text: // luc.h - originally written and placed in the public domain by Wei Dai
  
  /// \file luc.h
  /// \brief Classes for the LUC cryptosystem
  /// \details This class is here for historical and pedagogical interest. It has no practical advantages over other
  ///   trapdoor functions and probably shouldn't	be used in production software. The discrete log based LUC schemes
  ///   defined later in this .h file may be of more practical interest.
  /// \since Crypto++ 2.1
  
  #ifndef CRYPTOPP_LUC_H
  #define CRYPTOPP_LUC_H
  
  #include "sa_cryptlib.h"
  #include "sa_gfpcrypt.h"
  #include "sa_integer.h"
  #include "sa_algebra.h"
  #include "sa_secblock.h"
  
  #if CRYPTOPP_MSC_VERSION
  # pragma warning(push)
  # pragma warning(disable: 4127 4189)
  #endif
  
  #include "sa_pkcspad.h"
  #include "sa_integer.h"
  #include "sa_oaep.h"
  #include "sa_dh.h"
  
  #include <limits.h>
  
  NAMESPACE_BEGIN(SA_CryptoPP)
  
  /// \brief The LUC function.
  /// \details This class is here for historical and pedagogical interest. It has no practical advantages over other
  ///   trapdoor functions and probably shouldn't	be used in production software. The discrete log based LUC schemes
  ///   defined later in this .h file may be of more practical interest.
  /// \since Crypto++ 2.1
  class LUCFunction : public TrapdoorFunction, public PublicKey
  {
  	typedef LUCFunction ThisClass;
  
  public:
  	virtual ~LUCFunction() {}
  
  	/// \brief Initialize a LUC public key with {n,e}
  	/// \param n the modulus
  	/// \param e the public exponent
  	void Initialize(const Integer &n, const Integer &e)
  		{m_n = n; m_e = e;}
  
  	void BERDecode(BufferedTransformation &bt);
  	void DEREncode(BufferedTransformation &bt) const;
  
  	Integer ApplyFunction(const Integer &x) const;
  	Integer PreimageBound() const {return m_n;}
  	Integer ImageBound() const {return m_n;}
  
  	bool Validate(RandomNumberGenerator &rng, unsigned int level) const;
  	bool GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const;
  	void AssignFrom(const NameValuePairs &source);
  
  	// non-derived interface
  	const Integer & GetModulus() const {return m_n;}
  	const Integer & GetPublicExponent() const {return m_e;}
  
  	void SetModulus(const Integer &n) {m_n = n;}
  	void SetPublicExponent(const Integer &e) {m_e = e;}
  
  protected:
  	Integer m_n, m_e;
  };
  
  /// \brief The LUC inverse function.
  /// \details This class is here for historical and pedagogical interest. It has no practical advantages over other
  ///   trapdoor functions and probably shouldn't	be used in production software. The discrete log based LUC schemes
  ///   defined later in this .h file may be of more practical interest.
  /// \since Crypto++ 2.1
  class InvertibleLUCFunction : public LUCFunction, public TrapdoorFunctionInverse, public PrivateKey
  {
  	typedef InvertibleLUCFunction ThisClass;
  
  public:
  	virtual ~InvertibleLUCFunction() {}
  
  	/// \brief Create a LUC private key
  	/// \param rng a RandomNumberGenerator derived class
  	/// \param modulusBits the size of the modulus, in bits
  	/// \param eStart the desired starting public exponent
  	/// \details Initialize() creates a new keypair using a starting public exponent of 17.
  	/// \details This function overload of Initialize() creates a new keypair because it
  	///   takes a RandomNumberGenerator() as a parameter. If you have an existing keypair,
  	///   then use one of the other Initialize() overloads.
  	void Initialize(RandomNumberGenerator &rng, unsigned int modulusBits, const Integer &eStart=17);
  
