Crypto++  8.1
Free C++ class library of cryptographic schemes
mqv.h
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1 // mqv.h - originally written and placed in the public domain by Wei Dai
2 
3 /// \file mqv.h
4 /// \brief Classes for Menezes–Qu–Vanstone (MQV) key agreement
5 /// \since Crypto++ 3.0
6 
7 #ifndef CRYPTOPP_MQV_H
8 #define CRYPTOPP_MQV_H
9 
10 #include "cryptlib.h"
11 #include "gfpcrypt.h"
12 #include "modarith.h"
13 #include "integer.h"
14 #include "algebra.h"
15 #include "misc.h"
16 
17 NAMESPACE_BEGIN(CryptoPP)
18 
19 /// \brief MQV domain for performing authenticated key agreement
20 /// \tparam GROUP_PARAMETERS doamin parameters
21 /// \tparam COFACTOR_OPTION cofactor option
22 /// \details GROUP_PARAMETERS parameters include the curve coefcients and the base point.
23 /// Binary curves use a polynomial to represent its characteristic, while prime curves
24 /// use a prime number.
25 /// \sa MQV, HMQV, FHMQV, and AuthenticatedKeyAgreementDomain
26 /// \since Crypto++ 3.0
27 template <class GROUP_PARAMETERS, class COFACTOR_OPTION = typename GROUP_PARAMETERS::DefaultCofactorOption>
29 {
30 public:
31  typedef GROUP_PARAMETERS GroupParameters;
32  typedef typename GroupParameters::Element Element;
34 
35  /// \brief Construct a MQV domain
37 
38  /// \brief Construct a MQV domain
39  /// \param params group parameters and options
40  MQV_Domain(const GroupParameters &params)
41  : m_groupParameters(params) {}
42 
43  /// \brief Construct a MQV domain
44  /// \param bt BufferedTransformation with group parameters and options
46  {m_groupParameters.BERDecode(bt);}
47 
48  /// \brief Construct a MQV domain
49  /// \tparam T1 template parameter used as a constructor parameter
50  /// \tparam T2 template parameter used as a constructor parameter
51  /// \param v1 first parameter
52  /// \param v2 second parameter
53  /// \details v1 and v2 are passed directly to the GROUP_PARAMETERS object.
54  template <class T1, class T2>
55  MQV_Domain(T1 v1, T2 v2)
56  {m_groupParameters.Initialize(v1, v2);}
57 
58  /// \brief Construct a MQV domain
59  /// \tparam T1 template parameter used as a constructor parameter
60  /// \tparam T2 template parameter used as a constructor parameter
61  /// \tparam T3 template parameter used as a constructor parameter
62  /// \param v1 first parameter
63  /// \param v2 second parameter
64  /// \param v3 third parameter
65  /// \details v1, v2 and v3 are passed directly to the GROUP_PARAMETERS object.
66  template <class T1, class T2, class T3>
67  MQV_Domain(T1 v1, T2 v2, T3 v3)
68  {m_groupParameters.Initialize(v1, v2, v3);}
69 
70  /// \brief Construct a MQV domain
71  /// \tparam T1 template parameter used as a constructor parameter
72  /// \tparam T2 template parameter used as a constructor parameter
73  /// \tparam T3 template parameter used as a constructor parameter
74  /// \tparam T4 template parameter used as a constructor parameter
75  /// \param v1 first parameter
76  /// \param v2 second parameter
77  /// \param v3 third parameter
78  /// \param v4 third parameter
79  /// \details v1, v2, v3 and v4 are passed directly to the GROUP_PARAMETERS object.
