/src/cryptopp/pubkey.h

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// pubkey.h - originally written and placed in the public domain by Wei Dai

/// \file pubkey.h
/// \brief This file contains helper classes/functions for implementing public key algorithms.
/// \details The class hierarchies in this header file tend to look like this:
///
/// <pre>
///                   x1
///                  +--+
///                  |  |
///                 y1  z1
///                  |  |
///             x2<y1>  x2<z1>
///                  |  |
///                 y2  z2
///                  |  |
///             x3<y2>  x3<z2>
///                  |  |
///                 y3  z3
/// </pre>
///
/// <ul>
///  <li>x1, y1, z1 are abstract interface classes defined in cryptlib.h
///  <li>x2, y2, z2 are implementations of the interfaces using "abstract policies", which
///      are pure virtual functions that should return interfaces to interchangeable algorithms.
///      These classes have Base suffixes.
///  <li>x3, y3, z3 hold actual algorithms and implement those virtual functions.
///      These classes have Impl suffixes.
/// </ul>
///
/// \details The TF_ prefix means an implementation using trapdoor functions on integers.
/// \details The DL_ prefix means an implementation using group operations in groups where discrete log is hard.

#ifndef CRYPTOPP_PUBKEY_H
#define CRYPTOPP_PUBKEY_H

#include "config.h"

#if CRYPTOPP_MSC_VERSION
# pragma warning(push)
# pragma warning(disable: 4702)
#endif

#include "cryptlib.h"
#include "integer.h"
#include "algebra.h"
#include "modarith.h"
#include "filters.h"
#include "eprecomp.h"
#include "fips140.h"
#include "argnames.h"
#include "smartptr.h"
#include "stdcpp.h"

#if defined(__SUNPRO_CC)
# define MAYBE_RETURN(x) return x
#else
# define MAYBE_RETURN(x) CRYPTOPP_UNUSED(x)
#endif

NAMESPACE_BEGIN(CryptoPP)

/// \brief Provides range for plaintext and ciphertext lengths
/// \details A trapdoor function is a function that is easy to compute in one direction,
///  but difficult to compute in the opposite direction without special knowledge.
///  The special knowledge is usually the private key.
/// \details Trapdoor functions only handle messages of a limited length or size.
///  MaxPreimage is the plaintext's maximum length, and MaxImage is the
///  ciphertext's maximum length.
/// \sa TrapdoorFunctionBounds(), RandomizedTrapdoorFunction(), TrapdoorFunction(),
///  RandomizedTrapdoorFunctionInverse() and TrapdoorFunctionInverse()
class CRYPTOPP_DLL CRYPTOPP_NO_VTABLE TrapdoorFunctionBounds
{
public:
  virtual ~TrapdoorFunctionBounds() {}

  /// \brief Returns the maximum size of a message before the trapdoor function is applied
  /// \return the maximum size of a message before the trapdoor function is applied
  /// \details Derived classes must implement PreimageBound().
  virtual Integer PreimageBound() const =0;
  /// \brief Returns the maximum size of a representation after the trapdoor function is applied
  /// \return the maximum size of a representation after the trapdoor function is applied
  /// \details Derived classes must implement ImageBound().
  virtual Integer ImageBound() const =0;
  /// \brief Returns the maximum size of a message before the trapdoor function is applied bound to a public key
  /// \return the maximum size of a message before the trapdoor function is applied bound to a public key
  /// \details The default implementation returns <tt>PreimageBound() - 1</tt>.
  virtual Integer MaxPreimage() const {return --PreimageBound();}
  /// \brief Returns the maximum size of a representation after the trapdoor function is applied bound to a public key
  /// \return the maximum size of a representation after the trapdoor function is applied bound to a public key
  /// \details The default implementation returns <tt>ImageBound() - 1</tt>.
  virtual Integer MaxImage() const {return --ImageBound();}
};

/// \brief Applies the trapdoor function, using random data if required
/// \details ApplyFunction() is the foundation for encrypting a message under a public key.
///  Derived classes will override it at some point.
/// \sa TrapdoorFunctionBounds(), RandomizedTrapdoorFunction(), TrapdoorFunction(),
///  RandomizedTrapdoorFunctionInverse() and TrapdoorFunctionInverse()
class CRYPTOPP_DLL CRYPTOPP_NO_VTABLE RandomizedTrapdoorFunction : public TrapdoorFunctionBounds
{
public:
  virtual ~RandomizedTrapdoorFunction() {}

  /// \brief Applies the trapdoor function, using random data if required
  /// \param rng a RandomNumberGenerator derived class
  /// \param x the message on which the encryption function is applied
  /// \return the message x encrypted under the public key
  /// \details ApplyRandomizedFunction is a generalization of encryption under a public key
  ///  cryptosystem. The RandomNumberGenerator may (or may not) be required.
  ///  Derived classes must implement it.
  virtual Integer ApplyRandomizedFunction(RandomNumberGenerator &rng, const Integer &x) const =0;

  /// \brief Determines if the encryption algorithm is randomized
  /// \return true if the encryption algorithm is randomized, false otherwise
  /// \details If IsRandomized() returns false, then NullRNG() can be used.
  virtual bool IsRandomized() const {return true;}
};

/// \brief Applies the trapdoor function
/// \details ApplyFunction() is the foundation for encrypting a message under a public key.
///  Derived classes will override it at some point.
/// \sa TrapdoorFunctionBounds(), RandomizedTrapdoorFunction(), TrapdoorFunction(),
///  RandomizedTrapdoorFunctionInverse() and TrapdoorFunctionInverse()
class CRYPTOPP_DLL CRYPTOPP_NO_VTABLE TrapdoorFunction : public RandomizedTrapdoorFunction
{
public:
  virtual ~TrapdoorFunction() {}

  /// \brief Applies the trapdoor function
  /// \param rng a RandomNumberGenerator derived class
  /// \param x the message on which the encryption function is applied
  /// \details ApplyRandomizedFunction is a generalization of encryption under a public key
  ///  cryptosystem. The RandomNumberGenerator may (or may not) be required.
  /// \details Internally, ApplyRandomizedFunction() calls ApplyFunction()
  ///  without the RandomNumberGenerator.
  Integer ApplyRandomizedFunction(RandomNumberGenerator &rng, const Integer &x) const
    {CRYPTOPP_UNUSED(rng); return ApplyFunction(x);}
  bool IsRandomized() const {return false;}

  /// \brief Applies the trapdoor
  /// \param x the message on which the encryption function is applied
  /// \return the message x encrypted under the public key
  /// \details ApplyFunction is a generalization of encryption under a public key
  ///  cryptosystem. Derived classes must implement it.
  virtual Integer ApplyFunction(const Integer &x) const =0;
};

/// \brief Applies the inverse of the trapdoor function, using random data if required
/// \details CalculateInverse() is the foundation for decrypting a message under a private key
///  in a public key cryptosystem. Derived classes will override it at some point.
/// \sa TrapdoorFunctionBounds(), RandomizedTrapdoorFunction(), TrapdoorFunction(),
///  RandomizedTrapdoorFunctionInverse() and TrapdoorFunctionInverse()
class CRYPTOPP_DLL CRYPTOPP_NO_VTABLE RandomizedTrapdoorFunctionInverse
{
public:
  virtual ~RandomizedTrapdoorFunctionInverse() {}

  /// \brief Applies the inverse of the trapdoor function, using random data if required
  /// \param rng a RandomNumberGenerator derived class
  /// \param x the message on which the decryption function is applied
  /// \return the message x decrypted under the private key
  /// \details CalculateRandomizedInverse is a generalization of decryption using the private key
  ///  The RandomNumberGenerator may (or may not) be required. Derived classes must implement it.
  virtual Integer CalculateRandomizedInverse(RandomNumberGenerator &rng, const Integer &x) const =0;

  /// \brief Determines if the decryption algorithm is randomized
  /// \return true if the decryption algorithm is randomized, false otherwise
  /// \details If IsRandomized() returns false, then NullRNG() can be used.
  virtual bool IsRandomized() const {return true;}
};

/// \brief Applies the inverse of the trapdoor function
/// \details CalculateInverse() is the foundation for decrypting a message under a private key
///  in a public key cryptosystem. Derived classes will override it at some point.
/// \sa TrapdoorFunctionBounds(), RandomizedTrapdoorFunction(), TrapdoorFunction(),
///  RandomizedTrapdoorFunctionInverse() and TrapdoorFunctionInverse()
class CRYPTOPP_DLL CRYPTOPP_NO_VTABLE TrapdoorFunctionInverse : public RandomizedTrapdoorFunctionInverse
{
public:
  virtual ~TrapdoorFunctionInverse() {}

  /// \brief Applies the inverse of the trapdoor function
  /// \param rng a RandomNumberGenerator derived class
  /// \param x the message on which the decryption function is applied
  /// \return the message x decrypted under the private key
  /// \details CalculateRandomizedInverse is a generalization of decryption using the private key
  /// \details Internally, CalculateRandomizedInverse() calls CalculateInverse()
  ///  without the RandomNumberGenerator.
  Integer CalculateRandomizedInverse(RandomNumberGenerator &rng, const Integer &x) const
    {return CalculateInverse(rng, x);}

  /// \brief Determines if the decryption algorithm is randomized
  /// \return true if the decryption algorithm is randomized, false otherwise
  /// \details If IsRandomized() returns false, then NullRNG() can be used.
  bool IsRandomized() const {return false;}

  /// \brief Calculates the inverse of an element
  /// \param rng a RandomNumberGenerator derived class
  /// \param x the element
  /// \return the inverse of the element in the group
  virtual Integer CalculateInverse(RandomNumberGenerator &rng, const Integer &x) const =0;
};

// ********************************************************

/// \brief Message encoding method for public key encryption
class CRYPTOPP_NO_VTABLE PK_EncryptionMessageEncodingMethod
{
public:
  virtual ~PK_EncryptionMessageEncodingMethod() {}

  virtual bool ParameterSupported(const char *name) const
    {CRYPTOPP_UNUSED(name); return false;}

  /// max size of unpadded message in bytes, given max size of padded message in bits (1 less than size of modulus)
  virtual size_t MaxUnpaddedLength(size_t paddedLength) const =0;

  virtual void Pad(RandomNumberGenerator &rng, const byte *raw, size_t inputLength, byte *padded, size_t paddedBitLength, const NameValuePairs &parameters) const =0;

  virtual DecodingResult Unpad(const byte *padded, size_t paddedBitLength, byte *raw, const NameValuePairs &parameters) const =0;
};

// ********************************************************

/// \brief The base for trapdoor based cryptosystems
/// \tparam TFI trapdoor function interface derived class
/// \tparam MEI message encoding interface derived class
template <class TFI, class MEI>
class CRYPTOPP_NO_VTABLE TF_Base
{
protected:
  virtual ~TF_Base() {}

  virtual const TrapdoorFunctionBounds & GetTrapdoorFunctionBounds() const =0;

  typedef TFI TrapdoorFunctionInterface;
  virtual const TrapdoorFunctionInterface & GetTrapdoorFunctionInterface() const =0;

  typedef MEI MessageEncodingInterface;
  virtual const MessageEncodingInterface & GetMessageEncodingInterface() const =0;
};

// ********************************************************

/// \brief Public key trapdoor function default implementation
/// \tparam BASE public key cryptosystem with a fixed length
template <class BASE>
class CRYPTOPP_NO_VTABLE PK_FixedLengthCryptoSystemImpl : public BASE
{
public:
  virtual ~PK_FixedLengthCryptoSystemImpl() {}

  size_t MaxPlaintextLength(size_t ciphertextLength) const
    {return ciphertextLength == FixedCiphertextLength() ? FixedMaxPlaintextLength() : 0;}
  size_t CiphertextLength(size_t plaintextLength) const
    {return plaintextLength <= FixedMaxPlaintextLength() ? FixedCiphertextLength() : 0;}

  virtual size_t FixedMaxPlaintextLength() const =0;
  virtual size_t FixedCiphertextLength() const =0;
};

/// \brief Trapdoor function cryptosystem base class
/// \tparam INTFACE public key cryptosystem base interface
/// \tparam BASE public key cryptosystem implementation base
template <class INTFACE, class BASE>
class CRYPTOPP_NO_VTABLE TF_CryptoSystemBase : public PK_FixedLengthCryptoSystemImpl<INTFACE>, protected BASE
{
public:
  virtual ~TF_CryptoSystemBase() {}

  bool ParameterSupported(const char *name) const {return this->GetMessageEncodingInterface().ParameterSupported(name);}
  size_t FixedMaxPlaintextLength() const {return this->GetMessageEncodingInterface().MaxUnpaddedLength(PaddedBlockBitLength());}
  size_t FixedCiphertextLength() const {return this->GetTrapdoorFunctionBounds().MaxImage().ByteCount();}

protected:
  size_t PaddedBlockByteLength() const {return BitsToBytes(PaddedBlockBitLength());}
  // Coverity finding on potential overflow/underflow.
  size_t PaddedBlockBitLength() const {return SaturatingSubtract(this->GetTrapdoorFunctionBounds().PreimageBound().BitCount(),1U);}
};

/// \brief Trapdoor function cryptosystems decryption base class
class CRYPTOPP_DLL CRYPTOPP_NO_VTABLE TF_DecryptorBase : public TF_CryptoSystemBase<PK_Decryptor, TF_Base<TrapdoorFunctionInverse, PK_EncryptionMessageEncodingMethod> >
{
public:
  virtual ~TF_DecryptorBase() {}

  DecodingResult Decrypt(RandomNumberGenerator &rng, const byte *ciphertext, size_t ciphertextLength, byte *plaintext, const NameValuePairs &parameters = g_nullNameValuePairs) const;
};

