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] and for some operations involving
    24  // deprecated multi-prime keys.
    25  //
    26  // # Minimum key size
    27  //
    28  // [GenerateKey] returns an error if a key of less than 1024 bits is requested,
    29  // and all Sign, Verify, Encrypt, and Decrypt methods return an error if used
    30  // with a key smaller than 1024 bits. Such keys are insecure and should not be
    31  // used.
    32  //
    33  // The rsa1024min=0 GODEBUG setting suppresses this error, but we recommend
    34  // doing so only in tests, if necessary. Tests can set this option using
    35  // [testing.T.Setenv] or by including "//go:debug rsa1024min=0" in a *_test.go
    36  // source file.
    37  //
    38  // Alternatively, see the [GenerateKey (TestKey)] example for a pregenerated
    39  // test-only 2048-bit key.
    40  //
    41  // [GenerateKey (TestKey)]: https://pkg.go.dev/crypto/rsa#example-GenerateKey-TestKey
    42  package rsa
    43  
    44  import (
    45  	"crypto"
    46  	"crypto/internal/boring"
    47  	"crypto/internal/boring/bbig"
    48  	"crypto/internal/fips140/bigmod"
    49  	"crypto/internal/fips140/rsa"
    50  	"crypto/internal/fips140only"
    51  	"crypto/internal/rand"
    52  	cryptorand "crypto/rand"
    53  	"crypto/subtle"
    54  	"errors"
    55  	"fmt"
    56  	"internal/godebug"
    57  	"io"
    58  	"math"
    59  	"math/big"
    60  )
    61  
    62  var bigOne = big.NewInt(1)
    63  
    64  // A PublicKey represents the public part of an RSA key.
    65  //
    66  // The values of N and E are not considered confidential, and may leak through
    67  // side channels, or could be mathematically derived from other public values.
    68  type PublicKey struct {
    69  	N *big.Int // modulus
    70  	E int      // public exponent
    71  }
    72  
    73  // Any methods implemented on PublicKey might need to also be implemented on
    74  // PrivateKey, as the latter embeds the former and will expose its methods.
    75  
    76  // Size returns the modulus size in bytes. Raw signatures and ciphertexts
    77  // for or by this public key will have the same size.
    78  func (pub *PublicKey) Size() int {
    79  	return (pub.N.BitLen() + 7) / 8
    80  }
    81  
    82  // Equal reports whether pub and x have the same value.
    83  func (pub *PublicKey) Equal(x crypto.PublicKey) bool {
    84  	xx, ok := x.(*PublicKey)
    85  	if !ok {
    86  		return false
    87  	}
    88  	return bigIntEqual(pub.N, xx.N) && pub.E == xx.E
    89  }
    90  
    91  // OAEPOptions allows passing options to OAEP encryption and decryption
    92  // through the [PrivateKey.Decrypt] and [EncryptOAEPWithOptions] functions.
    93  type OAEPOptions struct {
    94  	// Hash is the hash function that will be used when generating the mask.
    95  	Hash crypto.Hash
    96  
    97  	// MGFHash is the hash function used for MGF1.
    98  	// If zero, Hash is used instead.
    99  	MGFHash crypto.Hash
   100  
   101  	// Label is an arbitrary byte string that must be equal to the value
   102  	// used when encrypting.
   103  	Label []byte
   104  }
   105  
   106  // A PrivateKey represents an RSA key.
   107  //
   108  // Its fields must not be modified after calling [PrivateKey.Precompute], and
   109  // should not be used directly as big.Int values for cryptographic purposes.
   110  type PrivateKey struct {
   111  	PublicKey            // public part.
   112  	D         *big.Int   // private exponent
   113  	Primes    []*big.Int // prime factors of N, has >= 2 elements.
   114  
   115  	// Precomputed contains precomputed values that speed up RSA operations,
   116  	// if available. It must be generated by calling PrivateKey.Precompute and
   117  	// must not be modified afterwards.
   118  	Precomputed PrecomputedValues
   119  }
   120  
   121  // Public returns the public key corresponding to priv.
   122  func (priv *PrivateKey) Public() crypto.PublicKey {
   123  	return &priv.PublicKey
   124  }
   125  
   126  // Equal reports whether priv and x have equivalent values. It ignores
   127  // Precomputed values.
