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// mqv.h - originally written and placed in the public domain by Wei Dai
/// \file mqv.h
/// \brief Classes for Menezes–Qu–Vanstone (MQV) key agreement
#ifndef CRYPTOPP_MQV_H
#define CRYPTOPP_MQV_H
#include "cryptlib.h"
#include "gfpcrypt.h"
#include "modarith.h"
#include "integer.h"
#include "algebra.h"
#include "misc.h"
NAMESPACE_BEGIN(CryptoPP)
/// \brief MQV domain for performing authenticated key agreement
/// \tparam GROUP_PARAMETERS doamin parameters
/// \tparam COFACTOR_OPTION cofactor option
/// \details GROUP_PARAMETERS parameters include the curve coefcients and the base point.
/// Binary curves use a polynomial to represent its characteristic, while prime curves
/// use a prime number.
/// \sa MQV, HMQV, FHMQV, and AuthenticatedKeyAgreementDomain
template <class GROUP_PARAMETERS, class COFACTOR_OPTION = typename GROUP_PARAMETERS::DefaultCofactorOption>
class MQV_Domain : public AuthenticatedKeyAgreementDomain
{
public:
typedef GROUP_PARAMETERS GroupParameters;
typedef typename GroupParameters::Element Element;
typedef MQV_Domain<GROUP_PARAMETERS, COFACTOR_OPTION> Domain;
/// \brief Construct a MQV domain
MQV_Domain() {}
/// \brief Construct a MQV domain
/// \param params group parameters and options
MQV_Domain(const GroupParameters ¶ms)
: m_groupParameters(params) {}
/// \brief Construct a MQV domain
/// \param bt BufferedTransformation with group parameters and options
MQV_Domain(BufferedTransformation &bt)
{m_groupParameters.BERDecode(bt);}
/// \brief Construct a MQV domain
/// \tparam T1 template parameter used as a constructor parameter
/// \tparam T2 template parameter used as a constructor parameter
/// \param v1 first parameter
/// \param v2 second parameter
/// \details v1 and v2 are passed directly to the GROUP_PARAMETERS object.
template <class T1, class T2>
MQV_Domain(T1 v1, T2 v2)
{m_groupParameters.Initialize(v1, v2);}
/// \brief Construct a MQV domain
/// \tparam T1 template parameter used as a constructor parameter
/// \tparam T2 template parameter used as a constructor parameter
/// \tparam T3 template parameter used as a constructor parameter
/// \param v1 first parameter
/// \param v2 second parameter
/// \param v3 third parameter
/// \details v1, v2 and v3 are passed directly to the GROUP_PARAMETERS object.
template <class T1, class T2, class T3>
MQV_Domain(T1 v1, T2 v2, T3 v3)
{m_groupParameters.Initialize(v1, v2, v3);}
/// \brief Construct a MQV domain
/// \tparam T1 template parameter used as a constructor parameter
/// \tparam T2 template parameter used as a constructor parameter
/// \tparam T3 template parameter used as a constructor parameter
/// \tparam T4 template parameter used as a constructor parameter
/// \param v1 first parameter
/// \param v2 second parameter
/// \param v3 third parameter
/// \param v4 third parameter
/// \details v1, v2, v3 and v4 are passed directly to the GROUP_PARAMETERS object.
template <class T1, class T2, class T3, class T4>
MQV_Domain(T1 v1, T2 v2, T3 v3, T4 v4)
{m_groupParameters.Initialize(v1, v2, v3, v4);}
/// \brief Retrieves the group parameters for this domain
/// \return the group parameters for this domain as a const reference
const GroupParameters & GetGroupParameters() const {return m_groupParameters;}
/// \brief Retrieves the group parameters for this domain
/// \return the group parameters for this domain as a non-const reference
GroupParameters & AccessGroupParameters() {return m_groupParameters;}
/// \brief Retrieves the crypto parameters for this domain
/// \return the crypto parameters for this domain as a non-const reference
CryptoParameters & AccessCryptoParameters() {return AccessAbstractGroupParameters();}
/// \brief Provides the size of the agreed value
/// \return size of agreed value produced in this domain
/// \details The length is calculated using <tt>GetEncodedElementSize(false)</tt>, which means the
/// element is encoded in a non-reversible format. A non-reversible format means its a raw byte array,
/// and it lacks presentation format like an ASN.1 BIT_STRING or OCTET_STRING.
unsigned int AgreedValueLength() const {return GetAbstractGroupParameters().GetEncodedElementSize(false);}
/// \brief Provides the size of the static private key
/// \return size of static private keys in this domain
/// \details The length is calculated using the byte count of the subgroup order.
unsigned int StaticPrivateKeyLength() const {return GetAbstractGroupParameters().GetSubgroupOrder().ByteCount();}
/// \brief Provides the size of the static public key
/// \return size of static public keys in this domain
/// \details The length is calculated using <tt>GetEncodedElementSize(true)</tt>, which means the
/// element is encoded in a reversible format. A reversible format means it has a presentation format,
/// and its an ANS.1 encoded element or point.
unsigned int StaticPublicKeyLength() const {return GetAbstractGroupParameters().GetEncodedElementSize(true);}
/// \brief Generate static private key in this domain
/// \param rng a RandomNumberGenerator derived class
/// \param privateKey a byte buffer for the generated private key in this domain
/// \details The private key is a random scalar used as an exponent in the range <tt>[1,MaxExponent()]</tt>.