/// \brief Trapdoor function cryptosystems encryption base class
class CRYPTOPP_DLL CRYPTOPP_NO_VTABLE TF_EncryptorBase : public TF_CryptoSystemBase<PK_Encryptor, TF_Base<RandomizedTrapdoorFunction, PK_EncryptionMessageEncodingMethod> >
{
public:
  virtual ~TF_EncryptorBase() {}

  void Encrypt(RandomNumberGenerator &rng, const byte *plaintext, size_t plaintextLength, byte *ciphertext, const NameValuePairs &parameters = g_nullNameValuePairs) const;
};

// ********************************************************

// Typedef change due to Clang, http://github.com/weidai11/cryptopp/issues/300
typedef std::pair<const byte *, unsigned int> HashIdentifier;

/// \brief Interface for message encoding method for public key signature schemes.
/// \details PK_SignatureMessageEncodingMethod provides interfaces for message
///  encoding method for public key signature schemes. The methods support both
///  trapdoor functions (<tt>TF_*</tt>) and discrete logarithm (<tt>DL_*</tt>)
///  based schemes.
class CRYPTOPP_NO_VTABLE PK_SignatureMessageEncodingMethod
{
public:
  virtual ~PK_SignatureMessageEncodingMethod() {}

  virtual size_t MinRepresentativeBitLength(size_t hashIdentifierLength, size_t digestLength) const
    {CRYPTOPP_UNUSED(hashIdentifierLength); CRYPTOPP_UNUSED(digestLength); return 0;}
  virtual size_t MaxRecoverableLength(size_t representativeBitLength, size_t hashIdentifierLength, size_t digestLength) const
    {CRYPTOPP_UNUSED(representativeBitLength); CRYPTOPP_UNUSED(representativeBitLength); CRYPTOPP_UNUSED(hashIdentifierLength); CRYPTOPP_UNUSED(digestLength); return 0;}

  /// \brief Determines whether an encoding method requires a random number generator
  /// \return true if the encoding method requires a RandomNumberGenerator()
  /// \details if IsProbabilistic() returns false, then NullRNG() can be passed to functions that take
  ///  RandomNumberGenerator().
  /// \sa Bellare and Rogaway<a href="http://grouper.ieee.org/groups/1363/P1363a/contributions/pss-submission.pdf">PSS:
  ///  Provably Secure Encoding Method for Digital Signatures</a>
  bool IsProbabilistic() const
    {return true;}
  bool AllowNonrecoverablePart() const
    {throw NotImplemented("PK_MessageEncodingMethod: this signature scheme does not support message recovery");}
  virtual bool RecoverablePartFirst() const
    {throw NotImplemented("PK_MessageEncodingMethod: this signature scheme does not support message recovery");}

  // for verification, DL
  virtual void ProcessSemisignature(HashTransformation &hash, const byte *semisignature, size_t semisignatureLength) const
    {CRYPTOPP_UNUSED(hash); CRYPTOPP_UNUSED(semisignature); CRYPTOPP_UNUSED(semisignatureLength);}

  // for signature
  virtual void ProcessRecoverableMessage(HashTransformation &hash,
    const byte *recoverableMessage, size_t recoverableMessageLength,
    const byte *presignature, size_t presignatureLength,
    SecByteBlock &semisignature) const
  {
    CRYPTOPP_UNUSED(hash);CRYPTOPP_UNUSED(recoverableMessage); CRYPTOPP_UNUSED(recoverableMessageLength);
    CRYPTOPP_UNUSED(presignature); CRYPTOPP_UNUSED(presignatureLength); CRYPTOPP_UNUSED(semisignature);
    if (RecoverablePartFirst())
      CRYPTOPP_ASSERT(!"ProcessRecoverableMessage() not implemented");
  }

  virtual void ComputeMessageRepresentative(RandomNumberGenerator &rng,
    const byte *recoverableMessage, size_t recoverableMessageLength,
    HashTransformation &hash, HashIdentifier hashIdentifier, bool messageEmpty,
    byte *representative, size_t representativeBitLength) const =0;

  virtual bool VerifyMessageRepresentative(
    HashTransformation &hash, HashIdentifier hashIdentifier, bool messageEmpty,
    byte *representative, size_t representativeBitLength) const =0;

  virtual DecodingResult RecoverMessageFromRepresentative(  // for TF
    HashTransformation &hash, HashIdentifier hashIdentifier, bool messageEmpty,
    byte *representative, size_t representativeBitLength,
    byte *recoveredMessage) const
    {CRYPTOPP_UNUSED(hash);CRYPTOPP_UNUSED(hashIdentifier); CRYPTOPP_UNUSED(messageEmpty);
    CRYPTOPP_UNUSED(representative); CRYPTOPP_UNUSED(representativeBitLength); CRYPTOPP_UNUSED(recoveredMessage);
    throw NotImplemented("PK_MessageEncodingMethod: this signature scheme does not support message recovery");}

  virtual DecodingResult RecoverMessageFromSemisignature(   // for DL
    HashTransformation &hash, HashIdentifier hashIdentifier,
    const byte *presignature, size_t presignatureLength,
    const byte *semisignature, size_t semisignatureLength,
    byte *recoveredMessage) const
    {CRYPTOPP_UNUSED(hash);CRYPTOPP_UNUSED(hashIdentifier); CRYPTOPP_UNUSED(presignature); CRYPTOPP_UNUSED(presignatureLength);
    CRYPTOPP_UNUSED(semisignature); CRYPTOPP_UNUSED(semisignatureLength); CRYPTOPP_UNUSED(recoveredMessage);
    throw NotImplemented("PK_MessageEncodingMethod: this signature scheme does not support message recovery");}

  // VC60 workaround
  struct HashIdentifierLookup
  {
    template <class H> struct HashIdentifierLookup2
    {
      static HashIdentifier CRYPTOPP_API Lookup()
      {
        return HashIdentifier(static_cast<const byte *>(NULLPTR), 0);
      }
    };
  };
};

/// \brief Interface for message encoding method for public key signature schemes.
/// \details PK_DeterministicSignatureMessageEncodingMethod provides interfaces
///  for message encoding method for public key signature schemes.
class CRYPTOPP_DLL CRYPTOPP_NO_VTABLE PK_DeterministicSignatureMessageEncodingMethod : public PK_SignatureMessageEncodingMethod
{
public:
  bool VerifyMessageRepresentative(
    HashTransformation &hash, HashIdentifier hashIdentifier, bool messageEmpty,
    byte *representative, size_t representativeBitLength) const;
};

/// \brief Interface for message encoding method for public key signature schemes.
/// \details PK_RecoverableSignatureMessageEncodingMethod provides interfaces
///  for message encoding method for public key signature schemes.
class CRYPTOPP_DLL CRYPTOPP_NO_VTABLE PK_RecoverableSignatureMessageEncodingMethod : public PK_SignatureMessageEncodingMethod
{
public:
  bool VerifyMessageRepresentative(
    HashTransformation &hash, HashIdentifier hashIdentifier, bool messageEmpty,
    byte *representative, size_t representativeBitLength) const;
};

/// \brief Interface for message encoding method for public key signature schemes.
/// \details DL_SignatureMessageEncodingMethod_DSA provides interfaces
///  for message encoding method for DSA.
class CRYPTOPP_DLL DL_SignatureMessageEncodingMethod_DSA : public PK_DeterministicSignatureMessageEncodingMethod
{
public:
  void ComputeMessageRepresentative(RandomNumberGenerator &rng,
    const byte *recoverableMessage, size_t recoverableMessageLength,
    HashTransformation &hash, HashIdentifier hashIdentifier, bool messageEmpty,
    byte *representative, size_t representativeBitLength) const;
};

/// \brief Interface for message encoding method for public key signature schemes.
/// \details DL_SignatureMessageEncodingMethod_NR provides interfaces
///  for message encoding method for Nyberg-Rueppel.
class CRYPTOPP_DLL DL_SignatureMessageEncodingMethod_NR : public PK_DeterministicSignatureMessageEncodingMethod
{
public:
  void ComputeMessageRepresentative(RandomNumberGenerator &rng,
    const byte *recoverableMessage, size_t recoverableMessageLength,
    HashTransformation &hash, HashIdentifier hashIdentifier, bool messageEmpty,
    byte *representative, size_t representativeBitLength) const;
};

#if 0
/// \brief Interface for message encoding method for public key signature schemes.
/// \details DL_SignatureMessageEncodingMethod_SM2 provides interfaces
///  for message encoding method for SM2.
class CRYPTOPP_DLL DL_SignatureMessageEncodingMethod_SM2 : public PK_DeterministicSignatureMessageEncodingMethod
{
public:
  void ComputeMessageRepresentative(RandomNumberGenerator &rng,
    const byte *recoverableMessage, size_t recoverableMessageLength,
    HashTransformation &hash, HashIdentifier hashIdentifier, bool messageEmpty,
    byte *representative, size_t representativeBitLength) const;
};
#endif

/// \brief Interface for message encoding method for public key signature schemes.
/// \details PK_MessageAccumulatorBase provides interfaces
///  for message encoding method.
class CRYPTOPP_DLL CRYPTOPP_NO_VTABLE PK_MessageAccumulatorBase : public PK_MessageAccumulator
{
public:
  PK_MessageAccumulatorBase() : m_empty(true) {}

  virtual HashTransformation & AccessHash() =0;

  void Update(const byte *input, size_t length)
  {
    AccessHash().Update(input, length);
    m_empty = m_empty && length == 0;
  }

  SecByteBlock m_recoverableMessage, m_representative, m_presignature, m_semisignature;
  Integer m_k, m_s;
  bool m_empty;
};

/// \brief Interface for message encoding method for public key signature schemes.
/// \details PK_MessageAccumulatorBase provides interfaces
///  for message encoding method.
template <class HASH_ALGORITHM>
class PK_MessageAccumulatorImpl : public PK_MessageAccumulatorBase, protected ObjectHolder<HASH_ALGORITHM>
{
public:
  HashTransformation & AccessHash() {return this->m_object;}
};

/// \brief Trapdoor Function (TF) Signature Scheme base class
/// \tparam INTFACE interface
/// \tparam BASE base class
template <class INTFACE, class BASE>
class CRYPTOPP_NO_VTABLE TF_SignatureSchemeBase : public INTFACE, protected BASE
{
public:
  virtual ~TF_SignatureSchemeBase() {}

  size_t SignatureLength() const
    {return this->GetTrapdoorFunctionBounds().MaxPreimage().ByteCount();}
  size_t MaxRecoverableLength() const
    {return this->GetMessageEncodingInterface().MaxRecoverableLength(MessageRepresentativeBitLength(), GetHashIdentifier().second, GetDigestSize());}
  size_t MaxRecoverableLengthFromSignatureLength(size_t signatureLength) const
    {CRYPTOPP_UNUSED(signatureLength); return this->MaxRecoverableLength();}

  bool IsProbabilistic() const
    {return this->GetTrapdoorFunctionInterface().IsRandomized() || this->GetMessageEncodingInterface().IsProbabilistic();}
  bool AllowNonrecoverablePart() const
    {return this->GetMessageEncodingInterface().AllowNonrecoverablePart();}
  bool RecoverablePartFirst() const
    {return this->GetMessageEncodingInterface().RecoverablePartFirst();}

protected:
  size_t MessageRepresentativeLength() const {return BitsToBytes(MessageRepresentativeBitLength());}
  // Coverity finding on potential overflow/underflow.
  size_t MessageRepresentativeBitLength() const {return SaturatingSubtract(this->GetTrapdoorFunctionBounds().ImageBound().BitCount(),1U);}
  virtual HashIdentifier GetHashIdentifier() const =0;
  virtual size_t GetDigestSize() const =0;
};

/// \brief Trapdoor Function (TF) Signer base class
class CRYPTOPP_DLL CRYPTOPP_NO_VTABLE TF_SignerBase : public TF_SignatureSchemeBase<PK_Signer, TF_Base<RandomizedTrapdoorFunctionInverse, PK_SignatureMessageEncodingMethod> >
{
public:
  virtual ~TF_SignerBase() {}

  void InputRecoverableMessage(PK_MessageAccumulator &messageAccumulator, const byte *recoverableMessage, size_t recoverableMessageLength) const;
  size_t SignAndRestart(RandomNumberGenerator &rng, PK_MessageAccumulator &messageAccumulator, byte *signature, bool restart=true) const;
};

/// \brief Trapdoor Function (TF) Verifier base class
class CRYPTOPP_DLL CRYPTOPP_NO_VTABLE TF_VerifierBase : public TF_SignatureSchemeBase<PK_Verifier, TF_Base<TrapdoorFunction, PK_SignatureMessageEncodingMethod> >
{
public:
  virtual ~TF_VerifierBase() {}

  void InputSignature(PK_MessageAccumulator &messageAccumulator, const byte *signature, size_t signatureLength) const;
  bool VerifyAndRestart(PK_MessageAccumulator &messageAccumulator) const;
  DecodingResult RecoverAndRestart(byte *recoveredMessage, PK_MessageAccumulator &recoveryAccumulator) const;
};

// ********************************************************

/// \brief Trapdoor Function (TF) scheme options
/// \tparam T1 algorithm info class
/// \tparam T2 keys class with public and private key
/// \tparam T3 message encoding class
template <class T1, class T2, class T3>
struct TF_CryptoSchemeOptions
{
  typedef T1 AlgorithmInfo;
  typedef T2 Keys;
  typedef typename Keys::PrivateKey PrivateKey;
  typedef typename Keys::PublicKey PublicKey;
  typedef T3 MessageEncodingMethod;
};

/// \brief Trapdoor Function (TF) signature scheme options
/// \tparam T1 algorithm info class
/// \tparam T2 keys class with public and private key
/// \tparam T3 message encoding class
/// \tparam T4 HashTransformation class
template <class T1, class T2, class T3, class T4>
struct TF_SignatureSchemeOptions : public TF_CryptoSchemeOptions<T1, T2, T3>
{
  typedef T4 HashFunction;
};

