gfpcrypt.h

Go to the documentation of this file.

// gfpcrypt.h - originally written and placed in the public domain by Wei Dai
//              RFC6979 deterministic signatures added by Douglas Roark
//              ECGDSA added by Jeffrey Walton
 
/// \file gfpcrypt.h
/// \brief Classes and functions for schemes based on Discrete Logs (DL) over GF(p)
 
#ifndef CRYPTOPP_GFPCRYPT_H
#define CRYPTOPP_GFPCRYPT_H
 
#include "config.h"
 
#if CRYPTOPP_MSC_VERSION
# pragma warning(push)
# pragma warning(disable: 4189 4231 4275)
#endif
 
#include "cryptlib.h"
#include "pubkey.h"
#include "integer.h"
#include "modexppc.h"
#include "algparam.h"
#include "smartptr.h"
#include "sha.h"
#include "asn.h"
#include "hmac.h"
#include "misc.h"
 
NAMESPACE_BEGIN(CryptoPP)
 
CRYPTOPP_DLL_TEMPLATE_CLASS DL_GroupParameters<Integer>;
 
/// \brief Integer-based GroupParameters specialization
class CRYPTOPP_DLL CRYPTOPP_NO_VTABLE DL_GroupParameters_IntegerBased : public ASN1CryptoMaterial<DL_GroupParameters<Integer> >
{
    typedef DL_GroupParameters_IntegerBased ThisClass;
 
public:
    virtual ~DL_GroupParameters_IntegerBased() {}
 
    /// \brief Initialize a group parameters over integers
    /// \param params the group parameters
    void Initialize(const DL_GroupParameters_IntegerBased &params)
        {Initialize(params.GetModulus(), params.GetSubgroupOrder(), params.GetSubgroupGenerator());}
 
    /// \brief Create a group parameters over integers
    /// \param rng a RandomNumberGenerator derived class
    /// \param pbits the size of p, in bits
    /// \details This function overload of Initialize() creates a new private key 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 pbits)
        {GenerateRandom(rng, MakeParameters("ModulusSize", (int)pbits));}
 
    /// \brief Initialize a group parameters over integers
    /// \param p the modulus
    /// \param g the generator
    void Initialize(const Integer &p, const Integer &g)
        {SetModulusAndSubgroupGenerator(p, g); SetSubgroupOrder(ComputeGroupOrder(p)/2);}
 
    /// \brief Initialize a group parameters over integers
    /// \param p the modulus
    /// \param q the subgroup order
    /// \param g the generator
    void Initialize(const Integer &p, const Integer &q, const Integer &g)
        {SetModulusAndSubgroupGenerator(p, g); SetSubgroupOrder(q);}
 
    // ASN1Object interface
    void BERDecode(BufferedTransformation &bt);
    void DEREncode(BufferedTransformation &bt) const;
 
    /// \brief Generate a random key
    /// \param rng a RandomNumberGenerator to produce keying material
    /// \param alg additional initialization parameters
    /// \details Recognised NameValuePairs are ModulusSize and
    ///  SubgroupOrderSize (optional)
    /// \throw KeyingErr if a key can't be generated or algorithm parameters
    ///  are invalid
    void GenerateRandom(RandomNumberGenerator &rng, const NameValuePairs &alg);
 
    /// \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;
 
    /// \brief Initialize or reinitialize this key
    /// \param source NameValuePairs to assign
    void AssignFrom(const NameValuePairs &source);
 
    // DL_GroupParameters
    const Integer & GetSubgroupOrder() const {return m_q;}
    Integer GetGroupOrder() const {return GetFieldType() == 1 ? GetModulus()-Integer::One() : GetModulus()+Integer::One();}
    bool ValidateGroup(RandomNumberGenerator &rng, unsigned int level) const;
    bool ValidateElement(unsigned int level, const Integer &element, const DL_FixedBasePrecomputation<Integer> *precomp) const;
 
    /// \brief Determine if subgroup membership check is fast
    /// \return true or false
    bool FastSubgroupCheckAvailable() const {return GetCofactor() == 2;}
 
    /// \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>
    /// \sa GetEncodedElementSize(), DecodeElement(), <A
    ///  HREF="http://github.com/weidai11/cryptopp/issues/40">Cygwin
    ///  i386 crash at -O3</A>
    void EncodeElement(bool reversible, const Element &element, byte *encoded) const;
 
    /// \brief Retrieve 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.
    /// \sa EncodeElement(), DecodeElement()
    unsigned int GetEncodedElementSize(bool reversible) const;
 
    /// \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>
    /// \sa GetEncodedElementSize(), EncodeElement()
    Integer DecodeElement(const byte *encoded, bool checkForGroupMembership) const;
 
    /// \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.
    Integer ConvertElementToInteger(const Element &element) const
        {return element;}
 
    /// \brief Retrieve the maximum exponent for the group
    /// \return the maximum exponent for the group
    Integer GetMaxExponent() const;
 