   128  func (priv *PrivateKey) Equal(x crypto.PrivateKey) bool {
   129  	xx, ok := x.(*PrivateKey)
   130  	if !ok {
   131  		return false
   132  	}
   133  	if !priv.PublicKey.Equal(&xx.PublicKey) || !bigIntEqual(priv.D, xx.D) {
   134  		return false
   135  	}
   136  	if len(priv.Primes) != len(xx.Primes) {
   137  		return false
   138  	}
   139  	for i := range priv.Primes {
   140  		if !bigIntEqual(priv.Primes[i], xx.Primes[i]) {
   141  			return false
   142  		}
   143  	}
   144  	return true
   145  }
   146  
   147  // bigIntEqual reports whether a and b are equal leaking only their bit length
   148  // through timing side-channels.
   149  func bigIntEqual(a, b *big.Int) bool {
   150  	return subtle.ConstantTimeCompare(a.Bytes(), b.Bytes()) == 1
   151  }
   152  
   153  // Sign signs digest with priv, reading randomness from rand. If opts is a
   154  // *[PSSOptions] then the PSS algorithm will be used, otherwise PKCS #1 v1.5 will
   155  // be used. digest must be the result of hashing the input message using
   156  // opts.HashFunc().
   157  //
   158  // This method implements [crypto.Signer], which is an interface to support keys
   159  // where the private part is kept in, for example, a hardware module. Common
   160  // uses should use the Sign* functions in this package directly.
   161  func (priv *PrivateKey) Sign(rand io.Reader, digest []byte, opts crypto.SignerOpts) ([]byte, error) {
   162  	if pssOpts, ok := opts.(*PSSOptions); ok {
   163  		return SignPSS(rand, priv, pssOpts.Hash, digest, pssOpts)
   164  	}
   165  
   166  	return SignPKCS1v15(rand, priv, opts.HashFunc(), digest)
   167  }
   168  
   169  // Decrypt decrypts ciphertext with priv. If opts is nil or of type
   170  // *[PKCS1v15DecryptOptions] then PKCS #1 v1.5 decryption is performed. Otherwise
   171  // opts must have type *[OAEPOptions] and OAEP decryption is done.
   172  func (priv *PrivateKey) Decrypt(rand io.Reader, ciphertext []byte, opts crypto.DecrypterOpts) (plaintext []byte, err error) {
   173  	if opts == nil {
   174  		return DecryptPKCS1v15(rand, priv, ciphertext)
   175  	}
   176  
   177  	switch opts := opts.(type) {
   178  	case *OAEPOptions:
   179  		if opts.MGFHash == 0 {
   180  			return decryptOAEP(opts.Hash.New(), opts.Hash.New(), priv, ciphertext, opts.Label)
   181  		} else {
   182  			return decryptOAEP(opts.Hash.New(), opts.MGFHash.New(), priv, ciphertext, opts.Label)
   183  		}
   184  
   185  	case *PKCS1v15DecryptOptions:
   186  		if l := opts.SessionKeyLen; l > 0 {
   187  			plaintext = make([]byte, l)
   188  			if _, err := io.ReadFull(rand, plaintext); err != nil {
   189  				return nil, err
   190  			}
   191  			if err := DecryptPKCS1v15SessionKey(rand, priv, ciphertext, plaintext); err != nil {
   192  				return nil, err
   193  			}
   194  			return plaintext, nil
   195  		} else {
   196  			return DecryptPKCS1v15(rand, priv, ciphertext)
   197  		}
   198  
   199  	default:
   200  		return nil, errors.New("crypto/rsa: invalid options for Decrypt")
   201  	}
   202  }
   203  
   204  type PrecomputedValues struct {
   205  	Dp, Dq *big.Int // D mod (P-1) (or mod Q-1)
   206  	Qinv   *big.Int // Q^-1 mod P
   207  
   208  	// CRTValues is used for the 3rd and subsequent primes. Due to a
   209  	// historical accident, the CRT for the first two primes is handled
   210  	// differently in PKCS #1 and interoperability is sufficiently
   211  	// important that we mirror this.
   212  	//
   213  	// Deprecated: These values are still filled in by Precompute for
   214  	// backwards compatibility but are not used. Multi-prime RSA is very rare,
   215  	// and is implemented by this package without CRT optimizations to limit
   216  	// complexity.