/// \brief Trapdoor Function (TF) base implementation
/// \tparam BASE base class
/// \tparam SCHEME_OPTIONS scheme options class
/// \tparam KEY_CLASS key class
template <class BASE, class SCHEME_OPTIONS, class KEY_CLASS>
class CRYPTOPP_NO_VTABLE TF_ObjectImplBase : public AlgorithmImpl<BASE, typename SCHEME_OPTIONS::AlgorithmInfo>
{
public:
  typedef SCHEME_OPTIONS SchemeOptions;
  typedef KEY_CLASS KeyClass;

  virtual ~TF_ObjectImplBase() {}

  PublicKey & AccessPublicKey() {return AccessKey();}
  const PublicKey & GetPublicKey() const {return GetKey();}

  PrivateKey & AccessPrivateKey() {return AccessKey();}
  const PrivateKey & GetPrivateKey() const {return GetKey();}

  virtual const KeyClass & GetKey() const =0;
  virtual KeyClass & AccessKey() =0;

  const KeyClass & GetTrapdoorFunction() const {return GetKey();}

  PK_MessageAccumulator * NewSignatureAccumulator(RandomNumberGenerator &rng) const
  {
    CRYPTOPP_UNUSED(rng);
    return new PK_MessageAccumulatorImpl<typename SCHEME_OPTIONS::HashFunction>;
  }
  PK_MessageAccumulator * NewVerificationAccumulator() const
  {
    return new PK_MessageAccumulatorImpl<typename SCHEME_OPTIONS::HashFunction>;
  }

protected:
  const typename BASE::MessageEncodingInterface & GetMessageEncodingInterface() const
    {return Singleton<typename SCHEME_OPTIONS::MessageEncodingMethod>().Ref();}
  const TrapdoorFunctionBounds & GetTrapdoorFunctionBounds() const
    {return GetKey();}
  const typename BASE::TrapdoorFunctionInterface & GetTrapdoorFunctionInterface() const
    {return GetKey();}

  // for signature scheme
  HashIdentifier GetHashIdentifier() const
  {
        typedef typename SchemeOptions::MessageEncodingMethod::HashIdentifierLookup::template HashIdentifierLookup2<typename SchemeOptions::HashFunction> L;
        return L::Lookup();
  }
  size_t GetDigestSize() const
  {
    typedef typename SchemeOptions::HashFunction H;
    return H::DIGESTSIZE;
  }
};

/// \brief Trapdoor Function (TF) signature with external reference
/// \tparam BASE base class
/// \tparam SCHEME_OPTIONS scheme options class
/// \tparam KEY key class
/// \details TF_ObjectImplExtRef() holds a pointer to an external key structure
template <class BASE, class SCHEME_OPTIONS, class KEY>
class TF_ObjectImplExtRef : public TF_ObjectImplBase<BASE, SCHEME_OPTIONS, KEY>
{
public:
  virtual ~TF_ObjectImplExtRef() {}

  TF_ObjectImplExtRef(const KEY *pKey = NULLPTR) : m_pKey(pKey) {}
  void SetKeyPtr(const KEY *pKey) {m_pKey = pKey;}

  const KEY & GetKey() const {return *m_pKey;}
  KEY & AccessKey() {throw NotImplemented("TF_ObjectImplExtRef: cannot modify refererenced key");}

private:
  const KEY * m_pKey;
};

/// \brief Trapdoor Function (TF) signature scheme options
/// \tparam BASE base class
/// \tparam SCHEME_OPTIONS scheme options class
/// \tparam KEY_CLASS key class
/// \details TF_ObjectImpl() holds a reference to a trapdoor function
template <class BASE, class SCHEME_OPTIONS, class KEY_CLASS>
class CRYPTOPP_NO_VTABLE TF_ObjectImpl : public TF_ObjectImplBase<BASE, SCHEME_OPTIONS, KEY_CLASS>
{
public:
  typedef KEY_CLASS KeyClass;

  virtual ~TF_ObjectImpl() {}

  const KeyClass & GetKey() const {return m_trapdoorFunction;}
  KeyClass & AccessKey() {return m_trapdoorFunction;}

private:
  KeyClass m_trapdoorFunction;
};

/// \brief Trapdoor Function (TF) decryptor options
/// \tparam SCHEME_OPTIONS scheme options class
template <class SCHEME_OPTIONS>
class TF_DecryptorImpl : public TF_ObjectImpl<TF_DecryptorBase, SCHEME_OPTIONS, typename SCHEME_OPTIONS::PrivateKey>
{
};

/// \brief Trapdoor Function (TF) encryptor options
/// \tparam SCHEME_OPTIONS scheme options class
template <class SCHEME_OPTIONS>
class TF_EncryptorImpl : public TF_ObjectImpl<TF_EncryptorBase, SCHEME_OPTIONS, typename SCHEME_OPTIONS::PublicKey>
{
};

/// \brief Trapdoor Function (TF) encryptor options
/// \tparam SCHEME_OPTIONS scheme options class
template <class SCHEME_OPTIONS>
class TF_SignerImpl : public TF_ObjectImpl<TF_SignerBase, SCHEME_OPTIONS, typename SCHEME_OPTIONS::PrivateKey>
{
};

/// \brief Trapdoor Function (TF) encryptor options
/// \tparam SCHEME_OPTIONS scheme options class
template <class SCHEME_OPTIONS>
class TF_VerifierImpl : public TF_ObjectImpl<TF_VerifierBase, SCHEME_OPTIONS, typename SCHEME_OPTIONS::PublicKey>
{
};

// ********************************************************

/// \brief Mask generation function interface
/// \sa P1363_KDF2, P1363_MGF1
/// \since Crypto++ 2.0
class CRYPTOPP_NO_VTABLE MaskGeneratingFunction
{
public:
  virtual ~MaskGeneratingFunction() {}

  /// \brief Generate and apply mask
  /// \param hash HashTransformation derived class
  /// \param output the destination byte array
  /// \param outputLength the size of the destination byte array
  /// \param input the message to hash
  /// \param inputLength the size of the message
  /// \param mask flag indicating whether to apply the mask
  virtual void GenerateAndMask(HashTransformation &hash, byte *output, size_t outputLength, const byte *input, size_t inputLength, bool mask = true) const =0;
};

/// \fn P1363_MGF1KDF2_Common
/// \brief P1363 mask generation function
/// \param hash HashTransformation derived class
/// \param output the destination byte array
/// \param outputLength the size of the destination byte array
/// \param input the message to hash
/// \param inputLength the size of the message
/// \param derivationParams additional derivation parameters
/// \param derivationParamsLength the size of the additional derivation parameters
/// \param mask flag indicating whether to apply the mask
/// \param counterStart starting counter value used in generation function
CRYPTOPP_DLL void CRYPTOPP_API P1363_MGF1KDF2_Common(HashTransformation &hash, byte *output, size_t outputLength, const byte *input, size_t inputLength, const byte *derivationParams, size_t derivationParamsLength, bool mask, unsigned int counterStart);

/// \brief P1363 mask generation function
/// \sa P1363_KDF2, MaskGeneratingFunction
/// \since Crypto++ 2.0
class P1363_MGF1 : public MaskGeneratingFunction
{
public:
  /// \brief The algorithm name
  /// \return the algorithm name
  /// \details StaticAlgorithmName returns the algorithm's name as a static
  ///  member function.
  CRYPTOPP_STATIC_CONSTEXPR const char* CRYPTOPP_API StaticAlgorithmName() {return "MGF1";}

  /// \brief P1363 mask generation function
  /// \param hash HashTransformation derived class
  /// \param output the destination byte array
  /// \param outputLength the size of the destination byte array
  /// \param input the message to hash
  /// \param inputLength the size of the message
  /// \param mask flag indicating whether to apply the mask
  void GenerateAndMask(HashTransformation &hash, byte *output, size_t outputLength, const byte *input, size_t inputLength, bool mask = true) const
  {
    P1363_MGF1KDF2_Common(hash, output, outputLength, input, inputLength, NULLPTR, 0, mask, 0);
  }
};

// ********************************************************

/// \brief P1363 key derivation function
/// \tparam H hash function used in the derivation
/// \sa P1363_MGF1, KeyDerivationFunction, <A
///  HREF="https://www.cryptopp.com/wiki/P1363_KDF2">P1363_KDF2</A>
///  on the Crypto++ wiki
/// \since Crypto++ 2.0
template <class H>
class P1363_KDF2
{
public:
  /// \brief P1363 key derivation function
  /// \param output the destination byte array
  /// \param outputLength the size of the destination byte array
  /// \param input the message to hash
  /// \param inputLength the size of the message
  /// \param derivationParams additional derivation parameters
  /// \param derivationParamsLength the size of the additional derivation parameters
  /// \details DeriveKey calls P1363_MGF1KDF2_Common
  static void CRYPTOPP_API DeriveKey(byte *output, size_t outputLength, const byte *input, size_t inputLength, const byte *derivationParams, size_t derivationParamsLength)
  {
    H h;
    P1363_MGF1KDF2_Common(h, output, outputLength, input, inputLength, derivationParams, derivationParamsLength, false, 1);
  }
};

// ********************************************************

/// \brief Exception thrown when an invalid group element is encountered
/// \details Thrown by DecodeElement and AgreeWithStaticPrivateKey
class DL_BadElement : public InvalidDataFormat
{
public:
  DL_BadElement() : InvalidDataFormat("CryptoPP: invalid group element") {}
};

/// \brief Interface for Discrete Log (DL) group parameters
/// \tparam T element in the group
/// \details The element is usually an Integer, \ref ECP "ECP::Point" or \ref EC2N "EC2N::Point"
template <class T>
class CRYPTOPP_NO_VTABLE DL_GroupParameters : public CryptoParameters
{
  typedef DL_GroupParameters<T> ThisClass;

public:
  typedef T Element;

  virtual ~DL_GroupParameters() {}

  DL_GroupParameters() : m_validationLevel(0) {}

  // CryptoMaterial
  bool Validate(RandomNumberGenerator &rng, unsigned int level) const
  {
    if (!GetBasePrecomputation().IsInitialized())
      return false;

    if (m_validationLevel > level)
      return true;

    CRYPTOPP_ASSERT(ValidateGroup(rng, level));
    bool pass = ValidateGroup(rng, level);
    CRYPTOPP_ASSERT(ValidateElement(level, GetSubgroupGenerator(), &GetBasePrecomputation()));
    pass = pass && ValidateElement(level, GetSubgroupGenerator(), &GetBasePrecomputation());

    m_validationLevel = pass ? level+1 : 0;

    return pass;
  }

  bool GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const
  {
    return GetValueHelper(this, name, valueType, pValue)
      CRYPTOPP_GET_FUNCTION_ENTRY(SubgroupOrder)
      CRYPTOPP_GET_FUNCTION_ENTRY(SubgroupGenerator)
      ;
  }

  /// \brief Determines whether the object supports precomputation
  /// \return true if the object supports precomputation, false otherwise
  /// \sa Precompute()
  bool SupportsPrecomputation() const {return true;}

  /// \brief Perform precomputation
  /// \param precomputationStorage the suggested number of objects for the precompute table
  /// \throw NotImplemented
  /// \details The exact semantics of Precompute() varies, but it typically means calculate
  ///  a table of n objects that can be used later to speed up computation.
  /// \details If a derived class does not override Precompute(), then the base class throws
  ///  NotImplemented.
  /// \sa SupportsPrecomputation(), LoadPrecomputation(), SavePrecomputation()
  void Precompute(unsigned int precomputationStorage=16)
  {
    AccessBasePrecomputation().Precompute(GetGroupPrecomputation(), GetSubgroupOrder().BitCount(), precomputationStorage);
  }

  /// \brief Retrieve previously saved precomputation
  /// \param storedPrecomputation BufferedTransformation with the saved precomputation
  /// \throw NotImplemented
  /// \sa SupportsPrecomputation(), Precompute()
  void LoadPrecomputation(BufferedTransformation &storedPrecomputation)
  {
    AccessBasePrecomputation().Load(GetGroupPrecomputation(), storedPrecomputation);
    m_validationLevel = 0;
  }

  /// \brief Save precomputation for later use
  /// \param storedPrecomputation BufferedTransformation to write the precomputation
  /// \throw NotImplemented
  /// \sa SupportsPrecomputation(), Precompute()
  void SavePrecomputation(BufferedTransformation &storedPrecomputation) const
  {
    GetBasePrecomputation().Save(GetGroupPrecomputation(), storedPrecomputation);
  }

  /// \brief Retrieves the subgroup generator
  /// \return the subgroup generator
  /// \details The subgroup generator is retrieved from the base precomputation
  virtual const Element & GetSubgroupGenerator() const {return GetBasePrecomputation().GetBase(GetGroupPrecomputation());}

  /// \brief Sets the subgroup generator
  /// \param base the new subgroup generator
  /// \details The subgroup generator is set in the base precomputation
  virtual void SetSubgroupGenerator(const Element &base) {AccessBasePrecomputation().SetBase(GetGroupPrecomputation(), base);}

  /// \brief Exponentiates the base
  /// \return the element after exponentiation
  /// \details ExponentiateBase() calls GetBasePrecomputation() and then exponentiates.
  virtual Element ExponentiateBase(const Integer &exponent) const
  {
    return GetBasePrecomputation().Exponentiate(GetGroupPrecomputation(), exponent);
  }

  /// \brief Exponentiates an element
  /// \param base the base element
  /// \param exponent the exponent to raise the base
  /// \return the result of the exponentiation
  /// \details Internally, ExponentiateElement() calls SimultaneousExponentiate().
  virtual Element ExponentiateElement(const Element &base, const Integer &exponent) const
  {
    Element result;
    SimultaneousExponentiate(&result, base, &exponent, 1);
    return result;
  }

  /// \brief Retrieves the group precomputation
  /// \return a const reference to the group precomputation
  virtual const DL_GroupPrecomputation<Element> & GetGroupPrecomputation() const =0;

  /// \brief Retrieves the group precomputation
  /// \return a const reference to the group precomputation using a fixed base
  virtual const DL_FixedBasePrecomputation<Element> & GetBasePrecomputation() const =0;