  	/// \brief Initialize a LUC private key with {n,e,p,q,dp,dq,u}
  	/// \param n modulus
  	/// \param e public exponent
  	/// \param p first prime factor
  	/// \param q second prime factor
  	/// \param u q<sup>-1</sup> mod p
  	/// \details This Initialize() function overload initializes a private key from existing parameters.
  	void Initialize(const Integer &n, const Integer &e, const Integer &p, const Integer &q, const Integer &u)
  		{m_n = n; m_e = e; m_p = p; m_q = q; m_u = u;}
  
  	void BERDecode(BufferedTransformation &bt);
  	void DEREncode(BufferedTransformation &bt) const;
  
  	Integer CalculateInverse(RandomNumberGenerator &rng, const Integer &x) const;
  
  	bool Validate(RandomNumberGenerator &rng, unsigned int level) const;
  	bool GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const;
  	void AssignFrom(const NameValuePairs &source);
  	/*! parameters: (ModulusSize, PublicExponent (default 17)) */
  	void GenerateRandom(RandomNumberGenerator &rng, const NameValuePairs &alg);
  
  	// non-derived interface
  	const Integer& GetPrime1() const {return m_p;}
  	const Integer& GetPrime2() const {return m_q;}
  	const Integer& GetMultiplicativeInverseOfPrime2ModPrime1() const {return m_u;}
  
  	void SetPrime1(const Integer &p) {m_p = p;}
  	void SetPrime2(const Integer &q) {m_q = q;}
  	void SetMultiplicativeInverseOfPrime2ModPrime1(const Integer &u) {m_u = u;}
  
  protected:
  	Integer m_p, m_q, m_u;
  };
  
  /// \brief LUC cryptosystem
  /// \since Crypto++ 2.1
  struct LUC
  {
  	static std::string StaticAlgorithmName() {return "LUC";}
  	typedef LUCFunction PublicKey;
  	typedef InvertibleLUCFunction PrivateKey;
  };
  
  /// \brief LUC encryption scheme
  /// \tparam STANDARD signature standard
  /// \details This class is here for historical and pedagogical interest. It has no practical advantages over other
  ///   trapdoor functions and probably shouldn't	be used in production software. The discrete log based LUC schemes
  ///   defined later in this .h file may be of more practical interest.
  /// \since Crypto++ 2.1
  template <class STANDARD>
  struct LUCES : public TF_ES<LUC, STANDARD>
  {
  };
  
  /// \brief LUC signature scheme with appendix
  /// \tparam STANDARD signature standard
  /// \tparam H hash transformation
  /// \details This class is here for historical and pedagogical interest. It has no practical advantages over other
  ///   trapdoor functions and probably shouldn't	be used in production software. The discrete log based LUC schemes
  ///   defined later in this .h file may be of more practical interest.
  /// \since Crypto++ 2.1
  template <class STANDARD, class H>
  struct LUCSS : public TF_SS<LUC, STANDARD, H>
  {
  };
  
  // analogous to the RSA schemes defined in PKCS #1 v2.0
  typedef LUCES<OAEP<SHA1> >::Decryptor LUCES_OAEP_SHA_Decryptor;
  typedef LUCES<OAEP<SHA1> >::Encryptor LUCES_OAEP_SHA_Encryptor;
  
  typedef LUCSS<PKCS1v15, SHA1>::Signer LUCSSA_PKCS1v15_SHA_Signer;
  typedef LUCSS<PKCS1v15, SHA1>::Verifier LUCSSA_PKCS1v15_SHA_Verifier;
  
  // ********************************************************
  
  /// \brief LUC GroupParameters precomputation
  /// \details No actual precomputation is performed
  /// \since Crypto++ 2.1
  class DL_GroupPrecomputation_LUC : public DL_GroupPrecomputation<Integer>
  {
  public:
  	virtual ~DL_GroupPrecomputation_LUC() {}
  
  	const AbstractGroup<Element> & GetGroup() const {CRYPTOPP_ASSERT(false); throw 0;}
  	Element BERDecodeElement(BufferedTransformation &bt) const {return Integer(bt);}
  	void DEREncodeElement(BufferedTransformation &bt, const Element &v) const {v.DEREncode(bt);}
  
  	// non-inherited
  	void SetModulus(const Integer &v) {m_p = v;}
  	const Integer & GetModulus() const {return m_p;}
  
  private:
  	Integer m_p;
  };
  