   217  	CRTValues []CRTValue
   218  
   219  	fips *rsa.PrivateKey
   220  }
   221  
   222  // CRTValue contains the precomputed Chinese remainder theorem values.
   223  type CRTValue struct {
   224  	Exp   *big.Int // D mod (prime-1).
   225  	Coeff *big.Int // R·Coeff ≡ 1 mod Prime.
   226  	R     *big.Int // product of primes prior to this (inc p and q).
   227  }
   228  
   229  // Validate performs basic sanity checks on the key.
   230  // It returns nil if the key is valid, or else an error describing a problem.
   231  //
   232  // It runs faster on valid keys if run after [PrivateKey.Precompute].
   233  func (priv *PrivateKey) Validate() error {
   234  	// We can operate on keys based on d alone, but they can't be encoded with
   235  	// [crypto/x509.MarshalPKCS1PrivateKey], which unfortunately doesn't return
   236  	// an error, so we need to reject them here.
   237  	if len(priv.Primes) < 2 {
   238  		return errors.New("crypto/rsa: missing primes")
   239  	}
   240  	// If Precomputed.fips is set and consistent, then the key has been
   241  	// validated by [rsa.NewPrivateKey] or [rsa.NewPrivateKeyWithoutCRT].
   242  	if priv.precomputedIsConsistent() {
   243  		return nil
   244  	}
   245  	if priv.Precomputed.fips != nil {
   246  		return errors.New("crypto/rsa: precomputed values are inconsistent with the key")
   247  	}
   248  	_, err := priv.precompute()
   249  	return err
   250  }
   251  
   252  func (priv *PrivateKey) precomputedIsConsistent() bool {
   253  	if priv.Precomputed.fips == nil {
   254  		return false
   255  	}
   256  	N, e, d, P, Q, dP, dQ, qInv := priv.Precomputed.fips.Export()
   257  	if !bigIntEqualToBytes(priv.N, N) || priv.E != e || !bigIntEqualToBytes(priv.D, d) {
   258  		return false
   259  	}
   260  	if len(priv.Primes) != 2 {
   261  		return P == nil && Q == nil && dP == nil && dQ == nil && qInv == nil
   262  	}
   263  	return bigIntEqualToBytes(priv.Primes[0], P) &&
   264  		bigIntEqualToBytes(priv.Primes[1], Q) &&
   265  		bigIntEqualToBytes(priv.Precomputed.Dp, dP) &&
   266  		bigIntEqualToBytes(priv.Precomputed.Dq, dQ) &&
   267  		bigIntEqualToBytes(priv.Precomputed.Qinv, qInv)
   268  }
   269  
   270  // bigIntEqual reports whether a and b are equal, ignoring leading zero bytes in
   271  // b, and leaking only their bit length through timing side-channels.
   272  func bigIntEqualToBytes(a *big.Int, b []byte) bool {
   273  	if a == nil || a.BitLen() > len(b)*8 {
   274  		return false
   275  	}
   276  	buf := a.FillBytes(make([]byte, len(b)))
   277  	return subtle.ConstantTimeCompare(buf, b) == 1
   278  }
   279  
   280  // rsa1024min is a GODEBUG that re-enables weak RSA keys if set to "0".
   281  // See https://go.dev/issue/68762.
   282  var rsa1024min = godebug.New("rsa1024min")
   283  
   284  func checkKeySize(size int) error {
   285  	if size >= 1024 {
   286  		return nil
   287  	}
   288  	if rsa1024min.Value() == "0" {
   289  		rsa1024min.IncNonDefault()
   290  		return nil
   291  	}
   292  	return fmt.Errorf("crypto/rsa: %d-bit keys are insecure (see https://go.dev/pkg/crypto/rsa#hdr-Minimum_key_size)", size)
   293  }
   294  
   295  func checkPublicKeySize(k *PublicKey) error {
   296  	if k.N == nil {
   297  		return errors.New("crypto/rsa: missing public modulus")
   298  	}
   299  	return checkKeySize(k.N.BitLen())
   300  }
   301  
   302  // GenerateKey generates a random RSA private key of the given bit size.