80  template <class T1, class T2, class T3, class T4>
81  MQV_Domain(T1 v1, T2 v2, T3 v3, T4 v4)
82  {m_groupParameters.Initialize(v1, v2, v3, v4);}
83 
84  /// \brief Retrieves the group parameters for this domain
85  /// \return the group parameters for this domain as a const reference
86  const GroupParameters & GetGroupParameters() const {return m_groupParameters;}
87 
88  /// \brief Retrieves the group parameters for this domain
89  /// \return the group parameters for this domain as a non-const reference
90  GroupParameters & AccessGroupParameters() {return m_groupParameters;}
91 
92  /// \brief Retrieves the crypto parameters for this domain
93  /// \return the crypto parameters for this domain as a non-const reference
94  CryptoParameters & AccessCryptoParameters() {return AccessAbstractGroupParameters();}
95 
96  /// \brief Provides the size of the agreed value
97  /// \return size of agreed value produced in this domain
98  /// \details The length is calculated using <tt>GetEncodedElementSize(false)</tt>, which means the
99  /// element is encoded in a non-reversible format. A non-reversible format means its a raw byte array,
100  /// and it lacks presentation format like an ASN.1 BIT_STRING or OCTET_STRING.
101  unsigned int AgreedValueLength() const {return GetAbstractGroupParameters().GetEncodedElementSize(false);}
102 
103  /// \brief Provides the size of the static private key
104  /// \return size of static private keys in this domain
105  /// \details The length is calculated using the byte count of the subgroup order.
106  unsigned int StaticPrivateKeyLength() const {return GetAbstractGroupParameters().GetSubgroupOrder().ByteCount();}
107 
108  /// \brief Provides the size of the static public key
109  /// \return size of static public keys in this domain
110  /// \details The length is calculated using <tt>GetEncodedElementSize(true)</tt>, which means the
111  /// element is encoded in a reversible format. A reversible format means it has a presentation format,
112  /// and its an ANS.1 encoded element or point.
113  unsigned int StaticPublicKeyLength() const {return GetAbstractGroupParameters().GetEncodedElementSize(true);}
114 
115  /// \brief Generate static private key in this domain
116  /// \param rng a RandomNumberGenerator derived class
117  /// \param privateKey a byte buffer for the generated private key in this domain
118  /// \details The private key is a random scalar used as an exponent in the range <tt>[1,MaxExponent()]</tt>.
119  /// \pre <tt>COUNTOF(privateKey) == PrivateStaticKeyLength()</tt>
120  void GenerateStaticPrivateKey(RandomNumberGenerator &rng, byte *privateKey) const
121  {
122  Integer x(rng, Integer::One(), GetAbstractGroupParameters().GetMaxExponent());
123  x.Encode(privateKey, StaticPrivateKeyLength());
124  }
125 
126  /// \brief Generate a static public key from a private key in this domain
127  /// \param rng a RandomNumberGenerator derived class
128  /// \param privateKey a byte buffer with the previously generated private key
129  /// \param publicKey a byte buffer for the generated public key in this domain
130  /// \details The public key is an element or point on the curve, and its stored in a revrsible format.
131  /// A reversible format means it has a presentation format, and its an ANS.1 encoded element or point.
132  /// \pre <tt>COUNTOF(publicKey) == PublicStaticKeyLength()</tt>
133  void GenerateStaticPublicKey(RandomNumberGenerator &rng, const byte *privateKey, byte *publicKey) const
134  {
135  CRYPTOPP_UNUSED(rng);
136  const DL_GroupParameters<Element> &params = GetAbstractGroupParameters();
137  Integer x(privateKey, StaticPrivateKeyLength());
138  Element y = params.ExponentiateBase(x);
139  params.EncodeElement(true, y, publicKey);
140  }
141 
143  unsigned int EphemeralPublicKeyLength() const {return StaticPublicKeyLength();}
144 
145  void GenerateEphemeralPrivateKey(RandomNumberGenerator &rng, byte *privateKey) const
146  {
147  const DL_GroupParameters<Element> &params = GetAbstractGroupParameters();