  /// \brief Retrieves the group precomputation
  /// \return a non-const reference to the group precomputation using a fixed base
  virtual DL_FixedBasePrecomputation<Element> & AccessBasePrecomputation() =0;

  /// \brief Retrieves the subgroup order
  /// \return the order of subgroup generated by the base element
  virtual const Integer & GetSubgroupOrder() const =0;

  /// \brief Retrieves the maximum exponent for the group
  /// \return the maximum exponent for the group
  virtual Integer GetMaxExponent() const =0;

  /// \brief Retrieves the order of the group
  /// \return the order of the group
  /// \details Either GetGroupOrder() or GetCofactor() must be overridden in a derived class.
  virtual Integer GetGroupOrder() const {return GetSubgroupOrder()*GetCofactor();}

  /// \brief Retrieves the cofactor
  /// \return the cofactor
  /// \details Either GetGroupOrder() or GetCofactor() must be overridden in a derived class.
  virtual Integer GetCofactor() const {return GetGroupOrder()/GetSubgroupOrder();}

  /// \brief Retrieves the encoded element's size
  /// \param reversible flag indicating the encoding format
  /// \return encoded element's size, in bytes
  /// \details The format of the encoded element varies by the underlying type of the element and the
  ///  reversible flag. GetEncodedElementSize() must be implemented in a derived class.
  /// \sa GetEncodedElementSize(), EncodeElement(), DecodeElement()
  virtual unsigned int GetEncodedElementSize(bool reversible) const =0;

  /// \brief Encodes the element
  /// \param reversible flag indicating the encoding format
  /// \param element reference to the element to encode
  /// \param encoded destination byte array for the encoded element
  /// \details EncodeElement() must be implemented in a derived class.
  /// \pre <tt>COUNTOF(encoded) == GetEncodedElementSize()</tt>
  virtual void EncodeElement(bool reversible, const Element &element, byte *encoded) const =0;

  /// \brief Decodes the element
  /// \param encoded byte array with the encoded element
  /// \param checkForGroupMembership flag indicating if the element should be validated
  /// \return Element after decoding
  /// \details DecodeElement() must be implemented in a derived class.
  /// \pre <tt>COUNTOF(encoded) == GetEncodedElementSize()</tt>
  virtual Element DecodeElement(const byte *encoded, bool checkForGroupMembership) const =0;

  /// \brief Converts an element to an Integer
  /// \param element the element to convert to an Integer
  /// \return Element after converting to an Integer
  /// \details ConvertElementToInteger() must be implemented in a derived class.
  virtual Integer ConvertElementToInteger(const Element &element) const =0;

  /// \brief Check the group for errors
  /// \param rng RandomNumberGenerator for objects which use randomized testing
  /// \param level level of thoroughness
  /// \return true if the tests succeed, false otherwise
  /// \details There are four levels of thoroughness:
  ///  <ul>
  ///  <li>0 - using this object won't cause a crash or exception
  ///  <li>1 - this object will probably function, and encrypt, sign, other operations correctly
  ///  <li>2 - ensure this object will function correctly, and perform reasonable security checks
  ///  <li>3 - perform reasonable security checks, and do checks that may take a long time
  ///  </ul>
  /// \details Level 0 does not require a RandomNumberGenerator. A NullRNG() can be used for level 0.
  ///  Level 1 may not check for weak keys and such. Levels 2 and 3 are recommended.
  /// \details ValidateGroup() must be implemented in a derived class.
  virtual bool ValidateGroup(RandomNumberGenerator &rng, unsigned int level) const =0;

  /// \brief Check the element for errors
  /// \param level level of thoroughness
  /// \param element element to check
  /// \param precomp optional pointer to DL_FixedBasePrecomputation
  /// \return true if the tests succeed, false otherwise
  /// \details There are four levels of thoroughness:
  ///  <ul>
  ///  <li>0 - using this object won't cause a crash or exception
  ///  <li>1 - this object will probably function, and encrypt, sign, other operations correctly
  ///  <li>2 - ensure this object will function correctly, and perform reasonable security checks
  ///  <li>3 - perform reasonable security checks, and do checks that may take a long time
  ///  </ul>
  /// \details Level 0 performs group membership checks. Level 1 may not check for weak keys and such.
  ///  Levels 2 and 3 are recommended.
  /// \details ValidateElement() must be implemented in a derived class.
  virtual bool ValidateElement(unsigned int level, const Element &element, const DL_FixedBasePrecomputation<Element> *precomp) const =0;

  virtual bool FastSubgroupCheckAvailable() const =0;

  /// \brief Determines if an element is an identity
  /// \param element element to check
  /// \return true if the element is an identity, false otherwise
  /// \details The identity element or or neutral element is a special element in a group that leaves
  ///  other elements unchanged when combined with it.
  /// \details IsIdentity() must be implemented in a derived class.
  virtual bool IsIdentity(const Element &element) const =0;

  /// \brief Exponentiates a base to multiple exponents
  /// \param results an array of Elements
  /// \param base the base to raise to the exponents
  /// \param exponents an array of exponents
  /// \param exponentsCount the number of exponents in the array
  /// \details SimultaneousExponentiate() raises the base to each exponent in the exponents array and stores the
  ///  result at the respective position in the results array.
  /// \details SimultaneousExponentiate() must be implemented in a derived class.
  /// \pre <tt>COUNTOF(results) == exponentsCount</tt>
  /// \pre <tt>COUNTOF(exponents) == exponentsCount</tt>
  virtual void SimultaneousExponentiate(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const =0;

protected:
  void ParametersChanged() {m_validationLevel = 0;}

private:
  mutable unsigned int m_validationLevel;
};

/// \brief Base implementation of Discrete Log (DL) group parameters
/// \tparam GROUP_PRECOMP group precomputation class
/// \tparam BASE_PRECOMP fixed base precomputation class
/// \tparam BASE class or type of an element
template <class GROUP_PRECOMP, class BASE_PRECOMP = DL_FixedBasePrecomputationImpl<typename GROUP_PRECOMP::Element>, class BASE = DL_GroupParameters<typename GROUP_PRECOMP::Element> >
class DL_GroupParametersImpl : public BASE
{
public:
  typedef GROUP_PRECOMP GroupPrecomputation;
  typedef typename GROUP_PRECOMP::Element Element;
  typedef BASE_PRECOMP BasePrecomputation;

  virtual ~DL_GroupParametersImpl() {}

  /// \brief Retrieves the group precomputation
  /// \return a const reference to the group precomputation
  const DL_GroupPrecomputation<Element> & GetGroupPrecomputation() const {return m_groupPrecomputation;}

  /// \brief Retrieves the group precomputation
  /// \return a const reference to the group precomputation using a fixed base
  const DL_FixedBasePrecomputation<Element> & GetBasePrecomputation() const {return m_gpc;}

  /// \brief Retrieves the group precomputation
  /// \return a non-const reference to the group precomputation using a fixed base
  DL_FixedBasePrecomputation<Element> & AccessBasePrecomputation() {return m_gpc;}

protected:
  GROUP_PRECOMP m_groupPrecomputation;
  BASE_PRECOMP m_gpc;
};

/// \brief Base class for a Discrete Log (DL) key
/// \tparam T class or type of an element
/// \details The element is usually an Integer, \ref ECP "ECP::Point" or \ref EC2N "EC2N::Point"
template <class T>
class CRYPTOPP_NO_VTABLE DL_Key
{
public:
  virtual ~DL_Key() {}

  /// \brief Retrieves abstract group parameters
  /// \return a const reference to the group parameters
  virtual const DL_GroupParameters<T> & GetAbstractGroupParameters() const =0;
  /// \brief Retrieves abstract group parameters
  /// \return a non-const reference to the group parameters
  virtual DL_GroupParameters<T> & AccessAbstractGroupParameters() =0;
};

/// \brief Interface for Discrete Log (DL) public keys
template <class T>
class CRYPTOPP_NO_VTABLE DL_PublicKey : public DL_Key<T>
{
  typedef DL_PublicKey<T> ThisClass;

public:
  typedef T Element;

  virtual ~DL_PublicKey();

  /// \brief Get a named value
  /// \param name the name of the object or value to retrieve
  /// \param valueType reference to a variable that receives the value
  /// \param pValue void pointer to a variable that receives the value
  /// \return true if the value was retrieved, false otherwise
  /// \details GetVoidValue() retrieves the value of name if it exists.
  /// \note GetVoidValue() is an internal function and should be implemented
  ///  by derived classes. Users should use one of the other functions instead.
  /// \sa GetValue(), GetValueWithDefault(), GetIntValue(), GetIntValueWithDefault(),
  ///  GetRequiredParameter() and GetRequiredIntParameter()
  bool GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const
  {
    return GetValueHelper(this, name, valueType, pValue, &this->GetAbstractGroupParameters())
        CRYPTOPP_GET_FUNCTION_ENTRY(PublicElement);
  }

  /// \brief Initialize or reinitialize this key
  /// \param source NameValuePairs to assign
  void AssignFrom(const NameValuePairs &source);

  /// \brief Retrieves the public element
  /// \return the public element
  virtual const Element & GetPublicElement() const {return GetPublicPrecomputation().GetBase(this->GetAbstractGroupParameters().GetGroupPrecomputation());}

  /// \brief Sets the public element
  /// \param y the public element
  virtual void SetPublicElement(const Element &y) {AccessPublicPrecomputation().SetBase(this->GetAbstractGroupParameters().GetGroupPrecomputation(), y);}

  /// \brief Exponentiates this element
  /// \param exponent the exponent to raise the base
  /// \return the public element raised to the exponent
  virtual Element ExponentiatePublicElement(const Integer &exponent) const
  {
    const DL_GroupParameters<T> &params = this->GetAbstractGroupParameters();
    return GetPublicPrecomputation().Exponentiate(params.GetGroupPrecomputation(), exponent);
  }

  /// \brief Exponentiates an element
  /// \param baseExp the first exponent
  /// \param publicExp the second exponent
  /// \return the public element raised to the exponent
  /// \details CascadeExponentiateBaseAndPublicElement raises the public element to
  ///  the base element and precomputation.
  virtual Element CascadeExponentiateBaseAndPublicElement(const Integer &baseExp, const Integer &publicExp) const
  {
    const DL_GroupParameters<T> &params = this->GetAbstractGroupParameters();
    return params.GetBasePrecomputation().CascadeExponentiate(params.GetGroupPrecomputation(), baseExp, GetPublicPrecomputation(), publicExp);
  }

  /// \brief Accesses the public precomputation
  /// \details GetPublicPrecomputation returns a const reference, while
  ///  AccessPublicPrecomputation returns a non-const reference. Must be
  ///  overridden in derived classes.
  virtual const DL_FixedBasePrecomputation<T> & GetPublicPrecomputation() const =0;

  /// \brief Accesses the public precomputation
  /// \details GetPublicPrecomputation returns a const reference, while
  ///  AccessPublicPrecomputation returns a non-const reference. Must be
  ///  overridden in derived classes.
  virtual DL_FixedBasePrecomputation<T> & AccessPublicPrecomputation() =0;
};

// Out-of-line dtor due to AIX and GCC, http://github.com/weidai11/cryptopp/issues/499
template<class T>
DL_PublicKey<T>::~DL_PublicKey() {}

/// \brief Interface for Discrete Log (DL) private keys
template <class T>
class CRYPTOPP_NO_VTABLE DL_PrivateKey : public DL_Key<T>
{
  typedef DL_PrivateKey<T> ThisClass;

public:
  typedef T Element;

  virtual ~DL_PrivateKey();

  /// \brief Initializes a public key from this key
  /// \param pub reference to a public key
  void MakePublicKey(DL_PublicKey<T> &pub) const
  {
    pub.AccessAbstractGroupParameters().AssignFrom(this->GetAbstractGroupParameters());
    pub.SetPublicElement(this->GetAbstractGroupParameters().ExponentiateBase(GetPrivateExponent()));
  }

  /// \brief Get a named value
  /// \param name the name of the object or value to retrieve
  /// \param valueType reference to a variable that receives the value
  /// \param pValue void pointer to a variable that receives the value
  /// \return true if the value was retrieved, false otherwise
  /// \details GetVoidValue() retrieves the value of name if it exists.
  /// \note GetVoidValue() is an internal function and should be implemented
  ///  by derived classes. Users should use one of the other functions instead.
  /// \sa GetValue(), GetValueWithDefault(), GetIntValue(), GetIntValueWithDefault(),
  ///  GetRequiredParameter() and GetRequiredIntParameter()
  bool GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const
  {
    return GetValueHelper(this, name, valueType, pValue, &this->GetAbstractGroupParameters())
        CRYPTOPP_GET_FUNCTION_ENTRY(PrivateExponent);
  }

  /// \brief Initialize or reinitialize this key
  /// \param source NameValuePairs to assign
  void AssignFrom(const NameValuePairs &source)
  {
    this->AccessAbstractGroupParameters().AssignFrom(source);
    AssignFromHelper(this, source)
      CRYPTOPP_SET_FUNCTION_ENTRY(PrivateExponent);
  }

  /// \brief Retrieves the private exponent
  /// \return the private exponent
  /// \details Must be overridden in derived classes.
  virtual const Integer & GetPrivateExponent() const =0;
  /// \brief Sets the private exponent
  /// \param x the private exponent
  /// \details Must be overridden in derived classes.
  virtual void SetPrivateExponent(const Integer &x) =0;
};

// Out-of-line dtor due to AIX and GCC, http://github.com/weidai11/cryptopp/issues/499
template<class T>
DL_PrivateKey<T>::~DL_PrivateKey() {}

template <class T>
void DL_PublicKey<T>::AssignFrom(const NameValuePairs &source)
{
  DL_PrivateKey<T> *pPrivateKey = NULLPTR;
  if (source.GetThisPointer(pPrivateKey))
    pPrivateKey->MakePublicKey(*this);
  else
  {
    this->AccessAbstractGroupParameters().AssignFrom(source);
    AssignFromHelper(this, source)
      CRYPTOPP_SET_FUNCTION_ENTRY(PublicElement);
  }
}

class OID;

