Crypto++  5.6.5
Free C++ class library of cryptographic schemes
rsa.cpp
1 // rsa.cpp - originally written and placed in the public domain by Wei Dai
2 
3 #include "pch.h"
4 #include "rsa.h"
5 #include "asn.h"
6 #include "sha.h"
7 #include "oids.h"
8 #include "modarith.h"
9 #include "nbtheory.h"
10 #include "algparam.h"
11 #include "fips140.h"
12 #include "pkcspad.h"
13 
14 #if defined(CRYPTOPP_DEBUG) && !defined(CRYPTOPP_DOXYGEN_PROCESSING) && !defined(CRYPTOPP_IS_DLL)
15 #include "sha3.h"
16 #include "pssr.h"
17 NAMESPACE_BEGIN(CryptoPP)
18 void RSA_TestInstantiations()
19 {
23  RSASS<PKCS1v15, SHA1>::Verifier x4(x2.GetKey());
25 #ifndef __MWERKS__
27  x3 = x2;
28  x6 = x2;
29 #endif
31 #ifndef __GNUC__
33 #endif
34  RSAES<OAEP<SHA1> >::Encryptor x9(x2);
35  x4 = x2.GetKey();
36 
40  RSASS<PKCS1v15, SHA3_256>::Verifier x13(x11.GetKey());
41 }
42 NAMESPACE_END
43 #endif
44 
45 #ifndef CRYPTOPP_IMPORTS
46 
47 NAMESPACE_BEGIN(CryptoPP)
48 
49 OID RSAFunction::GetAlgorithmID() const
50 {
51  return ASN1::rsaEncryption();
52 }
53 
55 {
56  BERSequenceDecoder seq(bt);
57  m_n.BERDecode(seq);
58  m_e.BERDecode(seq);
59  seq.MessageEnd();
60 }
61 
63 {
64  DERSequenceEncoder seq(bt);
65  m_n.DEREncode(seq);
66  m_e.DEREncode(seq);
67  seq.MessageEnd();
68 }
69 
71 {
73  return a_exp_b_mod_c(x, m_e, m_n);
74 }
75 
76 bool RSAFunction::Validate(RandomNumberGenerator& rng, unsigned int level) const
77 {
78  CRYPTOPP_UNUSED(rng), CRYPTOPP_UNUSED(level);
79 
80  bool pass = true;
81  pass = pass && m_n > Integer::One() && m_n.IsOdd();
82  CRYPTOPP_ASSERT(pass);
83  pass = pass && m_e > Integer::One() && m_e.IsOdd() && m_e < m_n;
84  CRYPTOPP_ASSERT(pass);
85  return pass;
86 }
87 
88 bool RSAFunction::GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const
89 {
90  return GetValueHelper(this, name, valueType, pValue).Assignable()
91  CRYPTOPP_GET_FUNCTION_ENTRY(Modulus)
92  CRYPTOPP_GET_FUNCTION_ENTRY(PublicExponent)
93  ;
94 }
95 
97 {
98  AssignFromHelper(this, source)
99  CRYPTOPP_SET_FUNCTION_ENTRY(Modulus)
100  CRYPTOPP_SET_FUNCTION_ENTRY(PublicExponent)
101  ;
102 }
103 
104 // *****************************************************************************
105 
107 {
108 public:
109  RSAPrimeSelector(const Integer &e) : m_e(e) {}
110  bool IsAcceptable(const Integer &candidate) const {return RelativelyPrime(m_e, candidate-Integer::One());}
111  Integer m_e;
112 };
113 
115 {
116  int modulusSize = 2048;
117  alg.GetIntValue(Name::ModulusSize(), modulusSize) || alg.GetIntValue(Name::KeySize(), modulusSize);
118 
119  CRYPTOPP_ASSERT(modulusSize >= 16);
120  if (modulusSize < 16)
121  throw InvalidArgument("InvertibleRSAFunction: specified modulus size is too small");
122 
124 
125  CRYPTOPP_ASSERT(m_e >= 3); CRYPTOPP_ASSERT(!m_e.IsEven());
126  if (m_e < 3 || m_e.IsEven())
127  throw InvalidArgument("InvertibleRSAFunction: invalid public exponent");
128 
129  RSAPrimeSelector selector(m_e);
130  AlgorithmParameters primeParam = MakeParametersForTwoPrimesOfEqualSize(modulusSize)