   303  //
   304  // If bits is less than 1024, [GenerateKey] returns an error. See the "[Minimum
   305  // key size]" section for further details.
   306  //
   307  // Since Go 1.26, a secure source of random bytes is always used, and the Reader is
   308  // ignored unless GODEBUG=cryptocustomrand=1 is set. This setting will be removed
   309  // in a future Go release. Instead, use [testing/cryptotest.SetGlobalRandom].
   310  //
   311  // [Minimum key size]: https://pkg.go.dev/crypto/rsa#hdr-Minimum_key_size
   312  func GenerateKey(random io.Reader, bits int) (*PrivateKey, error) {
   313  	if err := checkKeySize(bits); err != nil {
   314  		return nil, err
   315  	}
   316  
   317  	if boring.Enabled && rand.IsDefaultReader(random) &&
   318  		(bits == 2048 || bits == 3072 || bits == 4096) {
   319  		bN, bE, bD, bP, bQ, bDp, bDq, bQinv, err := boring.GenerateKeyRSA(bits)
   320  		if err != nil {
   321  			return nil, err
   322  		}
   323  		N := bbig.Dec(bN)
   324  		E := bbig.Dec(bE)
   325  		D := bbig.Dec(bD)
   326  		P := bbig.Dec(bP)
   327  		Q := bbig.Dec(bQ)
   328  		Dp := bbig.Dec(bDp)
   329  		Dq := bbig.Dec(bDq)
   330  		Qinv := bbig.Dec(bQinv)
   331  		e64 := E.Int64()
   332  		if !E.IsInt64() || int64(int(e64)) != e64 {
   333  			return nil, errors.New("crypto/rsa: generated key exponent too large")
   334  		}
   335  
   336  		key := &PrivateKey{
   337  			PublicKey: PublicKey{
   338  				N: N,
   339  				E: int(e64),
   340  			},
   341  			D:      D,
   342  			Primes: []*big.Int{P, Q},
   343  			Precomputed: PrecomputedValues{
   344  				Dp:        Dp,
   345  				Dq:        Dq,
   346  				Qinv:      Qinv,
   347  				CRTValues: make([]CRTValue, 0), // non-nil, to match Precompute
   348  			},
   349  		}
   350  		return key, nil
   351  	}
   352  
   353  	random = rand.CustomReader(random)
   354  
   355  	if fips140only.Enforced() && bits < 2048 {
   356  		return nil, errors.New("crypto/rsa: use of keys smaller than 2048 bits is not allowed in FIPS 140-only mode")
   357  	}
   358  	if fips140only.Enforced() && bits%2 == 1 {
   359  		return nil, errors.New("crypto/rsa: use of keys with odd size is not allowed in FIPS 140-only mode")
   360  	}
   361  	if fips140only.Enforced() && !fips140only.ApprovedRandomReader(random) {
   362  		return nil, errors.New("crypto/rsa: only crypto/rand.Reader is allowed in FIPS 140-only mode")
   363  	}
   364  
   365  	k, err := rsa.GenerateKey(random, bits)
   366  	if bits < 256 && err != nil {
   367  		// Toy-sized keys have a non-negligible chance of hitting two hard
   368  		// failure cases: p == q and d <= 2^(nlen / 2).
   369  		//
   370  		// Since these are impossible to hit for real keys, we don't want to
   371  		// make the production code path more complex and harder to think about
   372  		// to handle them.
   373  		//
   374  		// Instead, just rerun the whole process a total of 8 times, which
   375  		// brings the chance of failure for 32-bit keys down to the same as for
   376  		// 256-bit keys.
   377  		for i := 1; i < 8 && err != nil; i++ {
   378  			k, err = rsa.GenerateKey(random, bits)
   379  		}
   380  	}
   381  	if err != nil {
   382  		return nil, err
   383  	}
   384  	N, e, d, p, q, dP, dQ, qInv := k.Export()
   385  	key := &PrivateKey{
   386  		PublicKey: PublicKey{
   387  			N: new(big.Int).SetBytes(N),
   388  			E: e,
   389  		},
   390  		D: new(big.Int).SetBytes(d),
   391  		Primes: []*big.Int{
   392  			new(big.Int).SetBytes(p),
   393  			new(big.Int).SetBytes(q),
   394  		},
   395  		Precomputed: PrecomputedValues{
   396  			fips:      k,
   397  			Dp:        new(big.Int).SetBytes(dP),
   398  			Dq:        new(big.Int).SetBytes(dQ),
   399  			Qinv:      new(big.Int).SetBytes(qInv),
   400  			CRTValues: make([]CRTValue, 0), // non-nil, to match Precompute
   401  		},
   402  	}
   403  	return key, nil
   404  }
   405  
   406  // GenerateMultiPrimeKey generates a multi-prime RSA keypair of the given bit
   407  // size and the given random source.