/// \brief Discrete Log (DL) key base implementation
/// \tparam PK Key class
/// \tparam GP GroupParameters class
/// \tparam O OID class
template <class PK, class GP, class O = OID>
class DL_KeyImpl : public PK
{
public:
  typedef GP GroupParameters;

  virtual ~DL_KeyImpl() {}

  O GetAlgorithmID() const {return GetGroupParameters().GetAlgorithmID();}
  bool BERDecodeAlgorithmParameters(BufferedTransformation &bt)
    {AccessGroupParameters().BERDecode(bt); return true;}
  bool DEREncodeAlgorithmParameters(BufferedTransformation &bt) const
    {GetGroupParameters().DEREncode(bt); return true;}

  const GP & GetGroupParameters() const {return m_groupParameters;}
  GP & AccessGroupParameters() {return m_groupParameters;}

private:
  GP m_groupParameters;
};

class X509PublicKey;
class PKCS8PrivateKey;

/// \brief Discrete Log (DL) private key base implementation
/// \tparam GP GroupParameters class
template <class GP>
class DL_PrivateKeyImpl : public DL_PrivateKey<typename GP::Element>, public DL_KeyImpl<PKCS8PrivateKey, GP>
{
public:
  typedef typename GP::Element Element;

  virtual ~DL_PrivateKeyImpl() {}

  // GeneratableCryptoMaterial
  bool Validate(RandomNumberGenerator &rng, unsigned int level) const
  {
    CRYPTOPP_ASSERT(GetAbstractGroupParameters().Validate(rng, level));
    bool pass = GetAbstractGroupParameters().Validate(rng, level);

    const Integer &q = GetAbstractGroupParameters().GetSubgroupOrder();
    const Integer &x = GetPrivateExponent();

    CRYPTOPP_ASSERT(x.IsPositive());
    CRYPTOPP_ASSERT(x < q);
    pass = pass && x.IsPositive() && x < q;

    if (level >= 1)
    {
      CRYPTOPP_ASSERT(Integer::Gcd(x, q) == Integer::One());
      pass = pass && Integer::Gcd(x, q) == Integer::One();
    }
    return pass;
  }

  bool GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const
  {
    return GetValueHelper<DL_PrivateKey<Element> >(this, name, valueType, pValue).Assignable();
  }

  void AssignFrom(const NameValuePairs &source)
  {
    AssignFromHelper<DL_PrivateKey<Element> >(this, source);
  }

  void GenerateRandom(RandomNumberGenerator &rng, const NameValuePairs &params)
  {
    if (!params.GetThisObject(this->AccessGroupParameters()))
      this->AccessGroupParameters().GenerateRandom(rng, params);
    Integer x(rng, Integer::One(), GetAbstractGroupParameters().GetMaxExponent());
    SetPrivateExponent(x);
  }

  bool SupportsPrecomputation() const {return true;}

  void Precompute(unsigned int precomputationStorage=16)
    {AccessAbstractGroupParameters().Precompute(precomputationStorage);}

  void LoadPrecomputation(BufferedTransformation &storedPrecomputation)
    {AccessAbstractGroupParameters().LoadPrecomputation(storedPrecomputation);}

  void SavePrecomputation(BufferedTransformation &storedPrecomputation) const
    {GetAbstractGroupParameters().SavePrecomputation(storedPrecomputation);}

  // DL_Key
  const DL_GroupParameters<Element> & GetAbstractGroupParameters() const {return this->GetGroupParameters();}
  DL_GroupParameters<Element> & AccessAbstractGroupParameters() {return this->AccessGroupParameters();}

  // DL_PrivateKey
  const Integer & GetPrivateExponent() const {return m_x;}
  void SetPrivateExponent(const Integer &x) {m_x = x;}

  // PKCS8PrivateKey
  void BERDecodePrivateKey(BufferedTransformation &bt, bool, size_t)
    {m_x.BERDecode(bt);}
  void DEREncodePrivateKey(BufferedTransformation &bt) const
    {m_x.DEREncode(bt);}

private:
  Integer m_x;
};

template <class BASE, class SIGNATURE_SCHEME>
class DL_PrivateKey_WithSignaturePairwiseConsistencyTest : public BASE
{
public:
  virtual ~DL_PrivateKey_WithSignaturePairwiseConsistencyTest() {}

  void GenerateRandom(RandomNumberGenerator &rng, const NameValuePairs &params)
  {
    BASE::GenerateRandom(rng, params);

    if (FIPS_140_2_ComplianceEnabled())
    {
      typename SIGNATURE_SCHEME::Signer signer(*this);
      typename SIGNATURE_SCHEME::Verifier verifier(signer);
      SignaturePairwiseConsistencyTest_FIPS_140_Only(signer, verifier);
    }
  }
};

/// \brief Discrete Log (DL) public key base implementation
/// \tparam GP GroupParameters class
template <class GP>
class DL_PublicKeyImpl : public DL_PublicKey<typename GP::Element>, public DL_KeyImpl<X509PublicKey, GP>
{
public:
  typedef typename GP::Element Element;

  virtual ~DL_PublicKeyImpl();

  // CryptoMaterial
  bool Validate(RandomNumberGenerator &rng, unsigned int level) const
  {
    CRYPTOPP_ASSERT(GetAbstractGroupParameters().Validate(rng, level));
    bool pass = GetAbstractGroupParameters().Validate(rng, level);
    CRYPTOPP_ASSERT(GetAbstractGroupParameters().ValidateElement(level, this->GetPublicElement(), &GetPublicPrecomputation()));
    pass = pass && GetAbstractGroupParameters().ValidateElement(level, this->GetPublicElement(), &GetPublicPrecomputation());
    return pass;
  }

  bool GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const
  {
    return GetValueHelper<DL_PublicKey<Element> >(this, name, valueType, pValue).Assignable();
  }

  void AssignFrom(const NameValuePairs &source)
  {
    AssignFromHelper<DL_PublicKey<Element> >(this, source);
  }

  bool SupportsPrecomputation() const {return true;}

  void Precompute(unsigned int precomputationStorage=16)
  {
    AccessAbstractGroupParameters().Precompute(precomputationStorage);
    AccessPublicPrecomputation().Precompute(GetAbstractGroupParameters().GetGroupPrecomputation(), GetAbstractGroupParameters().GetSubgroupOrder().BitCount(), precomputationStorage);
  }

  void LoadPrecomputation(BufferedTransformation &storedPrecomputation)
  {
    AccessAbstractGroupParameters().LoadPrecomputation(storedPrecomputation);
    AccessPublicPrecomputation().Load(GetAbstractGroupParameters().GetGroupPrecomputation(), storedPrecomputation);
  }

  void SavePrecomputation(BufferedTransformation &storedPrecomputation) const
  {
    GetAbstractGroupParameters().SavePrecomputation(storedPrecomputation);
    GetPublicPrecomputation().Save(GetAbstractGroupParameters().GetGroupPrecomputation(), storedPrecomputation);
  }

  // DL_Key
  const DL_GroupParameters<Element> & GetAbstractGroupParameters() const {return this->GetGroupParameters();}
  DL_GroupParameters<Element> & AccessAbstractGroupParameters() {return this->AccessGroupParameters();}

  // DL_PublicKey
  const DL_FixedBasePrecomputation<Element> & GetPublicPrecomputation() const {return m_ypc;}
  DL_FixedBasePrecomputation<Element> & AccessPublicPrecomputation() {return m_ypc;}

  // non-inherited
  bool operator==(const DL_PublicKeyImpl<GP> &rhs) const
    {return this->GetGroupParameters() == rhs.GetGroupParameters() && this->GetPublicElement() == rhs.GetPublicElement();}

private:
  typename GP::BasePrecomputation m_ypc;
};

// Out-of-line dtor due to AIX and GCC, http://github.com/weidai11/cryptopp/issues/499
template<class GP>
DL_PublicKeyImpl<GP>::~DL_PublicKeyImpl() {}

/// \brief Interface for Elgamal-like signature algorithms
/// \tparam T Field element type or class
/// \details Field element <tt>T</tt> can be Integer, ECP or EC2N.
template <class T>
class CRYPTOPP_NO_VTABLE DL_ElgamalLikeSignatureAlgorithm
{
public:
  virtual ~DL_ElgamalLikeSignatureAlgorithm() {}

  /// \brief Sign a message using a private key
  /// \param params GroupParameters
  /// \param privateKey private key
  /// \param k signing exponent
  /// \param e encoded message
  /// \param r r part of signature
  /// \param s s part of signature
  virtual void Sign(const DL_GroupParameters<T> &params, const Integer &privateKey, const Integer &k, const Integer &e, Integer &r, Integer &s) const =0;

  /// \brief Verify a message using a public key
  /// \param params GroupParameters
  /// \param publicKey public key
  /// \param e encoded message
  /// \param r r part of signature
  /// \param s s part of signature
  virtual bool Verify(const DL_GroupParameters<T> &params, const DL_PublicKey<T> &publicKey, const Integer &e, const Integer &r, const Integer &s) const =0;

  /// \brief Recover a Presignature
  /// \param params GroupParameters
  /// \param publicKey public key
  /// \param r r part of signature
  /// \param s s part of signature
  virtual Integer RecoverPresignature(const DL_GroupParameters<T> &params, const DL_PublicKey<T> &publicKey, const Integer &r, const Integer &s) const
  {
    CRYPTOPP_UNUSED(params); CRYPTOPP_UNUSED(publicKey); CRYPTOPP_UNUSED(r); CRYPTOPP_UNUSED(s);
    throw NotImplemented("DL_ElgamalLikeSignatureAlgorithm: this signature scheme does not support message recovery");
    MAYBE_RETURN(Integer::Zero());
  }

  /// \brief Retrieve R length
  /// \param params GroupParameters
  virtual size_t RLen(const DL_GroupParameters<T> &params) const
    {return params.GetSubgroupOrder().ByteCount();}

  /// \brief Retrieve S length
  /// \param params GroupParameters
  virtual size_t SLen(const DL_GroupParameters<T> &params) const
    {return params.GetSubgroupOrder().ByteCount();}

  /// \brief Signature scheme flag
  /// \return true if the signature scheme is deterministic, false otherwise
  /// \details IsDeterministic() is provided for DL signers. It is used by RFC 6979 signature schemes.
  virtual bool IsDeterministic() const
    {return false;}
};

/// \brief Interface for deterministic signers
/// \details RFC 6979 signers which generate k based on the encoded message and private key
class CRYPTOPP_NO_VTABLE DeterministicSignatureAlgorithm
{
public:
  virtual ~DeterministicSignatureAlgorithm() {}

  /// \brief Generate k
  /// \param x private key
  /// \param q subgroup generator
  /// \param e encoded message
  virtual Integer GenerateRandom(const Integer &x, const Integer &q, const Integer &e) const =0;
};

/// \brief Interface for DL key agreement algorithms
/// \tparam T Field element type or class
/// \details Field element <tt>T</tt> can be Integer, ECP or EC2N.
/// \sa DLIES, ECIES, ECIES_P1363
template <class T>
class CRYPTOPP_NO_VTABLE DL_KeyAgreementAlgorithm
{
public:
  typedef T Element;

  virtual ~DL_KeyAgreementAlgorithm() {}

  virtual Element AgreeWithEphemeralPrivateKey(const DL_GroupParameters<Element> &params, const DL_FixedBasePrecomputation<Element> &publicPrecomputation, const Integer &privateExponent) const =0;
  virtual Element AgreeWithStaticPrivateKey(const DL_GroupParameters<Element> &params, const Element &publicElement, bool validateOtherPublicKey, const Integer &privateExponent) const =0;
};

/// \brief Interface for key derivation algorithms used in DL cryptosystems
/// \tparam T Field element type or class
/// \details Field element <tt>T</tt> can be Integer, ECP or EC2N.
/// \sa DLIES, ECIES, ECIES_P1363
template <class T>
class CRYPTOPP_NO_VTABLE DL_KeyDerivationAlgorithm
{
public:
  virtual ~DL_KeyDerivationAlgorithm() {}

  virtual bool ParameterSupported(const char *name) const
    {CRYPTOPP_UNUSED(name); return false;}
  virtual void Derive(const DL_GroupParameters<T> &groupParams, byte *derivedKey, size_t derivedLength, const T &agreedElement, const T &ephemeralPublicKey, const NameValuePairs &derivationParams) const =0;
};

/// \brief Interface for symmetric encryption algorithms used in DL cryptosystems
/// \sa DLIES, ECIES, ECIES_P1363
class CRYPTOPP_NO_VTABLE DL_SymmetricEncryptionAlgorithm
{
public:
  virtual ~DL_SymmetricEncryptionAlgorithm() {}

  virtual bool ParameterSupported(const char *name) const
    {CRYPTOPP_UNUSED(name); return false;}
  virtual size_t GetSymmetricKeyLength(size_t plaintextLength) const =0;
  virtual size_t GetSymmetricCiphertextLength(size_t plaintextLength) const =0;
  virtual size_t GetMaxSymmetricPlaintextLength(size_t ciphertextLength) const =0;
  virtual void SymmetricEncrypt(RandomNumberGenerator &rng, const byte *key, const byte *plaintext, size_t plaintextLength, byte *ciphertext, const NameValuePairs &parameters) const =0;
  virtual DecodingResult SymmetricDecrypt(const byte *key, const byte *ciphertext, size_t ciphertextLength, byte *plaintext, const NameValuePairs &parameters) const =0;
};