131  (Name::PointerToPrimeSelector(), selector.GetSelectorPointer());
132  m_p.GenerateRandom(rng, primeParam);
133  m_q.GenerateRandom(rng, primeParam);
134 
135  m_d = m_e.InverseMod(LCM(m_p-1, m_q-1));
136  CRYPTOPP_ASSERT(m_d.IsPositive());
137 
138  m_dp = m_d % (m_p-1);
139  m_dq = m_d % (m_q-1);
140  m_n = m_p * m_q;
141  m_u = m_q.InverseMod(m_p);
142 
144  {
145  RSASS<PKCS1v15, SHA1>::Signer signer(*this);
146  RSASS<PKCS1v15, SHA1>::Verifier verifier(signer);
147  SignaturePairwiseConsistencyTest_FIPS_140_Only(signer, verifier);
148 
149  RSAES<OAEP<SHA1> >::Decryptor decryptor(*this);
150  RSAES<OAEP<SHA1> >::Encryptor encryptor(decryptor);
151  EncryptionPairwiseConsistencyTest_FIPS_140_Only(encryptor, decryptor);
152  }
153 }
154 
155 void InvertibleRSAFunction::Initialize(RandomNumberGenerator &rng, unsigned int keybits, const Integer &e)
156 {
157  GenerateRandom(rng, MakeParameters(Name::ModulusSize(), (int)keybits)(Name::PublicExponent(), e+e.IsEven()));
158 }
159 
160 void InvertibleRSAFunction::Initialize(const Integer &n, const Integer &e, const Integer &d)
161 {
162  if (n.IsEven() || e.IsEven() | d.IsEven())
163  throw InvalidArgument("InvertibleRSAFunction: input is not a valid RSA private key");
164 
165  m_n = n;
166  m_e = e;
167  m_d = d;
168 
169  Integer r = --(d*e);
170  unsigned int s = 0;
171  while (r.IsEven())
172  {
173  r >>= 1;
174  s++;
175  }
176 
177  ModularArithmetic modn(n);
178  for (Integer i = 2; ; ++i)
179  {
180  Integer a = modn.Exponentiate(i, r);
181  if (a == 1)
182  continue;
183  Integer b;
184  unsigned int j = 0;
185  while (a != n-1)
186  {
187  b = modn.Square(a);
188  if (b == 1)
189  {
190  m_p = GCD(a-1, n);
191  m_q = n/m_p;
192  m_dp = m_d % (m_p-1);
193  m_dq = m_d % (m_q-1);
194  m_u = m_q.InverseMod(m_p);
195  return;
196  }
197  if (++j == s)
198  throw InvalidArgument("InvertibleRSAFunction: input is not a valid RSA private key");
199  a = b;
200  }
201  }
202 }
203 
205 {
206  BERSequenceDecoder privateKey(bt);
207  word32 version;
208  BERDecodeUnsigned<word32>(privateKey, version, INTEGER, 0, 0); // check version
209  m_n.BERDecode(privateKey);
210  m_e.BERDecode(privateKey);
211  m_d.BERDecode(privateKey);
212  m_p.BERDecode(privateKey);
213  m_q.BERDecode(privateKey);
214  m_dp.BERDecode(privateKey);
215  m_dq.BERDecode(privateKey);
216  m_u.BERDecode(privateKey);
217  privateKey.MessageEnd();
218 }
219 
221 {
222  DERSequenceEncoder privateKey(bt);
223  DEREncodeUnsigned<word32>(privateKey, 0); // version
224  m_n.DEREncode(privateKey);
225  m_e.DEREncode(privateKey);
226  m_d.DEREncode(privateKey);
227  m_p.DEREncode(privateKey);
228  m_q.DEREncode(privateKey);
229  m_dp.DEREncode(privateKey);
230  m_dq.DEREncode(privateKey);
231  m_u.DEREncode(privateKey);
232  privateKey.MessageEnd();
233 }
234 
236 {
238  ModularArithmetic modn(m_n);
239  Integer r, rInv;
240  do { // do this in a loop for people using small numbers for testing
241  r.Randomize(rng, Integer::One(), m_n - Integer::One());
242  rInv = modn.MultiplicativeInverse(r);