148  Integer x(rng, Integer::One(), params.GetMaxExponent());
149  x.Encode(privateKey, StaticPrivateKeyLength());
150  Element y = params.ExponentiateBase(x);
151  params.EncodeElement(true, y, privateKey+StaticPrivateKeyLength());
152  }
153 
154  void GenerateEphemeralPublicKey(RandomNumberGenerator &rng, const byte *privateKey, byte *publicKey) const
155  {
156  CRYPTOPP_UNUSED(rng);
157  memcpy(publicKey, privateKey+StaticPrivateKeyLength(), EphemeralPublicKeyLength());
158  }
159 
160  bool Agree(byte *agreedValue,
161  const byte *staticPrivateKey, const byte *ephemeralPrivateKey,
162  const byte *staticOtherPublicKey, const byte *ephemeralOtherPublicKey,
163  bool validateStaticOtherPublicKey=true) const
164  {
165  try
166  {
167  const DL_GroupParameters<Element> &params = GetAbstractGroupParameters();
168  Element WW = params.DecodeElement(staticOtherPublicKey, validateStaticOtherPublicKey);
169  Element VV = params.DecodeElement(ephemeralOtherPublicKey, true);
170 
171  Integer s(staticPrivateKey, StaticPrivateKeyLength());
172  Integer u(ephemeralPrivateKey, StaticPrivateKeyLength());
173  Element V = params.DecodeElement(ephemeralPrivateKey+StaticPrivateKeyLength(), false);
174 
175  const Integer &r = params.GetSubgroupOrder();
176  Integer h2 = Integer::Power2((r.BitCount()+1)/2);
177  Integer e = ((h2+params.ConvertElementToInteger(V)%h2)*s+u) % r;
178  Integer tt = h2 + params.ConvertElementToInteger(VV) % h2;
179 
180  if (COFACTOR_OPTION::ToEnum() == NO_COFACTOR_MULTIPLICTION)
181  {
182  Element P = params.ExponentiateElement(WW, tt);
183  P = m_groupParameters.MultiplyElements(P, VV);
184  Element R[2];
185  const Integer e2[2] = {r, e};
186  params.SimultaneousExponentiate(R, P, e2, 2);
187  if (!params.IsIdentity(R[0]) || params.IsIdentity(R[1]))
188  return false;
189  params.EncodeElement(false, R[1], agreedValue);
190  }
191  else
192  {
193  const Integer &k = params.GetCofactor();
194  if (COFACTOR_OPTION::ToEnum() == COMPATIBLE_COFACTOR_MULTIPLICTION)
195  e = ModularArithmetic(r).Divide(e, k);
196  Element P = m_groupParameters.CascadeExponentiate(VV, k*e, WW, k*(e*tt%r));
197  if (params.IsIdentity(P))
198  return false;
199  params.EncodeElement(false, P, agreedValue);
200  }
201  }
202  catch (DL_BadElement &)
203  {
204  return false;
205  }
206  return true;
207  }
208 
209 private:
210  DL_GroupParameters<Element> & AccessAbstractGroupParameters() {return m_groupParameters;}
211  const DL_GroupParameters<Element> & GetAbstractGroupParameters() const {return m_groupParameters;}
212 
213  GroupParameters m_groupParameters;
214 };
215 
216 /// Menezes-Qu-Vanstone in GF(p) with key validation, AKA <a href="http://www.weidai.com/scan-mirror/ka.html#MQV">MQV</a>
217 /// \sa MQV, HMQV_Domain, FHMQV_Domain, AuthenticatedKeyAgreementDomain
218 /// \since Crypto++ 3.0
220 
221 NAMESPACE_END
222 
223 #endif
void GenerateStaticPublicKey(RandomNumberGenerator &rng, const byte *privateKey, byte *publicKey) const
Generate a static public key from a private key in this domain.
Definition: mqv.h:133
MQV_Domain(T1 v1, T2 v2)
Construct a MQV domain.
Definition: mqv.h:55
virtual Integer GetCofactor() const
Retrieves the cofactor.
Definition: pubkey.h:884
const Integer & Divide(const Integer &a, const Integer &b) const
Divides elements in the ring.
Definition: modarith.h:202
Utility functions for the Crypto++ library.
bool Agree(byte *agreedValue, const byte *staticPrivateKey, const byte *ephemeralPrivateKey, const byte *staticOtherPublicKey, const byte *ephemeralOtherPublicKey, bool validateStaticOtherPublicKey=true) const
Derive agreed value.
Definition: mqv.h:160
Interface for Discrete Log (DL) group parameters.
Definition: pubkey.h:753
MQV_Domain(T1 v1, T2 v2, T3 v3, T4 v4)
Construct a MQV domain.
Definition: mqv.h:81
Abstract base classes that provide a uniform interface to this library.
virtual Integer ConvertElementToInteger(const Element &element) const =0
Converts an element to an Integer.
