product of nprimes numbers of the form 0.11...
   385  		//
   386  		// If α < 1/2 (which can happen for nprimes > 2), we need to
   387  		// shift todo to compensate for lost bits: the mean value of 0.11...
   388  		// is 7/8, so todo + shift - nprimes * log2(7/8) ~= bits - 1/2
   389  		// will give good results.
   390  		if nprimes >= 7 {
   391  			todo += (nprimes - 2) / 5
   392  		}
   393  		for i := 0; i < nprimes; i++ {
   394  			var err error
   395  			primes[i], err = rand.Prime(random, todo/(nprimes-i))
   396  			if err != nil {
   397  				return nil, err
   398  			}
   399  			todo -= primes[i].BitLen()
   400  		}
   401  
   402  		// Make sure that primes is pairwise unequal.
   403  		for i, prime := range primes {
   404  			for j := 0; j < i; j++ {
   405  				if prime.Cmp(primes[j]) == 0 {
   406  					continue NextSetOfPrimes
   407  				}
   408  			}
   409  		}
   410  
   411  		n := new(big.Int).Set(bigOne)
   412  		totient := new(big.Int).Set(bigOne)
   413  		pminus1 := new(big.Int)
   414  		for _, prime := range primes {
   415  			n.Mul(n, prime)
   416  			pminus1.Sub(prime, bigOne)
   417  			totient.Mul(totient, pminus1)
   418  		}
   419  		if n.BitLen() != bits {
   420  			// This should never happen for nprimes == 2 because
   421  			// crypto/rand should set the top two bits in each prime.
   422  			// For nprimes > 2 we hope it does not happen often.
   423  			continue NextSetOfPrimes
   424  		}
   425  
   426  		priv.D = new(big.Int)
   427  		e := big.NewInt(int64(priv.E))
   428  		ok := priv.D.ModInverse(e, totient)
   429  
   430  		if ok != nil {
   431  			priv.Primes = primes
   432  			priv.N = n
   433  			break
   434  		}
   435  	}
   436  
   437  	priv.Precompute()
   438  	return priv, nil
   439  }
   440  
   441  // incCounter increments a four byte, big-endian counter.
   442  func incCounter(c *[4]byte) {
   443  	if c[3]++; c[3] != 0 {
   444  		return
   445  	}
   446  	if c[2]++; c[2] != 0 {
   447  		return
   448  	}
   449  	if c[1]++; c[1] != 0 {
   450  		return
   451  	}
   452  	c[0]++
   453  }
   454  
   455  // mgf1XOR XORs the bytes in out with a mask generated using the MGF1 function
   456  // specified in PKCS #1 v2.1.
   457  func mgf1XOR(out []byte, hash hash.Hash, seed []byte) {
   458  	var counter [4]byte
   459  	var digest []byte
   460  
   461  	done := 0
   462  	for done < len(out) {
   463  		hash.Write(seed)
   464  		hash.Write(counter[0:4])
   465  		digest = hash.Sum(digest[:0])
   466  		hash.Reset()
   467  
   468  		for i := 0; i < len(digest) && done < len(out); i++ {
   469  			out[done] ^= digest[i]
   470  			done++
   471  		}
   472  		incCounter(&counter)
   473  	}
   474  }
   475  
   476  // ErrMessageTooLong is returned when attempting to encrypt or sign a message
   477  // which is too large for the size of the key. When using [SignPSS], this can also
   478  // be returned if the size of the salt is too large.
   479  var ErrMessageTooLong = errors.New("crypto/rsa: message too long for RSA key size")
   480  
   481  func encrypt(pub *PublicKey, plaintext []byte) ([]byte, error) {
   482  	boring.Unreachable()
   483  
   484  	N, err := bigmod.NewModulusFromBig(pub.N)
   485  	if err != nil {
   486  		return nil, err
   487  	}
   488  	m, err := bigmod.NewNat().SetBytes(plaintext, N)
   489  	if err != nil {
   490  		return nil, err
   491  	}
   492  	e := uint(pub.E)
   493  
   494  	return bigmod.NewNat().ExpShortVarTime(m, e, N).Bytes(N), nil
   495  }
   496  
   497  // EncryptOAEP encrypts the given message with RSA-OAEP.
   498  //
   499  // OAEP is parameterised by a hash function that is used as a random oracle.