243  } while (rInv.IsZero());
244  Integer re = modn.Exponentiate(r, m_e);
245  re = modn.Multiply(re, x); // blind
246  // here we follow the notation of PKCS #1 and let u=q inverse mod p
247  // but in ModRoot, u=p inverse mod q, so we reverse the order of p and q
248  Integer y = ModularRoot(re, m_dq, m_dp, m_q, m_p, m_u);
249  y = modn.Multiply(y, rInv); // unblind
250  if (modn.Exponentiate(y, m_e) != x) // check
251  throw Exception(Exception::OTHER_ERROR, "InvertibleRSAFunction: computational error during private key operation");
252  return y;
253 }
254 
255 bool InvertibleRSAFunction::Validate(RandomNumberGenerator &rng, unsigned int level) const
256 {
257  bool pass = RSAFunction::Validate(rng, level);
258  CRYPTOPP_ASSERT(pass);
259  pass = pass && m_p > Integer::One() && m_p.IsOdd() && m_p < m_n;
260  CRYPTOPP_ASSERT(pass);
261  pass = pass && m_q > Integer::One() && m_q.IsOdd() && m_q < m_n;
262  CRYPTOPP_ASSERT(pass);
263  pass = pass && m_d > Integer::One() && m_d.IsOdd() && m_d < m_n;
264  CRYPTOPP_ASSERT(pass);
265  pass = pass && m_dp > Integer::One() && m_dp.IsOdd() && m_dp < m_p;
266  CRYPTOPP_ASSERT(pass);
267  pass = pass && m_dq > Integer::One() && m_dq.IsOdd() && m_dq < m_q;
268  CRYPTOPP_ASSERT(pass);
269  pass = pass && m_u.IsPositive() && m_u < m_p;
270  CRYPTOPP_ASSERT(pass);
271  if (level >= 1)
272  {
273  pass = pass && m_p * m_q == m_n;
274  CRYPTOPP_ASSERT(pass);
275  pass = pass && m_e*m_d % LCM(m_p-1, m_q-1) == 1;
276  CRYPTOPP_ASSERT(pass);
277  pass = pass && m_dp == m_d%(m_p-1) && m_dq == m_d%(m_q-1);
278  CRYPTOPP_ASSERT(pass);
279  pass = pass && m_u * m_q % m_p == 1;
280  CRYPTOPP_ASSERT(pass);
281  }
282  if (level >= 2)
283  {
284  pass = pass && VerifyPrime(rng, m_p, level-2) && VerifyPrime(rng, m_q, level-2);
285  CRYPTOPP_ASSERT(pass);
286  }
287  return pass;
288 }
289 
290 bool InvertibleRSAFunction::GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const
291 {
292  return GetValueHelper<RSAFunction>(this, name, valueType, pValue).Assignable()
293  CRYPTOPP_GET_FUNCTION_ENTRY(Prime1)
294  CRYPTOPP_GET_FUNCTION_ENTRY(Prime2)
295  CRYPTOPP_GET_FUNCTION_ENTRY(PrivateExponent)
296  CRYPTOPP_GET_FUNCTION_ENTRY(ModPrime1PrivateExponent)
297  CRYPTOPP_GET_FUNCTION_ENTRY(ModPrime2PrivateExponent)
298  CRYPTOPP_GET_FUNCTION_ENTRY(MultiplicativeInverseOfPrime2ModPrime1)
299  ;
300 }
301 
303 {
304  AssignFromHelper<RSAFunction>(this, source)
305  CRYPTOPP_SET_FUNCTION_ENTRY(Prime1)
306  CRYPTOPP_SET_FUNCTION_ENTRY(Prime2)
307  CRYPTOPP_SET_FUNCTION_ENTRY(PrivateExponent)
308  CRYPTOPP_SET_FUNCTION_ENTRY(ModPrime1PrivateExponent)
309  CRYPTOPP_SET_FUNCTION_ENTRY(ModPrime2PrivateExponent)
310  CRYPTOPP_SET_FUNCTION_ENTRY(MultiplicativeInverseOfPrime2ModPrime1)
311  ;
312 }
313 
314 // *****************************************************************************
315 
317 {
319  return t % 16 == 12 ? t : m_n - t;
320 }
321 
323 {
325  return STDMIN(t, m_n-t);
326 }
327 
328 NAMESPACE_END
329 
330 #endif
Base class for all exceptions thrown by the library.