/// \brief Discrete Log (DL) base interface
/// \tparam KI public or private key interface
template <class KI>
class CRYPTOPP_NO_VTABLE DL_Base
{
protected:
  typedef KI KeyInterface;
  typedef typename KI::Element Element;

  virtual ~DL_Base() {}

  const DL_GroupParameters<Element> & GetAbstractGroupParameters() const {return GetKeyInterface().GetAbstractGroupParameters();}
  DL_GroupParameters<Element> & AccessAbstractGroupParameters() {return AccessKeyInterface().AccessAbstractGroupParameters();}

  virtual KeyInterface & AccessKeyInterface() =0;
  virtual const KeyInterface & GetKeyInterface() const =0;
};

/// \brief Discrete Log (DL) signature scheme base implementation
/// \tparam INTFACE PK_Signer or PK_Verifier derived class
/// \tparam KEY_INTFACE DL_Base key base used in the scheme
/// \details DL_SignatureSchemeBase provides common functions for signers and verifiers.
///  DL_Base<DL_PrivateKey> is used for signers, and DL_Base<DL_PublicKey> is used for verifiers.
template <class INTFACE, class KEY_INTFACE>
class CRYPTOPP_NO_VTABLE DL_SignatureSchemeBase : public INTFACE, public DL_Base<KEY_INTFACE>
{
public:
  virtual ~DL_SignatureSchemeBase() {}

  /// \brief Provides the signature length
  /// \return signature length, in bytes
  /// \details SignatureLength returns the size required for <tt>r+s</tt>.
  size_t SignatureLength() const
  {
    return GetSignatureAlgorithm().RLen(this->GetAbstractGroupParameters())
      + GetSignatureAlgorithm().SLen(this->GetAbstractGroupParameters());
  }

  /// \brief Provides the maximum recoverable length
  /// \return maximum recoverable length, in bytes
  size_t MaxRecoverableLength() const
    {return GetMessageEncodingInterface().MaxRecoverableLength(0, GetHashIdentifier().second, GetDigestSize());}

  /// \brief Provides the maximum recoverable length
  /// \param signatureLength the size of the signature
  /// \return maximum recoverable length based on signature length, in bytes
  /// \details this function is not implemented and always returns 0.
  size_t MaxRecoverableLengthFromSignatureLength(size_t signatureLength) const
    {CRYPTOPP_UNUSED(signatureLength); CRYPTOPP_ASSERT(false); return 0;}  // TODO

  /// \brief Determines if the scheme is probabilistic
  /// \return true if the scheme is probabilistic, false otherwise
  bool IsProbabilistic() const
    {return true;}

  /// \brief Determines if the scheme has non-recoverable part
  /// \return true if the message encoding has a non-recoverable part, false otherwise.
  bool AllowNonrecoverablePart() const
    {return GetMessageEncodingInterface().AllowNonrecoverablePart();}

  /// \brief Determines if the scheme allows recoverable part first
  /// \return true if the message encoding allows the recoverable part, false otherwise.
  bool RecoverablePartFirst() const
    {return GetMessageEncodingInterface().RecoverablePartFirst();}

protected:
  size_t MessageRepresentativeLength() const {return BitsToBytes(MessageRepresentativeBitLength());}
  size_t MessageRepresentativeBitLength() const {return this->GetAbstractGroupParameters().GetSubgroupOrder().BitCount();}

  // true if the scheme conforms to RFC 6979
  virtual bool IsDeterministic() const {return false;}

  virtual const DL_ElgamalLikeSignatureAlgorithm<typename KEY_INTFACE::Element> & GetSignatureAlgorithm() const =0;
  virtual const PK_SignatureMessageEncodingMethod & GetMessageEncodingInterface() const =0;
  virtual HashIdentifier GetHashIdentifier() const =0;
  virtual size_t GetDigestSize() const =0;
};

/// \brief Discrete Log (DL) signature scheme signer base implementation
/// \tparam T Field element type or class
/// \details Field element <tt>T</tt> can be Integer, ECP or EC2N.
template <class T>
class CRYPTOPP_NO_VTABLE DL_SignerBase : public DL_SignatureSchemeBase<PK_Signer, DL_PrivateKey<T> >
{
public:
  virtual ~DL_SignerBase() {}

  /// \brief Testing interface
  /// \param k Integer
  /// \param e Integer
  /// \param r Integer
  /// \param s Integer
  void RawSign(const Integer &k, const Integer &e, Integer &r, Integer &s) const
  {
    const DL_ElgamalLikeSignatureAlgorithm<T> &alg = this->GetSignatureAlgorithm();
    const DL_GroupParameters<T> &params = this->GetAbstractGroupParameters();
    const DL_PrivateKey<T> &key = this->GetKeyInterface();

    r = params.ConvertElementToInteger(params.ExponentiateBase(k));
    alg.Sign(params, key.GetPrivateExponent(), k, e, r, s);
  }

  void InputRecoverableMessage(PK_MessageAccumulator &messageAccumulator, const byte *recoverableMessage, size_t recoverableMessageLength) const
  {
    PK_MessageAccumulatorBase &ma = static_cast<PK_MessageAccumulatorBase &>(messageAccumulator);
    ma.m_recoverableMessage.Assign(recoverableMessage, recoverableMessageLength);
    this->GetMessageEncodingInterface().ProcessRecoverableMessage(ma.AccessHash(),
      recoverableMessage, recoverableMessageLength,
      ma.m_presignature, ma.m_presignature.size(),
      ma.m_semisignature);
  }

  size_t SignAndRestart(RandomNumberGenerator &rng, PK_MessageAccumulator &messageAccumulator, byte *signature, bool restart) const
  {
    this->GetMaterial().DoQuickSanityCheck();

    PK_MessageAccumulatorBase &ma = static_cast<PK_MessageAccumulatorBase &>(messageAccumulator);
    const DL_ElgamalLikeSignatureAlgorithm<T> &alg = this->GetSignatureAlgorithm();
    const DL_GroupParameters<T> &params = this->GetAbstractGroupParameters();
    const DL_PrivateKey<T> &key = this->GetKeyInterface();

    SecByteBlock representative(this->MessageRepresentativeLength());
    this->GetMessageEncodingInterface().ComputeMessageRepresentative(
      rng,
      ma.m_recoverableMessage, ma.m_recoverableMessage.size(),
      ma.AccessHash(), this->GetHashIdentifier(), ma.m_empty,
      representative, this->MessageRepresentativeBitLength());
    ma.m_empty = true;
    Integer e(representative, representative.size());

    // hash message digest into random number k to prevent reusing the same k on
    // different messages after virtual machine rollback
    if (rng.CanIncorporateEntropy())
      rng.IncorporateEntropy(representative, representative.size());

    Integer k, ks;
    const Integer& q = params.GetSubgroupOrder();
    if (alg.IsDeterministic())
    {
      const Integer& x = key.GetPrivateExponent();
      const DeterministicSignatureAlgorithm& det = dynamic_cast<const DeterministicSignatureAlgorithm&>(alg);
      k = det.GenerateRandom(x, q, e);
    }
    else
    {
      k.Randomize(rng, 1, params.GetSubgroupOrder()-1);
    }

    // Due to timing attack on nonce length by Jancar
    // https://github.com/weidai11/cryptopp/issues/869
    ks = k + q;
    if (ks.BitCount() == q.BitCount()) {
      ks += q;
    }

    Integer r, s;
    r = params.ConvertElementToInteger(params.ExponentiateBase(ks));
    alg.Sign(params, key.GetPrivateExponent(), k, e, r, s);

    /*
    Integer r, s;
    if (this->MaxRecoverableLength() > 0)
      r.Decode(ma.m_semisignature, ma.m_semisignature.size());
    else
      r.Decode(ma.m_presignature, ma.m_presignature.size());
    alg.Sign(params, key.GetPrivateExponent(), ma.m_k, e, r, s);
    */

    const size_t rLen = alg.RLen(params);
    r.Encode(signature, rLen);
    s.Encode(signature+rLen, alg.SLen(params));

    if (restart)
      RestartMessageAccumulator(rng, ma);

    return this->SignatureLength();
  }

protected:
  void RestartMessageAccumulator(RandomNumberGenerator &rng, PK_MessageAccumulatorBase &ma) const
  {
    // k needs to be generated before hashing for signature schemes with recovery
    // but to defend against VM rollbacks we need to generate k after hashing.
    // so this code is commented out, since no DL-based signature scheme with recovery
    // has been implemented in Crypto++ anyway
    /*
    const DL_ElgamalLikeSignatureAlgorithm<T> &alg = this->GetSignatureAlgorithm();
    const DL_GroupParameters<T> &params = this->GetAbstractGroupParameters();
    ma.m_k.Randomize(rng, 1, params.GetSubgroupOrder()-1);
    ma.m_presignature.New(params.GetEncodedElementSize(false));
    params.ConvertElementToInteger(params.ExponentiateBase(ma.m_k)).Encode(ma.m_presignature, ma.m_presignature.size());
    */
    CRYPTOPP_UNUSED(rng); CRYPTOPP_UNUSED(ma);
  }
};

/// \brief Discret Log (DL) Verifier base class
/// \tparam T Field element type or class
/// \details Field element <tt>T</tt> can be Integer, ECP or EC2N.
template <class T>
class CRYPTOPP_NO_VTABLE DL_VerifierBase : public DL_SignatureSchemeBase<PK_Verifier, DL_PublicKey<T> >
{
public:
  virtual ~DL_VerifierBase() {}

  void InputSignature(PK_MessageAccumulator &messageAccumulator, const byte *signature, size_t signatureLength) const
  {
    PK_MessageAccumulatorBase &ma = static_cast<PK_MessageAccumulatorBase &>(messageAccumulator);
    const DL_ElgamalLikeSignatureAlgorithm<T> &alg = this->GetSignatureAlgorithm();
    const DL_GroupParameters<T> &params = this->GetAbstractGroupParameters();

    // Validation due to https://github.com/weidai11/cryptopp/issues/981
    // We allow a caller to provide R and S in oversized buffer. R and S
    // are read based on the field element size, and not the buffer size.
    const size_t rLen = alg.RLen(params);
    const size_t sLen = alg.SLen(params);
    CRYPTOPP_ASSERT(signatureLength >= rLen + sLen);
    if (signatureLength < rLen + sLen)
      throw InvalidDataFormat("DL_VerifierBase: signature length is not valid.");

    ma.m_semisignature.Assign(signature, rLen);
    ma.m_s.Decode(signature+rLen, sLen);

    this->GetMessageEncodingInterface().ProcessSemisignature(ma.AccessHash(), ma.m_semisignature, ma.m_semisignature.size());
  }

  bool VerifyAndRestart(PK_MessageAccumulator &messageAccumulator) const
  {
    this->GetMaterial().DoQuickSanityCheck();

    PK_MessageAccumulatorBase &ma = static_cast<PK_MessageAccumulatorBase &>(messageAccumulator);
    const DL_ElgamalLikeSignatureAlgorithm<T> &alg = this->GetSignatureAlgorithm();
    const DL_GroupParameters<T> &params = this->GetAbstractGroupParameters();
    const DL_PublicKey<T> &key = this->GetKeyInterface();

    SecByteBlock representative(this->MessageRepresentativeLength());
    this->GetMessageEncodingInterface().ComputeMessageRepresentative(NullRNG(), ma.m_recoverableMessage, ma.m_recoverableMessage.size(),
      ma.AccessHash(), this->GetHashIdentifier(), ma.m_empty,
      representative, this->MessageRepresentativeBitLength());
    ma.m_empty = true;
    Integer e(representative, representative.size());

    Integer r(ma.m_semisignature, ma.m_semisignature.size());
    return alg.Verify(params, key, e, r, ma.m_s);
  }

  DecodingResult RecoverAndRestart(byte *recoveredMessage, PK_MessageAccumulator &messageAccumulator) const
  {
    this->GetMaterial().DoQuickSanityCheck();

    PK_MessageAccumulatorBase &ma = static_cast<PK_MessageAccumulatorBase &>(messageAccumulator);
    const DL_ElgamalLikeSignatureAlgorithm<T> &alg = this->GetSignatureAlgorithm();
    const DL_GroupParameters<T> &params = this->GetAbstractGroupParameters();
    const DL_PublicKey<T> &key = this->GetKeyInterface();

    SecByteBlock representative(this->MessageRepresentativeLength());
    this->GetMessageEncodingInterface().ComputeMessageRepresentative(
      NullRNG(),
      ma.m_recoverableMessage, ma.m_recoverableMessage.size(),
      ma.AccessHash(), this->GetHashIdentifier(), ma.m_empty,
      representative, this->MessageRepresentativeBitLength());
    ma.m_empty = true;
    Integer e(representative, representative.size());

    ma.m_presignature.New(params.GetEncodedElementSize(false));
    Integer r(ma.m_semisignature, ma.m_semisignature.size());
    alg.RecoverPresignature(params, key, r, ma.m_s).Encode(ma.m_presignature, ma.m_presignature.size());

    return this->GetMessageEncodingInterface().RecoverMessageFromSemisignature(
      ma.AccessHash(), this->GetHashIdentifier(),
      ma.m_presignature, ma.m_presignature.size(),
      ma.m_semisignature, ma.m_semisignature.size(),
      recoveredMessage);
  }
};

/// \brief Discrete Log (DL) cryptosystem base implementation
/// \tparam PK field element type
/// \tparam KI public or private key interface
template <class PK, class KI>
class CRYPTOPP_NO_VTABLE DL_CryptoSystemBase : public PK, public DL_Base<KI>
{
public:
  typedef typename DL_Base<KI>::Element Element;

  virtual ~DL_CryptoSystemBase() {}

  size_t MaxPlaintextLength(size_t ciphertextLength) const
  {
    unsigned int minLen = this->GetAbstractGroupParameters().GetEncodedElementSize(true);
    return ciphertextLength < minLen ? 0 : GetSymmetricEncryptionAlgorithm().GetMaxSymmetricPlaintextLength(ciphertextLength - minLen);
  }

  size_t CiphertextLength(size_t plaintextLength) const
  {
    size_t len = GetSymmetricEncryptionAlgorithm().GetSymmetricCiphertextLength(plaintextLength);
    return len == 0 ? 0 : this->GetAbstractGroupParameters().GetEncodedElementSize(true) + len;
  }

  bool ParameterSupported(const char *name) const
    {return GetKeyDerivationAlgorithm().ParameterSupported(name) || GetSymmetricEncryptionAlgorithm().ParameterSupported(name);}

protected:
  virtual const DL_KeyAgreementAlgorithm<Element> & GetKeyAgreementAlgorithm() const =0;
  virtual const DL_KeyDerivationAlgorithm<Element> & GetKeyDerivationAlgorithm() const =0;
  virtual const DL_SymmetricEncryptionAlgorithm & GetSymmetricEncryptionAlgorithm() const =0;
};