Ring of congruence classes modulo n.
Definition: modarith.h:38
Interface for random number generators.
Definition: cryptlib.h:1383
MQV_Domain(BufferedTransformation &bt)
Construct a MQV domain.
Definition: mqv.h:45
Classes for performing mathematics over different fields.
Interface for buffered transformations.
Definition: cryptlib.h:1598
virtual Element ExponentiateBase(const Integer &exponent) const
Exponentiates the base.
Definition: pubkey.h:839
static const Integer & One()
Integer representing 1.
Definition: integer.cpp:4868
MQV_Domain< DL_GroupParameters_GFP_DefaultSafePrime > MQV
Menezes-Qu-Vanstone in GF(p) with key validation, AKA MQV
Definition: mqv.h:219
Cofactor multiplication compatible with ordinary Diffie-Hellman.
Definition: pubkey.h:2066
MQV domain for performing authenticated key agreement.
Definition: mqv.h:28
No cofactor multiplication applied.
Definition: pubkey.h:2062
virtual void SimultaneousExponentiate(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const =0
Exponentiates a base to multiple exponents.
static Integer Power2(size_t e)
Exponentiates to a power of 2.
Definition: integer.cpp:3079
Multiple precision integer with arithmetic operations.
Definition: integer.h:49
unsigned int EphemeralPublicKeyLength() const
Provides the size of ephemeral public key.
Definition: mqv.h:143
unsigned int StaticPrivateKeyLength() const
Provides the size of the static private key.
Definition: mqv.h:106
Classes and functions for schemes based on Discrete Logs (DL) over GF(p)
virtual Element DecodeElement(const byte *encoded, bool checkForGroupMembership) const =0
Decodes the element.
void GenerateEphemeralPrivateKey(RandomNumberGenerator &rng, byte *privateKey) const
Generate ephemeral private key.
Definition: mqv.h:145
Exception thrown when an invalid group element is encountered.
Definition: pubkey.h:743
void GenerateEphemeralPublicKey(RandomNumberGenerator &rng, const byte *privateKey, byte *publicKey) const
Generate ephemeral public key.
Definition: mqv.h:154
unsigned int BitCount() const
Determines the number of bits required to represent the Integer.
Definition: integer.cpp:3345
void GenerateStaticPrivateKey(RandomNumberGenerator &rng, byte *privateKey) const
Generate static private key in this domain.
Definition: mqv.h:120
unsigned int StaticPublicKeyLength() const
Provides the size of the static public key.
Definition: mqv.h:113
MQV_Domain(const GroupParameters &params)
Construct a MQV domain.
Definition: mqv.h:40
virtual void EncodeElement(bool reversible, const Element &element, byte *encoded) const =0
Encodes the element.
Multiple precision integer with arithmetic operations.
MQV_Domain(T1 v1, T2 v2, T3 v3)
Construct a MQV domain.
Definition: mqv.h:67
MQV_Domain()
Construct a MQV domain.
Definition: mqv.h:36
Interface for crypto prameters.
Definition: cryptlib.h:2435
virtual Integer GetMaxExponent() const =0
Retrieves the maximum exponent for the group.
CryptoParameters & AccessCryptoParameters()
Retrieves the crypto parameters for this domain.
Definition: mqv.h:94
unsigned int EphemeralPrivateKeyLength() const
Provides the size of ephemeral private key.
Definition: mqv.h:142
Class file for performing modular arithmetic.
Crypto++ library namespace.
unsigned int AgreedValueLength() const
Provides the size of the agreed value.
Definition: mqv.h:101
Interface for domains of authenticated key agreement protocols.
Definition: cryptlib.h:2956
GroupParameters & AccessGroupParameters()
Retrieves the group parameters for this domain.
Definition: mqv.h:90
const GroupParameters & GetGroupParameters() const
Retrieves the group parameters for this domain.
Definition: mqv.h:86
virtual Element ExponentiateElement(const Element &base, const Integer &exponent) const
Exponentiates an element.
Definition: pubkey.h:849
virtual bool IsIdentity(const Element &element) const =0
Determines if an element is an identity.
virtual const Integer & GetSubgroupOrder() const =0
Retrieves the subgroup order.