   408  //
   409  // Table 1 in "[On the Security of Multi-prime RSA]" suggests maximum numbers of
   410  // primes for a given bit size.
   411  //
   412  // Although the public keys are compatible (actually, indistinguishable) from
   413  // the 2-prime case, the private keys are not. Thus it may not be possible to
   414  // export multi-prime private keys in certain formats or to subsequently import
   415  // them into other code.
   416  //
   417  // This package does not implement CRT optimizations for multi-prime RSA, so the
   418  // keys with more than two primes will have worse performance.
   419  //
   420  // Since Go 1.26, a secure source of random bytes is always used, and the Reader is
   421  // ignored unless GODEBUG=cryptocustomrand=1 is set. This setting will be removed
   422  // in a future Go release. Instead, use [testing/cryptotest.SetGlobalRandom].
   423  //
   424  // Deprecated: The use of this function with a number of primes different from
   425  // two is not recommended for the above security, compatibility, and performance
   426  // reasons. Use [GenerateKey] instead.
   427  //
   428  // [On the Security of Multi-prime RSA]: http://www.cacr.math.uwaterloo.ca/techreports/2006/cacr2006-16.pdf
   429  func GenerateMultiPrimeKey(random io.Reader, nprimes int, bits int) (*PrivateKey, error) {
   430  	if nprimes == 2 {
   431  		return GenerateKey(random, bits)
   432  	}
   433  	if fips140only.Enforced() {
   434  		return nil, errors.New("crypto/rsa: multi-prime RSA is not allowed in FIPS 140-only mode")
   435  	}
   436  
   437  	random = rand.CustomReader(random)
   438  
   439  	priv := new(PrivateKey)
   440  	priv.E = 65537
   441  
   442  	if nprimes < 2 {
   443  		return nil, errors.New("crypto/rsa: GenerateMultiPrimeKey: nprimes must be >= 2")
   444  	}
   445  
   446  	if bits < 64 {
   447  		primeLimit := float64(uint64(1) << uint(bits/nprimes))
   448  		// pi approximates the number of primes less than primeLimit
   449  		pi := primeLimit / (math.Log(primeLimit) - 1)
   450  		// Generated primes start with 11 (in binary) so we can only
   451  		// use a quarter of them.
   452  		pi /= 4
   453  		// Use a factor of two to ensure that key generation terminates
   454  		// in a reasonable amount of time.
   455  		pi /= 2
   456  		if pi <= float64(nprimes) {
   457  			return nil, errors.New("crypto/rsa: too few primes of given length to generate an RSA key")
   458  		}
   459  	}
   460  
   461  	primes := make([]*big.Int, nprimes)
   462  
   463  NextSetOfPrimes:
   464  	for {
   465  		todo := bits
   466  		// crypto/rand should set the top two bits in each prime.
   467  		// Thus each prime has the form
   468  		//   p_i = 2^bitlen(p_i) × 0.11... (in base 2).
   469  		// And the product is:
   470  		//   P = 2^todo × α
   471  		// where α is the product of nprimes numbers of the form 0.11...
   472  		//
   473  		// If α < 1/2 (which can happen for nprimes > 2), we need to
   474  		// shift todo to compensate for lost bits: the mean value of 0.11...
   475  		// is 7/8, so todo + shift - nprimes * log2(7/8) ~= bits - 1/2
   476  		// will give good results.
   477  		if nprimes >= 7 {
   478  			todo += (nprimes - 2) / 5
   479  		}
   480  		for i := 0; i < nprimes; i++ {
   481  			var err error
   482  			primes[i], err = cryptorand.Prime(random, todo/(nprimes-i))
   483  			if err != nil {
   484  				return nil, err
   485  			}
   486  			todo -= primes[i].BitLen()
   487  		}
   488  
   489  		// Make sure that primes is pairwise unequal.