   500  // Encryption and decryption of a given message must use the same hash function
   501  // and sha256.New() is a reasonable choice.
   502  //
   503  // The random parameter is used as a source of entropy to ensure that
   504  // encrypting the same message twice doesn't result in the same ciphertext.
   505  // Most applications should use [crypto/rand.Reader] as random.
   506  //
   507  // The label parameter may contain arbitrary data that will not be encrypted,
   508  // but which gives important context to the message. For example, if a given
   509  // public key is used to encrypt two types of messages then distinct label
   510  // values could be used to ensure that a ciphertext for one purpose cannot be
   511  // used for another by an attacker. If not required it can be empty.
   512  //
   513  // The message must be no longer than the length of the public modulus minus
   514  // twice the hash length, minus a further 2.
   515  func EncryptOAEP(hash hash.Hash, random io.Reader, pub *PublicKey, msg []byte, label []byte) ([]byte, error) {
   516  	// Note that while we don't commit to deterministic execution with respect
   517  	// to the random stream, we also don't apply MaybeReadByte, so per Hyrum's
   518  	// Law it's probably relied upon by some. It's a tolerable promise because a
   519  	// well-specified number of random bytes is included in the ciphertext, in a
   520  	// well-specified way.
   521  
   522  	if err := checkPub(pub); err != nil {
   523  		return nil, err
   524  	}
   525  	hash.Reset()
   526  	k := pub.Size()
   527  	if len(msg) > k-2*hash.Size()-2 {
   528  		return nil, ErrMessageTooLong
   529  	}
   530  
   531  	if boring.Enabled && random == boring.RandReader {
   532  		bkey, err := boringPublicKey(pub)
   533  		if err != nil {
   534  			return nil, err
   535  		}
   536  		return boring.EncryptRSAOAEP(hash, hash, bkey, msg, label)
   537  	}
   538  	boring.UnreachableExceptTests()
   539  
   540  	hash.Write(label)
   541  	lHash := hash.Sum(nil)
   542  	hash.Reset()
   543  
   544  	em := make([]byte, k)
   545  	seed := em[1 : 1+hash.Size()]
   546  	db := em[1+hash.Size():]
   547  
   548  	copy(db[0:hash.Size()], lHash)
   549  	db[len(db)-len(msg)-1] = 1
   550  	copy(db[len(db)-len(msg):], msg)
   551  
   552  	_, err := io.ReadFull(random, seed)
   553  	if err != nil {
   554  		return nil, err
   555  	}
   556  
   557  	mgf1XOR(db, hash, seed)
   558  	mgf1XOR(seed, hash, db)
   559  
   560  	if boring.Enabled {
   561  		var bkey *boring.PublicKeyRSA
   562  		bkey, err = boringPublicKey(pub)
   563  		if err != nil {
   564  			return nil, err
   565  		}
   566  		return boring.EncryptRSANoPadding(bkey, em)
   567  	}
   568  
   569  	return encrypt(pub, em)
   570  }
   571  
   572  // ErrDecryption represents a failure to decrypt a message.
   573  // It is deliberately vague to avoid adaptive attacks.
   574  var ErrDecryption = errors.New("crypto/rsa: decryption error")
   575  
   576  // ErrVerification represents a failure to verify a signature.
   577  // It is deliberately vague to avoid adaptive attacks.
   578  var ErrVerification = errors.New("crypto/rsa: verification error")
   579  
   580  // Precompute performs some calculations that speed up private key operations
   581  // in the future.
   582  func (priv *PrivateKey) Precompute() {
   583  	if priv.Precomputed.n == nil && len(priv.Primes) == 2 {
   584  		// Precomputed values _should_ always be valid, but if they aren't
   585  		// just return. We could also panic.
   586  		var err error
   587  		priv.Precomputed.n, err = bigmod.NewModulusFromBig(priv.N)
   588  		if err != nil {
   589  			return
   590  		}
   591  		priv.Precomputed.p, err = bigmod.NewModulusFromBig(priv.Primes[0])
   592  		if err != nil {
   593  			// Unset previous values, so we either have everything or nothing
   594  			priv.Precomputed.n = nil
   595  			return
   596  		}
   597  		priv.Precomputed.q, err = bigmod.NewModulusFromBig(priv.Primes[1])
   598  		if err != nil {
   599  			// Unset previous values, so we either have everything or nothing
   600  			priv.Precomputed.n, priv.Precomputed.p = nil, nil
   601  			return
   602  		}
   603  	}
   604  
   605  	// Fill in the backwards-compatibility *big.Int values.