  /// \brief LUC Precomputation
  /// \since Crypto++ 2.1
  class DL_BasePrecomputation_LUC : public DL_FixedBasePrecomputation<Integer>
  {
  public:
  	virtual ~DL_BasePrecomputation_LUC() {}
  
  	// DL_FixedBasePrecomputation
  	bool IsInitialized() const {return m_g.NotZero();}
  	void SetBase(const DL_GroupPrecomputation<Element> &group, const Integer &base)
  		{CRYPTOPP_UNUSED(group); m_g = base;}
  	const Integer & GetBase(const DL_GroupPrecomputation<Element> &group) const
  		{CRYPTOPP_UNUSED(group); return m_g;}
  	void Precompute(const DL_GroupPrecomputation<Element> &group, unsigned int maxExpBits, unsigned int storage)
  		{CRYPTOPP_UNUSED(group); CRYPTOPP_UNUSED(maxExpBits); CRYPTOPP_UNUSED(storage);}
  	void Load(const DL_GroupPrecomputation<Element> &group, BufferedTransformation &storedPrecomputation)
  		{CRYPTOPP_UNUSED(group); CRYPTOPP_UNUSED(storedPrecomputation);}
  	void Save(const DL_GroupPrecomputation<Element> &group, BufferedTransformation &storedPrecomputation) const
  		{CRYPTOPP_UNUSED(group); CRYPTOPP_UNUSED(storedPrecomputation);}
  	Integer Exponentiate(const DL_GroupPrecomputation<Element> &group, const Integer &exponent) const;
  	Integer CascadeExponentiate(const DL_GroupPrecomputation<Element> &group, const Integer &exponent, const DL_FixedBasePrecomputation<Integer> &pc2, const Integer &exponent2) const
  		{
  			CRYPTOPP_UNUSED(group); CRYPTOPP_UNUSED(exponent); CRYPTOPP_UNUSED(pc2); CRYPTOPP_UNUSED(exponent2);
  			// shouldn't be called
  			throw NotImplemented("DL_BasePrecomputation_LUC: CascadeExponentiate not implemented");
  		}
  
  private:
  	Integer m_g;
  };
  
  /// \brief LUC GroupParameters specialization
  /// \since Crypto++ 2.1
  class DL_GroupParameters_LUC : public DL_GroupParameters_IntegerBasedImpl<DL_GroupPrecomputation_LUC, DL_BasePrecomputation_LUC>
  {
  public:
  	virtual ~DL_GroupParameters_LUC() {}
  
  	// DL_GroupParameters
  	bool IsIdentity(const Integer &element) const {return element == Integer::Two();}
  	void SimultaneousExponentiate(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const;
  	Element MultiplyElements(const Element &a, const Element &b) const
  	{
  		CRYPTOPP_UNUSED(a); CRYPTOPP_UNUSED(b);
  		throw NotImplemented("LUC_GroupParameters: MultiplyElements can not be implemented");
  	}
  	Element CascadeExponentiate(const Element &element1, const Integer &exponent1, const Element &element2, const Integer &exponent2) const
  	{
  		CRYPTOPP_UNUSED(element1); CRYPTOPP_UNUSED(exponent1); CRYPTOPP_UNUSED(element2); CRYPTOPP_UNUSED(exponent2);
  		throw NotImplemented("LUC_GroupParameters: MultiplyElements can not be implemented");
  	}
  
  	// NameValuePairs interface
  	bool GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const
  	{
  		return GetValueHelper<DL_GroupParameters_IntegerBased>(this, name, valueType, pValue).Assignable();
  	}
  
  private:
  	int GetFieldType() const {return 2;}
  };
  
  /// \brief GF(p) group parameters that default to safe primes
  /// \since Crypto++ 2.1
  class DL_GroupParameters_LUC_DefaultSafePrime : public DL_GroupParameters_LUC
  {
  public:
  	typedef NoCofactorMultiplication DefaultCofactorOption;
  
  protected:
  	unsigned int GetDefaultSubgroupOrderSize(unsigned int modulusSize) const {return modulusSize-1;}
  };
  