/// \brief Discrete Log (DL) decryptor base implementation
/// \tparam T Field element type or class
/// \details Field element <tt>T</tt> can be Integer, ECP or EC2N.
template <class T>
class CRYPTOPP_NO_VTABLE DL_DecryptorBase : public DL_CryptoSystemBase<PK_Decryptor, DL_PrivateKey<T> >
{
public:
  typedef T Element;

  virtual ~DL_DecryptorBase() {}

  DecodingResult Decrypt(RandomNumberGenerator &rng, const byte *ciphertext, size_t ciphertextLength, byte *plaintext, const NameValuePairs &parameters = g_nullNameValuePairs) const
  {
    try
    {
      CRYPTOPP_UNUSED(rng);
      const DL_KeyAgreementAlgorithm<T> &agreeAlg = this->GetKeyAgreementAlgorithm();
      const DL_KeyDerivationAlgorithm<T> &derivAlg = this->GetKeyDerivationAlgorithm();
      const DL_SymmetricEncryptionAlgorithm &encAlg = this->GetSymmetricEncryptionAlgorithm();
      const DL_GroupParameters<T> &params = this->GetAbstractGroupParameters();
      const DL_PrivateKey<T> &key = this->GetKeyInterface();

      Element q = params.DecodeElement(ciphertext, true);
      size_t elementSize = params.GetEncodedElementSize(true);
      ciphertext += elementSize;
      ciphertextLength -= elementSize;

      Element z = agreeAlg.AgreeWithStaticPrivateKey(params, q, true, key.GetPrivateExponent());

      SecByteBlock derivedKey(encAlg.GetSymmetricKeyLength(encAlg.GetMaxSymmetricPlaintextLength(ciphertextLength)));
      derivAlg.Derive(params, derivedKey, derivedKey.size(), z, q, parameters);

      return encAlg.SymmetricDecrypt(derivedKey, ciphertext, ciphertextLength, plaintext, parameters);
    }
    catch (DL_BadElement &)
    {
      return DecodingResult();
    }
  }
};

/// \brief Discrete Log (DL) encryptor base implementation
/// \tparam T Field element type or class
/// \details Field element <tt>T</tt> can be Integer, ECP or EC2N.
template <class T>
class CRYPTOPP_NO_VTABLE DL_EncryptorBase : public DL_CryptoSystemBase<PK_Encryptor, DL_PublicKey<T> >
{
public:
  typedef T Element;

  virtual ~DL_EncryptorBase() {}

  void Encrypt(RandomNumberGenerator &rng, const byte *plaintext, size_t plaintextLength, byte *ciphertext, const NameValuePairs &parameters = g_nullNameValuePairs) const
  {
    const DL_KeyAgreementAlgorithm<T> &agreeAlg = this->GetKeyAgreementAlgorithm();
    const DL_KeyDerivationAlgorithm<T> &derivAlg = this->GetKeyDerivationAlgorithm();
    const DL_SymmetricEncryptionAlgorithm &encAlg = this->GetSymmetricEncryptionAlgorithm();
    const DL_GroupParameters<T> &params = this->GetAbstractGroupParameters();
    const DL_PublicKey<T> &key = this->GetKeyInterface();

    Integer x(rng, Integer::One(), params.GetMaxExponent());
    Element q = params.ExponentiateBase(x);
    params.EncodeElement(true, q, ciphertext);
    unsigned int elementSize = params.GetEncodedElementSize(true);
    ciphertext += elementSize;

    Element z = agreeAlg.AgreeWithEphemeralPrivateKey(params, key.GetPublicPrecomputation(), x);

    SecByteBlock derivedKey(encAlg.GetSymmetricKeyLength(plaintextLength));
    derivAlg.Derive(params, derivedKey, derivedKey.size(), z, q, parameters);

    encAlg.SymmetricEncrypt(rng, derivedKey, plaintext, plaintextLength, ciphertext, parameters);
  }
};

/// \brief Discrete Log (DL) scheme options
/// \tparam T1 algorithm information
/// \tparam T2 group parameters for the scheme
template <class T1, class T2>
struct DL_SchemeOptionsBase
{
  typedef T1 AlgorithmInfo;
  typedef T2 GroupParameters;
  typedef typename GroupParameters::Element Element;
};

/// \brief Discrete Log (DL) key options
/// \tparam T1 algorithm information
/// \tparam T2 keys used in the scheme
template <class T1, class T2>
struct DL_KeyedSchemeOptions : public DL_SchemeOptionsBase<T1, typename T2::PublicKey::GroupParameters>
{
  typedef T2 Keys;
  typedef typename Keys::PrivateKey PrivateKey;
  typedef typename Keys::PublicKey PublicKey;
};

/// \brief Discrete Log (DL) signature scheme options
/// \tparam T1 algorithm information
/// \tparam T2 keys used in the scheme
/// \tparam T3 signature algorithm
/// \tparam T4 message encoding method
/// \tparam T5 hash function
template <class T1, class T2, class T3, class T4, class T5>
struct DL_SignatureSchemeOptions : public DL_KeyedSchemeOptions<T1, T2>
{
  typedef T3 SignatureAlgorithm;
  typedef T4 MessageEncodingMethod;
  typedef T5 HashFunction;
};

/// \brief Discrete Log (DL) crypto scheme options
/// \tparam T1 algorithm information
/// \tparam T2 keys used in the scheme
/// \tparam T3 key agreement algorithm
/// \tparam T4 key derivation algorithm
/// \tparam T5 symmetric encryption algorithm
template <class T1, class T2, class T3, class T4, class T5>
struct DL_CryptoSchemeOptions : public DL_KeyedSchemeOptions<T1, T2>
{
  typedef T3 KeyAgreementAlgorithm;
  typedef T4 KeyDerivationAlgorithm;
  typedef T5 SymmetricEncryptionAlgorithm;
};

/// \brief Discrete Log (DL) base object implementation
/// \tparam BASE TODO
/// \tparam SCHEME_OPTIONS options for the scheme
/// \tparam KEY key used in the scheme
template <class BASE, class SCHEME_OPTIONS, class KEY>
class CRYPTOPP_NO_VTABLE DL_ObjectImplBase : public AlgorithmImpl<BASE, typename SCHEME_OPTIONS::AlgorithmInfo>
{
public:
  typedef SCHEME_OPTIONS SchemeOptions;
  typedef typename KEY::Element Element;

  virtual ~DL_ObjectImplBase() {}

  PrivateKey & AccessPrivateKey() {return m_key;}
  PublicKey & AccessPublicKey() {return m_key;}

  // KeyAccessor
  const KEY & GetKey() const {return m_key;}
  KEY & AccessKey() {return m_key;}

protected:
  typename BASE::KeyInterface & AccessKeyInterface() {return m_key;}
  const typename BASE::KeyInterface & GetKeyInterface() const {return m_key;}

  // for signature scheme
  HashIdentifier GetHashIdentifier() const
  {
    typedef typename SchemeOptions::MessageEncodingMethod::HashIdentifierLookup HashLookup;
    return HashLookup::template HashIdentifierLookup2<typename SchemeOptions::HashFunction>::Lookup();
  }
  size_t GetDigestSize() const
  {
    typedef typename SchemeOptions::HashFunction H;
    return H::DIGESTSIZE;
  }

private:
  KEY m_key;
};

/// \brief Discrete Log (DL) object implementation
/// \tparam BASE TODO
/// \tparam SCHEME_OPTIONS options for the scheme
/// \tparam KEY key used in the scheme
template <class BASE, class SCHEME_OPTIONS, class KEY>
class CRYPTOPP_NO_VTABLE DL_ObjectImpl : public DL_ObjectImplBase<BASE, SCHEME_OPTIONS, KEY>
{
public:
  typedef typename KEY::Element Element;

  virtual ~DL_ObjectImpl() {}

protected:
  const DL_ElgamalLikeSignatureAlgorithm<Element> & GetSignatureAlgorithm() const
    {return Singleton<typename SCHEME_OPTIONS::SignatureAlgorithm>().Ref();}
  const DL_KeyAgreementAlgorithm<Element> & GetKeyAgreementAlgorithm() const
    {return Singleton<typename SCHEME_OPTIONS::KeyAgreementAlgorithm>().Ref();}
  const DL_KeyDerivationAlgorithm<Element> & GetKeyDerivationAlgorithm() const
    {return Singleton<typename SCHEME_OPTIONS::KeyDerivationAlgorithm>().Ref();}
  const DL_SymmetricEncryptionAlgorithm & GetSymmetricEncryptionAlgorithm() const
    {return Singleton<typename SCHEME_OPTIONS::SymmetricEncryptionAlgorithm>().Ref();}
  HashIdentifier GetHashIdentifier() const
    {return HashIdentifier();}
  const PK_SignatureMessageEncodingMethod & GetMessageEncodingInterface() const
    {return Singleton<typename SCHEME_OPTIONS::MessageEncodingMethod>().Ref();}
};

/// \brief Discrete Log (DL) signer implementation
/// \tparam SCHEME_OPTIONS options for the scheme
template <class SCHEME_OPTIONS>
class DL_SignerImpl : public DL_ObjectImpl<DL_SignerBase<typename SCHEME_OPTIONS::Element>, SCHEME_OPTIONS, typename SCHEME_OPTIONS::PrivateKey>
{
public:
  PK_MessageAccumulator * NewSignatureAccumulator(RandomNumberGenerator &rng) const
  {
    member_ptr<PK_MessageAccumulatorBase> p(new PK_MessageAccumulatorImpl<typename SCHEME_OPTIONS::HashFunction>);
    this->RestartMessageAccumulator(rng, *p);
    return p.release();
  }
};

/// \brief Discrete Log (DL) verifier implementation
/// \tparam SCHEME_OPTIONS options for the scheme
template <class SCHEME_OPTIONS>
class DL_VerifierImpl : public DL_ObjectImpl<DL_VerifierBase<typename SCHEME_OPTIONS::Element>, SCHEME_OPTIONS, typename SCHEME_OPTIONS::PublicKey>
{
public:
  PK_MessageAccumulator * NewVerificationAccumulator() const
  {
    return new PK_MessageAccumulatorImpl<typename SCHEME_OPTIONS::HashFunction>;
  }
};

/// \brief Discrete Log (DL) encryptor implementation
/// \tparam SCHEME_OPTIONS options for the scheme
template <class SCHEME_OPTIONS>
class DL_EncryptorImpl : public DL_ObjectImpl<DL_EncryptorBase<typename SCHEME_OPTIONS::Element>, SCHEME_OPTIONS, typename SCHEME_OPTIONS::PublicKey>
{
};

/// \brief Discrete Log (DL) decryptor implementation
/// \tparam SCHEME_OPTIONS options for the scheme
template <class SCHEME_OPTIONS>
class DL_DecryptorImpl : public DL_ObjectImpl<DL_DecryptorBase<typename SCHEME_OPTIONS::Element>, SCHEME_OPTIONS, typename SCHEME_OPTIONS::PrivateKey>
{
};

// ********************************************************

/// \brief Discrete Log (DL) simple key agreement base implementation
/// \tparam T class or type
template <class T>
class CRYPTOPP_NO_VTABLE DL_SimpleKeyAgreementDomainBase : public SimpleKeyAgreementDomain
{
public:
  typedef T Element;

  virtual ~DL_SimpleKeyAgreementDomainBase() {}

  CryptoParameters & AccessCryptoParameters() {return AccessAbstractGroupParameters();}
  unsigned int AgreedValueLength() const {return GetAbstractGroupParameters().GetEncodedElementSize(false);}
  unsigned int PrivateKeyLength() const {return GetAbstractGroupParameters().GetSubgroupOrder().ByteCount();}
  unsigned int PublicKeyLength() const {return GetAbstractGroupParameters().GetEncodedElementSize(true);}

  void GeneratePrivateKey(RandomNumberGenerator &rng, byte *privateKey) const
  {
    Integer x(rng, Integer::One(), GetAbstractGroupParameters().GetMaxExponent());
    x.Encode(privateKey, PrivateKeyLength());
  }

  void GeneratePublicKey(RandomNumberGenerator &rng, const byte *privateKey, byte *publicKey) const
  {
    CRYPTOPP_UNUSED(rng);
    const DL_GroupParameters<T> &params = GetAbstractGroupParameters();
    Integer x(privateKey, PrivateKeyLength());
    Element y = params.ExponentiateBase(x);
    params.EncodeElement(true, y, publicKey);
  }

  bool Agree(byte *agreedValue, const byte *privateKey, const byte *otherPublicKey, bool validateOtherPublicKey=true) const
  {
    try
    {
      const DL_GroupParameters<T> &params = GetAbstractGroupParameters();
      Integer x(privateKey, PrivateKeyLength());
      Element w = params.DecodeElement(otherPublicKey, validateOtherPublicKey);

      Element z = GetKeyAgreementAlgorithm().AgreeWithStaticPrivateKey(
        GetAbstractGroupParameters(), w, validateOtherPublicKey, x);
      params.EncodeElement(false, z, agreedValue);
    }
    catch (DL_BadElement &)
    {
      return false;
    }
    return true;
  }

