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