   606  	if priv.Precomputed.Dp != nil {
   607  		return
   608  	}
   609  
   610  	priv.Precomputed.Dp = new(big.Int).Sub(priv.Primes[0], bigOne)
   611  	priv.Precomputed.Dp.Mod(priv.D, priv.Precomputed.Dp)
   612  
   613  	priv.Precomputed.Dq = new(big.Int).Sub(priv.Primes[1], bigOne)
   614  	priv.Precomputed.Dq.Mod(priv.D, priv.Precomputed.Dq)
   615  
   616  	priv.Precomputed.Qinv = new(big.Int).ModInverse(priv.Primes[1], priv.Primes[0])
   617  
   618  	r := new(big.Int).Mul(priv.Primes[0], priv.Primes[1])
   619  	priv.Precomputed.CRTValues = make([]CRTValue, len(priv.Primes)-2)
   620  	for i := 2; i < len(priv.Primes); i++ {
   621  		prime := priv.Primes[i]
   622  		values := &priv.Precomputed.CRTValues[i-2]
   623  
   624  		values.Exp = new(big.Int).Sub(prime, bigOne)
   625  		values.Exp.Mod(priv.D, values.Exp)
   626  
   627  		values.R = new(big.Int).Set(r)
   628  		values.Coeff = new(big.Int).ModInverse(r, prime)
   629  
   630  		r.Mul(r, prime)
   631  	}
   632  }
   633  
   634  const withCheck = true
   635  const noCheck = false
   636  
   637  // decrypt performs an RSA decryption of ciphertext into out. If check is true,
   638  // m^e is calculated and compared with ciphertext, in order to defend against
   639  // errors in the CRT computation.
   640  func decrypt(priv *PrivateKey, ciphertext []byte, check bool) ([]byte, error) {
   641  	if len(priv.Primes) <= 2 {
   642  		boring.Unreachable()
   643  	}
   644  
   645  	var (
   646  		err  error
   647  		m, c *bigmod.Nat
   648  		N    *bigmod.Modulus
   649  		t0   = bigmod.NewNat()
   650  	)
   651  	if priv.Precomputed.n == nil {
   652  		N, err = bigmod.NewModulusFromBig(priv.N)
   653  		if err != nil {
   654  			return nil, ErrDecryption
   655  		}
   656  		c, err = bigmod.NewNat().SetBytes(ciphertext, N)
   657  		if err != nil {
   658  			return nil, ErrDecryption
   659  		}
   660  		m = bigmod.NewNat().Exp(c, priv.D.Bytes(), N)
   661  	} else {
   662  		N = priv.Precomputed.n
   663  		P, Q := priv.Precomputed.p, priv.Precomputed.q
   664  		Qinv, err := bigmod.NewNat().SetBytes(priv.Precomputed.Qinv.Bytes(), P)
   665  		if err != nil {
   666  			return nil, ErrDecryption
   667  		}
   668  		c, err = bigmod.NewNat().SetBytes(ciphertext, N)
   669  		if err != nil {
   670  			return nil, ErrDecryption
   671  		}
   672  
   673  		// m = c ^ Dp mod p
   674  		m = bigmod.NewNat().Exp(t0.Mod(c, P), priv.Precomputed.Dp.Bytes(), P)
   675  		// m2 = c ^ Dq mod q
   676  		m2 := bigmod.NewNat().Exp(t0.Mod(c, Q), priv.Precomputed.Dq.Bytes(), Q)
   677  		// m = m - m2 mod p
   678  		m.Sub(t0.Mod(m2, P), P)
   679  		// m = m * Qinv mod p
   680  		m.Mul(Qinv, P)
   681  		// m = m * q mod N
   682  		m.ExpandFor(N).Mul(t0.Mod(Q.Nat(), N), N)
   683  		// m = m + m2 mod N
   684  		m.Add(m2.ExpandFor(N), N)
   685  	}
   686  
   687  	if check {
   688  		c1 := bigmod.NewNat().ExpShortVarTime(m, uint(priv.E), N)
   689  		if c1.Equal(c) != 1 {
   690  			return nil, ErrDecryption
   691  		}
   692  	}
   693  
   694  	return m.Bytes(N), nil
   695  }
   696  
   697  // DecryptOAEP decrypts ciphertext using RSA-OAEP.