/// \pre <tt>COUNTOF(privateKey) == PrivateStaticKeyLength()</tt>
void GenerateStaticPrivateKey(RandomNumberGenerator &rng, byte *privateKey) const
{
Integer x(rng, Integer::One(), GetAbstractGroupParameters().GetMaxExponent());
x.Encode(privateKey, StaticPrivateKeyLength());
}
/// \brief Generate a static public key from a private key in this domain
/// \param rng a RandomNumberGenerator derived class
/// \param privateKey a byte buffer with the previously generated private key
/// \param publicKey a byte buffer for the generated public key in this domain
/// \details The public key is an element or point on the curve, and its stored in a revrsible format.
/// A reversible format means it has a presentation format, and its an ANS.1 encoded element or point.
/// \pre <tt>COUNTOF(publicKey) == PublicStaticKeyLength()</tt>
void GenerateStaticPublicKey(RandomNumberGenerator &rng, const byte *privateKey, byte *publicKey) const
{
CRYPTOPP_UNUSED(rng);
const DL_GroupParameters<Element> ¶ms = GetAbstractGroupParameters();
Integer x(privateKey, StaticPrivateKeyLength());
Element y = params.ExponentiateBase(x);
params.EncodeElement(true, y, publicKey);
}
unsigned int EphemeralPrivateKeyLength() const {return StaticPrivateKeyLength() + StaticPublicKeyLength();}
unsigned int EphemeralPublicKeyLength() const {return StaticPublicKeyLength();}
void GenerateEphemeralPrivateKey(RandomNumberGenerator &rng, byte *privateKey) const
{
const DL_GroupParameters<Element> ¶ms = GetAbstractGroupParameters();
Integer x(rng, Integer::One(), params.GetMaxExponent());
x.Encode(privateKey, StaticPrivateKeyLength());
Element y = params.ExponentiateBase(x);
params.EncodeElement(true, y, privateKey+StaticPrivateKeyLength());
}
void GenerateEphemeralPublicKey(RandomNumberGenerator &rng, const byte *privateKey, byte *publicKey) const
{
CRYPTOPP_UNUSED(rng);
memcpy(publicKey, privateKey+StaticPrivateKeyLength(), EphemeralPublicKeyLength());
}
bool Agree(byte *agreedValue,
const byte *staticPrivateKey, const byte *ephemeralPrivateKey,
const byte *staticOtherPublicKey, const byte *ephemeralOtherPublicKey,
bool validateStaticOtherPublicKey=true) const
{
try
{
const DL_GroupParameters<Element> ¶ms = GetAbstractGroupParameters();
Element WW = params.DecodeElement(staticOtherPublicKey, validateStaticOtherPublicKey);
Element VV = params.DecodeElement(ephemeralOtherPublicKey, true);
Integer s(staticPrivateKey, StaticPrivateKeyLength());
Integer u(ephemeralPrivateKey, StaticPrivateKeyLength());
Element V = params.DecodeElement(ephemeralPrivateKey+StaticPrivateKeyLength(), false);
const Integer &r = params.GetSubgroupOrder();
Integer h2 = Integer::Power2((r.BitCount()+1)/2);
Integer e = ((h2+params.ConvertElementToInteger(V)%h2)*s+u) % r;
Integer tt = h2 + params.ConvertElementToInteger(VV) % h2;
if (COFACTOR_OPTION::ToEnum() == NO_COFACTOR_MULTIPLICTION)
{
Element P = params.ExponentiateElement(WW, tt);
P = m_groupParameters.MultiplyElements(P, VV);
Element R[2];
const Integer e2[2] = {r, e};
params.SimultaneousExponentiate(R, P, e2, 2);
if (!params.IsIdentity(R[0]) || params.IsIdentity(R[1]))
return false;
params.EncodeElement(false, R[1], agreedValue);
}
else
{
const Integer &k = params.GetCofactor();
if (COFACTOR_OPTION::ToEnum() == COMPATIBLE_COFACTOR_MULTIPLICTION)
e = ModularArithmetic(r).Divide(e, k);
Element P = m_groupParameters.CascadeExponentiate(VV, k*e, WW, k*(e*tt%r));
if (params.IsIdentity(P))
return false;
params.EncodeElement(false, P, agreedValue);
}
}
catch (DL_BadElement &)
{
return false;
}
return true;
}
private:
DL_GroupParameters<Element> & AccessAbstractGroupParameters() {return m_groupParameters;}
const DL_GroupParameters<Element> & GetAbstractGroupParameters() const {return m_groupParameters;}
GroupParameters m_groupParameters;
};
/// Menezes-Qu-Vanstone in GF(p) with key validation, AKA <a href="http://www.weidai.com/scan-mirror/ka.html#MQV">MQV</a>
/// \sa MQV, HMQV_Domain, FHMQV_Domain, AuthenticatedKeyAgreementDomain
typedef MQV_Domain<DL_GroupParameters_GFP_DefaultSafePrime> MQV;
NAMESPACE_END
#endif
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