  /// \brief Retrieves a reference to the group generator
  /// \return const reference to the group generator
  const Element &GetGenerator() const {return GetAbstractGroupParameters().GetSubgroupGenerator();}

protected:
  virtual const DL_KeyAgreementAlgorithm<Element> & GetKeyAgreementAlgorithm() const =0;
  virtual DL_GroupParameters<Element> & AccessAbstractGroupParameters() =0;
  const DL_GroupParameters<Element> & GetAbstractGroupParameters() const {return const_cast<DL_SimpleKeyAgreementDomainBase<Element> *>(this)->AccessAbstractGroupParameters();}
};

/// \brief Methods for avoiding "Small-Subgroup" attacks on Diffie-Hellman Key Agreement
/// \details Additional methods exist and include public key validation and choice of prime p.
/// \sa <A HREF="http://tools.ietf.org/html/rfc2785">Methods for Avoiding the "Small-Subgroup" Attacks on the
///  Diffie-Hellman Key Agreement Method for S/MIME</A>
enum CofactorMultiplicationOption {
  /// \brief No cofactor multiplication applied
  NO_COFACTOR_MULTIPLICTION,
  /// \brief Cofactor multiplication compatible with ordinary Diffie-Hellman
  /// \details Modifies the computation of ZZ by including j (the cofactor) in the computations and is
  ///  compatible with ordinary Diffie-Hellman.
  COMPATIBLE_COFACTOR_MULTIPLICTION,
  /// \brief Cofactor multiplication incompatible with ordinary Diffie-Hellman
  /// \details Modifies the computation of ZZ by including j (the cofactor) in the computations but is
  ///  not compatible with ordinary Diffie-Hellman.
  INCOMPATIBLE_COFACTOR_MULTIPLICTION};

typedef EnumToType<CofactorMultiplicationOption, NO_COFACTOR_MULTIPLICTION> NoCofactorMultiplication;
typedef EnumToType<CofactorMultiplicationOption, COMPATIBLE_COFACTOR_MULTIPLICTION> CompatibleCofactorMultiplication;
typedef EnumToType<CofactorMultiplicationOption, INCOMPATIBLE_COFACTOR_MULTIPLICTION> IncompatibleCofactorMultiplication;

/// \brief Diffie-Hellman key agreement algorithm
template <class ELEMENT, class COFACTOR_OPTION>
class DL_KeyAgreementAlgorithm_DH : public DL_KeyAgreementAlgorithm<ELEMENT>
{
public:
  typedef ELEMENT Element;

  CRYPTOPP_STATIC_CONSTEXPR const char* CRYPTOPP_API StaticAlgorithmName()
    {return COFACTOR_OPTION::ToEnum() == INCOMPATIBLE_COFACTOR_MULTIPLICTION ? "DHC" : "DH";}

  virtual ~DL_KeyAgreementAlgorithm_DH() {}

  Element AgreeWithEphemeralPrivateKey(const DL_GroupParameters<Element> &params, const DL_FixedBasePrecomputation<Element> &publicPrecomputation, const Integer &privateExponent) const
  {
    return publicPrecomputation.Exponentiate(params.GetGroupPrecomputation(),
      COFACTOR_OPTION::ToEnum() == INCOMPATIBLE_COFACTOR_MULTIPLICTION ? privateExponent*params.GetCofactor() : privateExponent);
  }

  Element AgreeWithStaticPrivateKey(const DL_GroupParameters<Element> &params, const Element &publicElement, bool validateOtherPublicKey, const Integer &privateExponent) const
  {
    if (COFACTOR_OPTION::ToEnum() == COMPATIBLE_COFACTOR_MULTIPLICTION)
    {
      const Integer &k = params.GetCofactor();
      return params.ExponentiateElement(publicElement,
        ModularArithmetic(params.GetSubgroupOrder()).Divide(privateExponent, k)*k);
    }
    else if (COFACTOR_OPTION::ToEnum() == INCOMPATIBLE_COFACTOR_MULTIPLICTION)
      return params.ExponentiateElement(publicElement, privateExponent*params.GetCofactor());
    else
    {
      CRYPTOPP_ASSERT(COFACTOR_OPTION::ToEnum() == NO_COFACTOR_MULTIPLICTION);

      if (!validateOtherPublicKey)
        return params.ExponentiateElement(publicElement, privateExponent);

      if (params.FastSubgroupCheckAvailable())
      {
        if (!params.ValidateElement(2, publicElement, NULLPTR))
          throw DL_BadElement();
        return params.ExponentiateElement(publicElement, privateExponent);
      }
      else
      {
        const Integer e[2] = {params.GetSubgroupOrder(), privateExponent};
        Element r[2];
        params.SimultaneousExponentiate(r, publicElement, e, 2);
        if (!params.IsIdentity(r[0]))
          throw DL_BadElement();
        return r[1];
      }
    }
  }
};

// ********************************************************

/// \brief Template implementing constructors for public key algorithm classes
template <class BASE>
class CRYPTOPP_NO_VTABLE PK_FinalTemplate : public BASE
{
public:
  PK_FinalTemplate() {}

  PK_FinalTemplate(const CryptoMaterial &key)
    {this->AccessKey().AssignFrom(key);}

  PK_FinalTemplate(BufferedTransformation &bt)
    {this->AccessKey().BERDecode(bt);}

  PK_FinalTemplate(const AsymmetricAlgorithm &algorithm)
    {this->AccessKey().AssignFrom(algorithm.GetMaterial());}

  PK_FinalTemplate(const Integer &v1)
    {this->AccessKey().Initialize(v1);}

  template <class T1, class T2>
  PK_FinalTemplate(const T1 &v1, const T2 &v2)
    {this->AccessKey().Initialize(v1, v2);}

  template <class T1, class T2, class T3>
  PK_FinalTemplate(const T1 &v1, const T2 &v2, const T3 &v3)
    {this->AccessKey().Initialize(v1, v2, v3);}

  template <class T1, class T2, class T3, class T4>
  PK_FinalTemplate(const T1 &v1, const T2 &v2, const T3 &v3, const T4 &v4)
    {this->AccessKey().Initialize(v1, v2, v3, v4);}

  template <class T1, class T2, class T3, class T4, class T5>
  PK_FinalTemplate(const T1 &v1, const T2 &v2, const T3 &v3, const T4 &v4, const T5 &v5)
    {this->AccessKey().Initialize(v1, v2, v3, v4, v5);}

  template <class T1, class T2, class T3, class T4, class T5, class T6>
  PK_FinalTemplate(const T1 &v1, const T2 &v2, const T3 &v3, const T4 &v4, const T5 &v5, const T6 &v6)
    {this->AccessKey().Initialize(v1, v2, v3, v4, v5, v6);}

  template <class T1, class T2, class T3, class T4, class T5, class T6, class T7>
  PK_FinalTemplate(const T1 &v1, const T2 &v2, const T3 &v3, const T4 &v4, const T5 &v5, const T6 &v6, const T7 &v7)
    {this->AccessKey().Initialize(v1, v2, v3, v4, v5, v6, v7);}

  template <class T1, class T2, class T3, class T4, class T5, class T6, class T7, class T8>
  PK_FinalTemplate(const T1 &v1, const T2 &v2, const T3 &v3, const T4 &v4, const T5 &v5, const T6 &v6, const T7 &v7, const T8 &v8)
    {this->AccessKey().Initialize(v1, v2, v3, v4, v5, v6, v7, v8);}

  template <class T1, class T2>
  PK_FinalTemplate(T1 &v1, const T2 &v2)
    {this->AccessKey().Initialize(v1, v2);}

  template <class T1, class T2, class T3>
  PK_FinalTemplate(T1 &v1, const T2 &v2, const T3 &v3)
    {this->AccessKey().Initialize(v1, v2, v3);}

  template <class T1, class T2, class T3, class T4>
  PK_FinalTemplate(T1 &v1, const T2 &v2, const T3 &v3, const T4 &v4)
    {this->AccessKey().Initialize(v1, v2, v3, v4);}

  template <class T1, class T2, class T3, class T4, class T5>
  PK_FinalTemplate(T1 &v1, const T2 &v2, const T3 &v3, const T4 &v4, const T5 &v5)
    {this->AccessKey().Initialize(v1, v2, v3, v4, v5);}

  template <class T1, class T2, class T3, class T4, class T5, class T6>
  PK_FinalTemplate(T1 &v1, const T2 &v2, const T3 &v3, const T4 &v4, const T5 &v5, const T6 &v6)
    {this->AccessKey().Initialize(v1, v2, v3, v4, v5, v6);}

  template <class T1, class T2, class T3, class T4, class T5, class T6, class T7>
  PK_FinalTemplate(T1 &v1, const T2 &v2, const T3 &v3, const T4 &v4, const T5 &v5, const T6 &v6, const T7 &v7)
    {this->AccessKey().Initialize(v1, v2, v3, v4, v5, v6, v7);}

  template <class T1, class T2, class T3, class T4, class T5, class T6, class T7, class T8>
  PK_FinalTemplate(T1 &v1, const T2 &v2, const T3 &v3, const T4 &v4, const T5 &v5, const T6 &v6, const T7 &v7, const T8 &v8)
    {this->AccessKey().Initialize(v1, v2, v3, v4, v5, v6, v7, v8);}
};

/// \brief Base class for public key encryption standard classes.
/// \details These classes are used to select from variants of algorithms.
///  Not all standards apply to all algorithms.
struct EncryptionStandard {};

/// \brief Base class for public key signature standard classes.
/// \details These classes are used to select from variants of algorithms.
///  Not all standards apply to all algorithms.
struct SignatureStandard {};

/// \brief Trapdoor Function (TF) encryption scheme
/// \tparam STANDARD standard
/// \tparam KEYS keys used in the encryption scheme
/// \tparam ALG_INFO algorithm information
template <class KEYS, class STANDARD, class ALG_INFO>
class TF_ES;

template <class KEYS, class STANDARD, class ALG_INFO = TF_ES<KEYS, STANDARD, int> >
class TF_ES : public KEYS
{
  typedef typename STANDARD::EncryptionMessageEncodingMethod MessageEncodingMethod;

public:
  /// see EncryptionStandard for a list of standards
  typedef STANDARD Standard;
  typedef TF_CryptoSchemeOptions<ALG_INFO, KEYS, MessageEncodingMethod> SchemeOptions;

  static std::string CRYPTOPP_API StaticAlgorithmName() {return std::string(KEYS::StaticAlgorithmName()) + "/" + MessageEncodingMethod::StaticAlgorithmName();}

  /// implements PK_Decryptor interface
  typedef PK_FinalTemplate<TF_DecryptorImpl<SchemeOptions> > Decryptor;
  /// implements PK_Encryptor interface
  typedef PK_FinalTemplate<TF_EncryptorImpl<SchemeOptions> > Encryptor;
};

/// \brief Trapdoor Function (TF) Signature Scheme
/// \tparam STANDARD standard
/// \tparam H hash function
/// \tparam KEYS keys used in the signature scheme
/// \tparam ALG_INFO algorithm information
template <class KEYS, class STANDARD, class H, class ALG_INFO>
class TF_SS;

template <class KEYS, class STANDARD, class H, class ALG_INFO = TF_SS<KEYS, STANDARD, H, int> >
class TF_SS : public KEYS
{
public:
  /// see SignatureStandard for a list of standards
  typedef STANDARD Standard;
  typedef typename Standard::SignatureMessageEncodingMethod MessageEncodingMethod;
  typedef TF_SignatureSchemeOptions<ALG_INFO, KEYS, MessageEncodingMethod, H> SchemeOptions;

  static std::string CRYPTOPP_API StaticAlgorithmName() {return std::string(KEYS::StaticAlgorithmName()) + "/" + MessageEncodingMethod::StaticAlgorithmName() + "(" + H::StaticAlgorithmName() + ")";}

  /// implements PK_Signer interface
  typedef PK_FinalTemplate<TF_SignerImpl<SchemeOptions> > Signer;
  /// implements PK_Verifier interface
  typedef PK_FinalTemplate<TF_VerifierImpl<SchemeOptions> > Verifier;
};

/// \brief Discrete Log (DL) signature scheme
/// \tparam KEYS keys used in the signature scheme
/// \tparam SA signature algorithm
/// \tparam MEM message encoding method
/// \tparam H hash function
/// \tparam ALG_INFO algorithm information
template <class KEYS, class SA, class MEM, class H, class ALG_INFO>
class DL_SS;

template <class KEYS, class SA, class MEM, class H, class ALG_INFO = DL_SS<KEYS, SA, MEM, H, int> >
class DL_SS : public KEYS
{
  typedef DL_SignatureSchemeOptions<ALG_INFO, KEYS, SA, MEM, H> SchemeOptions;

public:
  static std::string StaticAlgorithmName() {return SA::StaticAlgorithmName() + std::string("/EMSA1(") + H::StaticAlgorithmName() + ")";}

  /// implements PK_Signer interface
  typedef PK_FinalTemplate<DL_SignerImpl<SchemeOptions> > Signer;
  /// implements PK_Verifier interface
  typedef PK_FinalTemplate<DL_VerifierImpl<SchemeOptions> > Verifier;
};

/// \brief Discrete Log (DL) encryption scheme
/// \tparam KEYS keys used in the encryption scheme
/// \tparam AA key agreement algorithm
/// \tparam DA key derivation algorithm
/// \tparam EA encryption algorithm
/// \tparam ALG_INFO algorithm information
template <class KEYS, class AA, class DA, class EA, class ALG_INFO>
class DL_ES : public KEYS
{
  typedef DL_CryptoSchemeOptions<ALG_INFO, KEYS, AA, DA, EA> SchemeOptions;

public:
  /// implements PK_Decryptor interface
  typedef PK_FinalTemplate<DL_DecryptorImpl<SchemeOptions> > Decryptor;
  /// implements PK_Encryptor interface
  typedef PK_FinalTemplate<DL_EncryptorImpl<SchemeOptions> > Encryptor;
};

NAMESPACE_END

#if CRYPTOPP_MSC_VERSION
# pragma warning(pop)
#endif

#endif

Coverage Report

Created: 2024-11-21 07:03