Definition: cryptlib.h:157
const char * MultiplicativeInverseOfPrime2ModPrime1()
Integer.
Definition: argnames.h:47
An invalid argument was detected.
Definition: cryptlib.h:201
Classes for working with NameValuePairs.
const Integer & Square(const Integer &a) const
Square an element in the ring.
Definition: modarith.h:182
const char * Prime2()
Integer.
Definition: argnames.h:44
T GetValueWithDefault(const char *name, T defaultValue) const
Get a named value.
Definition: cryptlib.h:365
void DEREncode(BufferedTransformation &bt) const
Encode in DER format.
Definition: integer.cpp:3397
void BERDecodePrivateKey(BufferedTransformation &bt, bool parametersPresent, size_t size)
decode privateKey part of privateKeyInfo, without the OCTET STRING header
Definition: rsa.cpp:204
void GenerateRandom(RandomNumberGenerator &rng, const NameValuePairs &alg)
Generate a random key or crypto parameters.
Definition: rsa.cpp:114
bool GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const
Get a named value.
Definition: rsa.cpp:290
const Integer & MultiplicativeInverse(const Integer &a) const
Calculate the multiplicative inverse of an element in the ring.
Definition: modarith.h:195
Some other error occurred not belonging to other categories.
Definition: cryptlib.h:176
ASN.1 object identifiers for algorthms and schemes.
Ring of congruence classes modulo n.
Definition: modarith.h:39
Interface for random number generators.
Definition: cryptlib.h:1333
void Randomize(RandomNumberGenerator &rng, size_t bitCount)
Set this Integer to random integer.
Definition: integer.cpp:3468
Integer InverseMod(const Integer &n) const
calculate multiplicative inverse of *this mod n
Definition: integer.cpp:4380
bool Validate(RandomNumberGenerator &rng, unsigned int level) const
Check this object for errors.
Definition: rsa.cpp:255
BER Sequence Decoder.
Definition: asn.h:303
Interface for buffered transformations.
Definition: cryptlib.h:1480
static const Integer & One()
Integer representing 1.
Definition: integer.cpp:4802
void BERDecodePublicKey(BufferedTransformation &bt, bool parametersPresent, size_t size)
decode subjectPublicKey part of subjectPublicKeyInfo, without the BIT STRING header ...
Definition: rsa.cpp:54
const char * PrivateExponent()
Integer.
Definition: argnames.h:35
Integer ApplyFunction(const Integer &x) const
Applies the trapdoor.
Definition: rsa.cpp:70
bool GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const
Get a named value.
Definition: rsa.cpp:88
const char * Prime1()
Integer.
Definition: argnames.h:43
void DoQuickSanityCheck() const
Perform a quick sanity check.
Definition: cryptlib.h:2270
bool FIPS_140_2_ComplianceEnabled()
Determines whether the library provides FIPS validated cryptography.
Definition: fips140.cpp:29
Classes for PKCS padding schemes.
void Initialize(RandomNumberGenerator &rng, unsigned int modulusBits, const Integer &e=17)
Create a RSA private key.
Definition: rsa.cpp:155
const Integer & Multiply(const Integer &a, const Integer &b) const
Multiplies elements in the ring.