   698  //
   699  // OAEP is parameterised by a hash function that is used as a random oracle.
   700  // Encryption and decryption of a given message must use the same hash function
   701  // and sha256.New() is a reasonable choice.
   702  //
   703  // The random parameter is legacy and ignored, and it can be nil.
   704  //
   705  // The label parameter must match the value given when encrypting. See
   706  // [EncryptOAEP] for details.
   707  func DecryptOAEP(hash hash.Hash, random io.Reader, priv *PrivateKey, ciphertext []byte, label []byte) ([]byte, error) {
   708  	return decryptOAEP(hash, hash, random, priv, ciphertext, label)
   709  }
   710  
   711  func decryptOAEP(hash, mgfHash hash.Hash, random io.Reader, priv *PrivateKey, ciphertext []byte, label []byte) ([]byte, error) {
   712  	if err := checkPub(&priv.PublicKey); err != nil {
   713  		return nil, err
   714  	}
   715  	k := priv.Size()
   716  	if len(ciphertext) > k ||
   717  		k < hash.Size()*2+2 {
   718  		return nil, ErrDecryption
   719  	}
   720  
   721  	if boring.Enabled {
   722  		bkey, err := boringPrivateKey(priv)
   723  		if err != nil {
   724  			return nil, err
   725  		}
   726  		out, err := boring.DecryptRSAOAEP(hash, mgfHash, bkey, ciphertext, label)
   727  		if err != nil {
   728  			return nil, ErrDecryption
   729  		}
   730  		return out, nil
   731  	}
   732  
   733  	em, err := decrypt(priv, ciphertext, noCheck)
   734  	if err != nil {
   735  		return nil, err
   736  	}
   737  
   738  	hash.Write(label)
   739  	lHash := hash.Sum(nil)
   740  	hash.Reset()
   741  
   742  	firstByteIsZero := subtle.ConstantTimeByteEq(em[0], 0)
   743  
   744  	seed := em[1 : hash.Size()+1]
   745  	db := em[hash.Size()+1:]
   746  
   747  	mgf1XOR(seed, mgfHash, db)
   748  	mgf1XOR(db, mgfHash, seed)
   749  
   750  	lHash2 := db[0:hash.Size()]
   751  
   752  	// We have to validate the plaintext in constant time in order to avoid
   753  	// attacks like: J. Manger. A Chosen Ciphertext Attack on RSA Optimal
   754  	// Asymmetric Encryption Padding (OAEP) as Standardized in PKCS #1
   755  	// v2.0. In J. Kilian, editor, Advances in Cryptology.
   756  	lHash2Good := subtle.ConstantTimeCompare(lHash, lHash2)
   757  
   758  	// The remainder of the plaintext must be zero or more 0x00, followed
   759  	// by 0x01, followed by the message.
   760  	//   lookingForIndex: 1 iff we are still looking for the 0x01
   761  	//   index: the offset of the first 0x01 byte
   762  	//   invalid: 1 iff we saw a non-zero byte before the 0x01.
   763  	var lookingForIndex, index, invalid int
   764  	lookingForIndex = 1
   765  	rest := db[hash.Size():]
   766  
   767  	for i := 0; i < len(rest); i++ {
   768  		equals0 := subtle.ConstantTimeByteEq(rest[i], 0)
   769  		equals1 := subtle.ConstantTimeByteEq(rest[i], 1)
   770  		index = subtle.ConstantTimeSelect(lookingForIndex&equals1, i, index)
   771  		lookingForIndex = subtle.ConstantTimeSelect(equals1, 0, lookingForIndex)
   772  		invalid = subtle.ConstantTimeSelect(lookingForIndex&^equals0, 1, invalid)
   773  	}
   774  
   775  	if firstByteIsZero&lHash2Good&^invalid&^lookingForIndex != 1 {
   776  		return nil, ErrDecryption
   777  	}
   778  
   779  	return rest[index+1:], nil
   780  }
   781
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