   490  		for i, prime := range primes {
   491  			for j := 0; j < i; j++ {
   492  				if prime.Cmp(primes[j]) == 0 {
   493  					continue NextSetOfPrimes
   494  				}
   495  			}
   496  		}
   497  
   498  		n := new(big.Int).Set(bigOne)
   499  		totient := new(big.Int).Set(bigOne)
   500  		pminus1 := new(big.Int)
   501  		for _, prime := range primes {
   502  			n.Mul(n, prime)
   503  			pminus1.Sub(prime, bigOne)
   504  			totient.Mul(totient, pminus1)
   505  		}
   506  		if n.BitLen() != bits {
   507  			// This should never happen for nprimes == 2 because
   508  			// crypto/rand should set the top two bits in each prime.
   509  			// For nprimes > 2 we hope it does not happen often.
   510  			continue NextSetOfPrimes
   511  		}
   512  
   513  		priv.D = new(big.Int)
   514  		e := big.NewInt(int64(priv.E))
   515  		ok := priv.D.ModInverse(e, totient)
   516  
   517  		if ok != nil {
   518  			priv.Primes = primes
   519  			priv.N = n
   520  			break
   521  		}
   522  	}
   523  
   524  	priv.Precompute()
   525  	if err := priv.Validate(); err != nil {
   526  		return nil, err
   527  	}
   528  
   529  	return priv, nil
   530  }
   531  
   532  // ErrMessageTooLong is returned when attempting to encrypt or sign a message
   533  // which is too large for the size of the key. When using [SignPSS], this can also
   534  // be returned if the size of the salt is too large.
   535  var ErrMessageTooLong = errors.New("crypto/rsa: message too long for RSA key size")
   536  
   537  // ErrDecryption represents a failure to decrypt a message.
   538  // It is deliberately vague to avoid adaptive attacks.
   539  var ErrDecryption = errors.New("crypto/rsa: decryption error")
   540  
   541  // ErrVerification represents a failure to verify a signature.
   542  // It is deliberately vague to avoid adaptive attacks.
   543  var ErrVerification = errors.New("crypto/rsa: verification error")
   544  
   545  // Precompute performs some calculations that speed up private key operations
   546  // in the future. It is safe to run on non-validated private keys.
   547  func (priv *PrivateKey) Precompute() {
   548  	if priv.precomputedIsConsistent() {
   549  		return
   550  	}
   551  
   552  	precomputed, err := priv.precompute()
   553  	if err != nil {
   554  		// We don't have a way to report errors, so just leave Precomputed.fips
   555  		// nil. Validate will re-run precompute and report its error.
   556  		priv.Precomputed.fips = nil
   557  		return
   558  	}
   559  	priv.Precomputed = precomputed
   560  }
   561  
   562  func (priv *PrivateKey) precompute() (PrecomputedValues, error) {
   563  	var precomputed PrecomputedValues
   564  
   565  	if priv.N == nil {
   566  		return precomputed, errors.New("crypto/rsa: missing public modulus")
   567  	}
   568  	if priv.D == nil {
   569  		return precomputed, errors.New("crypto/rsa: missing private exponent")
   570  	}
   571  	if len(priv.Primes) != 2 {
   572  		return priv.precomputeLegacy()
   573  	}
   574  	if priv.Primes[0] == nil {
   575  		return precomputed, errors.New("crypto/rsa: prime P is nil")
   576  	}
   577  	if priv.Primes[1] == nil {
   578  		return precomputed, errors.New("crypto/rsa: prime Q is nil")
   579  	}
   580  
   581  	// If the CRT values are already set, use them.