Definition: modarith.h:175
AlgorithmParameters MakeParameters(const char *name, const T &value, bool throwIfNotUsed=true)
Create an object that implements NameValuePairs.
Definition: algparam.h:516
const char * PublicExponent()
Integer.
Definition: argnames.h:34
bool IsZero() const
Determines if the Integer is 0.
Definition: integer.h:330
bool VerifyPrime(RandomNumberGenerator &rng, const Integer &p, unsigned int level=1)
Verifies a prime number.
Definition: nbtheory.cpp:247
void AssignFrom(const NameValuePairs &source)
Assign values to this object.
Definition: rsa.cpp:96
const char * ModPrime1PrivateExponent()
Integer.
Definition: argnames.h:45
Classes for SHA3 message digests.
Application callback to signal suitability of a cabdidate prime.
Definition: nbtheory.h:80
Multiple precision integer with arithmetic operations.
Definition: integer.h:49
virtual Element Exponentiate(const Element &a, const Integer &e) const
Raises a base to an exponent in the group.
Definition: algebra.cpp:316
const char * ModPrime2PrivateExponent()
Integer.
Definition: argnames.h:46
void AssignFrom(const NameValuePairs &source)
Assign values to this object.
Definition: rsa.cpp:302
Integer CalculateInverse(RandomNumberGenerator &rng, const Integer &x) const
Calculates the inverse of an element.
Definition: rsa.cpp:235
bool IsEven() const
Determines if the Integer is even parity.
Definition: integer.h:348
RandomNumberGenerator & NullRNG()
Random Number Generator that does not produce random numbers.
Definition: cryptlib.cpp:378
const T & STDMIN(const T &a, const T &b)
Replacement function for std::min.
Definition: misc.h:499
#define CRYPTOPP_ASSERT(exp)
Debugging and diagnostic assertion.
Definition: trap.h:60
Classes and functions for working with ANS.1 objects.
Classes for SHA-1 and SHA-2 family of message digests.
const char * PointerToPrimeSelector()
const PrimeSelector *
Definition: argnames.h:42
Classes and functions for number theoretic operations.
const char * KeySize()
int, in bits
Definition: argnames.h:29
DER Sequence Encoder.
Definition: asn.h:313
Classes for the RSA cryptosystem.
bool Validate(RandomNumberGenerator &rng, unsigned int level) const
Check this object for errors.
Definition: rsa.cpp:76
Classes and functions for the FIPS 140-2 validated library.
Integer CalculateInverse(RandomNumberGenerator &rng, const Integer &x) const
Calculates the inverse of an element.
Definition: rsa.cpp:322
An object that implements NameValuePairs.
Definition: algparam.h:433
const char * Modulus()
Integer.
Definition: argnames.h:33
RSA encryption algorithm.
Definition: rsa.h:178
Integer ApplyFunction(const Integer &x) const
Applies the trapdoor.
Definition: rsa.cpp:316
void BERDecode(const byte *input, size_t inputLen)
Decode from BER format.
Definition: integer.cpp:3404
Class file for performing modular arithmetic.
Crypto++ library namespace.
const char * ModulusSize()
int, in bits
Definition: argnames.h:30
bool GetIntValue(const char *name, int &value) const
Get a named value with type int.
Definition: cryptlib.h:388
void DEREncodePublicKey(BufferedTransformation &bt) const
encode subjectPublicKey part of subjectPublicKeyInfo, without the BIT STRING header ...
Definition: rsa.cpp:62
Object Identifier.
Definition: asn.h:166
Classes for probablistic signature schemes.
void DEREncodePrivateKey(BufferedTransformation &bt) const
encode privateKey part of privateKeyInfo, without the OCTET STRING header
Definition: rsa.cpp:220
RSA trapdoor function using the public key.
Definition: rsa.h:24
bool IsOdd() const
Determines if the Integer is odd parity.
Definition: integer.h:351
Interface for retrieving values given their names.
Definition: cryptlib.h:294
Template implementing constructors for public key algorithm classes.
Definition: pubkey.h:2106