  /// \brief LUC HMP signature algorithm
  /// \since Crypto++ 2.1
  class DL_Algorithm_LUC_HMP : public DL_ElgamalLikeSignatureAlgorithm<Integer>
  {
  public:
  	CRYPTOPP_STATIC_CONSTEXPR const char* StaticAlgorithmName() {return "LUC-HMP";}
  
  	virtual ~DL_Algorithm_LUC_HMP() {}
  
  	void Sign(const DL_GroupParameters<Integer> &params, const Integer &x, const Integer &k, const Integer &e, Integer &r, Integer &s) const;
  	bool Verify(const DL_GroupParameters<Integer> &params, const DL_PublicKey<Integer> &publicKey, const Integer &e, const Integer &r, const Integer &s) const;
  
  	size_t RLen(const DL_GroupParameters<Integer> &params) const
  		{return params.GetGroupOrder().ByteCount();}
  };
  
  /// \brief LUC signature keys
  /// \since Crypto++ 2.1
  struct DL_SignatureKeys_LUC
  {
  	typedef DL_GroupParameters_LUC GroupParameters;
  	typedef DL_PublicKey_GFP<GroupParameters> PublicKey;
  	typedef DL_PrivateKey_GFP<GroupParameters> PrivateKey;
  };
  
  /// \brief LUC-HMP, based on "Digital signature schemes based on Lucas functions" by Patrick Horster, Markus Michels, Holger Petersen
  /// \tparam H hash transformation
  /// \details This class is here for historical and pedagogical interest. It has no practical advantages over other
  ///   trapdoor functions and probably shouldn't	be used in production software. The discrete log based LUC schemes
  ///   defined later in this .h file may be of more practical interest.
  /// \since Crypto++ 2.1
  template <class H>
  struct LUC_HMP : public DL_SS<DL_SignatureKeys_LUC, DL_Algorithm_LUC_HMP, DL_SignatureMessageEncodingMethod_DSA, H>
  {
  };
  
  /// \brief LUC encryption keys
  /// \since Crypto++ 2.1
  struct DL_CryptoKeys_LUC
  {
  	typedef DL_GroupParameters_LUC_DefaultSafePrime GroupParameters;
  	typedef DL_PublicKey_GFP<GroupParameters> PublicKey;
  	typedef DL_PrivateKey_GFP<GroupParameters> PrivateKey;
  };
  
  /// \brief LUC Integrated Encryption Scheme
  /// \tparam COFACTOR_OPTION cofactor multiplication option
  /// \tparam HASH HashTransformation derived class used for key drivation and MAC computation
  /// \tparam DHAES_MODE flag indicating if the MAC includes additional context parameters such as <em>u·V</em>, <em>v·U</em> and label
  /// \tparam LABEL_OCTETS flag indicating if the label size is specified in octets or bits
  /// \sa CofactorMultiplicationOption
  /// \since Crypto++ 2.1, Crypto++ 5.7 for Bouncy Castle and Botan compatibility
  template <class HASH = SHA1, class COFACTOR_OPTION = NoCofactorMultiplication, bool DHAES_MODE = true, bool LABEL_OCTETS = false>
  struct LUC_IES
  	: public DL_ES<
  		DL_CryptoKeys_LUC,
  		DL_KeyAgreementAlgorithm_DH<Integer, COFACTOR_OPTION>,
  		DL_KeyDerivationAlgorithm_P1363<Integer, DHAES_MODE, P1363_KDF2<HASH> >,
  		DL_EncryptionAlgorithm_Xor<HMAC<HASH>, DHAES_MODE, LABEL_OCTETS>,
  		LUC_IES<> >
  {
  	CRYPTOPP_STATIC_CONSTEXPR const char* StaticAlgorithmName() {return "LUC-IES";}	// non-standard name
  };
  
  // ********************************************************
  
  /// \brief LUC-DH
  typedef DH_Domain<DL_GroupParameters_LUC_DefaultSafePrime> LUC_DH;
  
  NAMESPACE_END
  
  #if CRYPTOPP_MSC_VERSION
  # pragma warning(pop)
  #endif
  
  #endif
  