   582  	if priv.Precomputed.Dp != nil && priv.Precomputed.Dq != nil && priv.Precomputed.Qinv != nil {
   583  		k, err := rsa.NewPrivateKeyWithPrecomputation(priv.N.Bytes(), priv.E, priv.D.Bytes(),
   584  			priv.Primes[0].Bytes(), priv.Primes[1].Bytes(),
   585  			priv.Precomputed.Dp.Bytes(), priv.Precomputed.Dq.Bytes(), priv.Precomputed.Qinv.Bytes())
   586  		if err != nil {
   587  			return precomputed, err
   588  		}
   589  		precomputed = priv.Precomputed
   590  		precomputed.fips = k
   591  		precomputed.CRTValues = make([]CRTValue, 0)
   592  		return precomputed, nil
   593  	}
   594  
   595  	k, err := rsa.NewPrivateKey(priv.N.Bytes(), priv.E, priv.D.Bytes(),
   596  		priv.Primes[0].Bytes(), priv.Primes[1].Bytes())
   597  	if err != nil {
   598  		return precomputed, err
   599  	}
   600  
   601  	precomputed.fips = k
   602  	_, _, _, _, _, dP, dQ, qInv := k.Export()
   603  	precomputed.Dp = new(big.Int).SetBytes(dP)
   604  	precomputed.Dq = new(big.Int).SetBytes(dQ)
   605  	precomputed.Qinv = new(big.Int).SetBytes(qInv)
   606  	precomputed.CRTValues = make([]CRTValue, 0)
   607  	return precomputed, nil
   608  }
   609  
   610  func (priv *PrivateKey) precomputeLegacy() (PrecomputedValues, error) {
   611  	var precomputed PrecomputedValues
   612  
   613  	k, err := rsa.NewPrivateKeyWithoutCRT(priv.N.Bytes(), priv.E, priv.D.Bytes())
   614  	if err != nil {
   615  		return precomputed, err
   616  	}
   617  	precomputed.fips = k
   618  
   619  	if len(priv.Primes) < 2 {
   620  		return precomputed, nil
   621  	}
   622  
   623  	// Ensure the Mod and ModInverse calls below don't panic.
   624  	for _, prime := range priv.Primes {
   625  		if prime == nil {
   626  			return precomputed, errors.New("crypto/rsa: prime factor is nil")
   627  		}
   628  		if prime.Cmp(bigOne) <= 0 {
   629  			return precomputed, errors.New("crypto/rsa: prime factor is <= 1")
   630  		}
   631  	}
   632  
   633  	precomputed.Dp = new(big.Int).Sub(priv.Primes[0], bigOne)
   634  	precomputed.Dp.Mod(priv.D, precomputed.Dp)
   635  
   636  	precomputed.Dq = new(big.Int).Sub(priv.Primes[1], bigOne)
   637  	precomputed.Dq.Mod(priv.D, precomputed.Dq)
   638  
   639  	precomputed.Qinv = new(big.Int).ModInverse(priv.Primes[1], priv.Primes[0])
   640  	if precomputed.Qinv == nil {
   641  		return precomputed, errors.New("crypto/rsa: prime factors are not relatively prime")
   642  	}
   643  
   644  	r := new(big.Int).Mul(priv.Primes[0], priv.Primes[1])
   645  	precomputed.CRTValues = make([]CRTValue, len(priv.Primes)-2)
   646  	for i := 2; i < len(priv.Primes); i++ {
   647  		prime := priv.Primes[i]
   648  		values := &precomputed.CRTValues[i-2]
   649  
   650  		values.Exp = new(big.Int).Sub(prime, bigOne)
   651  		values.Exp.Mod(priv.D, values.Exp)
   652  
   653  		values.R = new(big.Int).Set(r)
   654  		values.Coeff = new(big.Int).ModInverse(r, prime)
   655  		if values.Coeff == nil {
   656  			return precomputed, errors.New("crypto/rsa: prime factors are not relatively prime")
   657  		}
   658  
   659  		r.Mul(r, prime)
   660  	}
   661  
   662  	return precomputed, nil
   663  }
   664  
   665  func fipsPublicKey(pub *PublicKey) (*rsa.PublicKey, error) {
   666  	N, err := bigmod.NewModulus(pub.N.Bytes())
   667  	if err != nil {
   668  		return nil, err
   669  	}
   670  	return &rsa.PublicKey{N: N, E: pub.E}, nil
   671  }
   672  
   673  func fipsPrivateKey(priv *PrivateKey) (*rsa.PrivateKey, error) {
   674  	if priv.Precomputed.fips != nil {
   675  		return priv.Precomputed.fips, nil
   676  	}
   677  	precomputed, err := priv.precompute()
   678  	if err != nil {
   679  		return nil, err
   680  	}
   681  	return precomputed.fips, nil
   682  }
   683
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