    /// \brief Retrieve the OID of the algorithm
    /// \return OID of the algorithm
    OID GetAlgorithmID() const;
 
    /// \brief Retrieve the modulus for the group
    /// \return the modulus for the group
    virtual const Integer & GetModulus() const =0;
 
    /// \brief Set group parameters
    /// \param p the prime modulus
    /// \param g the group generator
    virtual void SetModulusAndSubgroupGenerator(const Integer &p, const Integer &g) =0;
 
    /// \brief Set subgroup order
    /// \param q the subgroup order
    void SetSubgroupOrder(const Integer &q)
        {m_q = q; ParametersChanged();}
 
    static std::string CRYPTOPP_API StaticAlgorithmNamePrefix() {return "";}
 
protected:
    Integer ComputeGroupOrder(const Integer &modulus) const
        {return modulus-(GetFieldType() == 1 ? 1 : -1);}
 
    // GF(p) = 1, GF(p^2) = 2
    virtual int GetFieldType() const =0;
    virtual unsigned int GetDefaultSubgroupOrderSize(unsigned int modulusSize) const;
 
private:
    Integer m_q;
};
 
/// \brief Integer-based GroupParameters default implementation
/// \tparam GROUP_PRECOMP group parameters precomputation specialization
/// \tparam BASE_PRECOMP base class precomputation specialization
template <class GROUP_PRECOMP, class BASE_PRECOMP = DL_FixedBasePrecomputationImpl<typename GROUP_PRECOMP::Element> >
class CRYPTOPP_NO_VTABLE DL_GroupParameters_IntegerBasedImpl : public DL_GroupParametersImpl<GROUP_PRECOMP, BASE_PRECOMP, DL_GroupParameters_IntegerBased>
{
    typedef DL_GroupParameters_IntegerBasedImpl<GROUP_PRECOMP, BASE_PRECOMP> ThisClass;
 
public:
    typedef typename GROUP_PRECOMP::Element Element;
 
    virtual ~DL_GroupParameters_IntegerBasedImpl() {}
 
    // GeneratibleCryptoMaterial interface
    bool GetVoidValue(const char *name, const std::type_info &valueType, void *pValue) const
        {return GetValueHelper<DL_GroupParameters_IntegerBased>(this, name, valueType, pValue).Assignable();}
 
    void AssignFrom(const NameValuePairs &source)
        {AssignFromHelper<DL_GroupParameters_IntegerBased>(this, source);}
 
    // DL_GroupParameters
    const DL_FixedBasePrecomputation<Element> & GetBasePrecomputation() const {return this->m_gpc;}
    DL_FixedBasePrecomputation<Element> & AccessBasePrecomputation() {return this->m_gpc;}
 
    // IntegerGroupParameters
    /// \brief Retrieve the modulus for the group
    /// \return the modulus for the group
    const Integer & GetModulus() const {return this->m_groupPrecomputation.GetModulus();}
 
    /// \brief Retrieves a reference to the group generator
    /// \return const reference to the group generator
    const Integer & GetGenerator() const {return this->m_gpc.GetBase(this->GetGroupPrecomputation());}
 
    void SetModulusAndSubgroupGenerator(const Integer &p, const Integer &g)        // these have to be set together
        {this->m_groupPrecomputation.SetModulus(p); this->m_gpc.SetBase(this->GetGroupPrecomputation(), g); this->ParametersChanged();}
 
    // non-inherited
    bool operator==(const DL_GroupParameters_IntegerBasedImpl<GROUP_PRECOMP, BASE_PRECOMP> &rhs) const
        {return GetModulus() == rhs.GetModulus() && GetGenerator() == rhs.GetGenerator() && this->GetSubgroupOrder() == rhs.GetSubgroupOrder();}
    bool operator!=(const DL_GroupParameters_IntegerBasedImpl<GROUP_PRECOMP, BASE_PRECOMP> &rhs) const
        {return !operator==(rhs);}
};
 
CRYPTOPP_DLL_TEMPLATE_CLASS DL_GroupParameters_IntegerBasedImpl<ModExpPrecomputation>;
 
/// \brief GF(p) group parameters
class CRYPTOPP_DLL DL_GroupParameters_GFP : public DL_GroupParameters_IntegerBasedImpl<ModExpPrecomputation>
{
public:
    virtual ~DL_GroupParameters_GFP() {}
 
    /// \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.
    bool IsIdentity(const Integer &element) const {return element == Integer::One();}
 
    /// \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>
    void SimultaneousExponentiate(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const;
 
    /// \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<DL_GroupParameters_IntegerBased>(this, name, valueType, pValue).Assignable();
    }
 
    // used by MQV
    Element MultiplyElements(const Element &a, const Element &b) const;
    Element CascadeExponentiate(const Element &element1, const Integer &exponent1, const Element &element2, const Integer &exponent2) const;
 
protected:
    int GetFieldType() const {return 1;}
};
 
/// \brief GF(p) group parameters that default to safe primes
class CRYPTOPP_DLL DL_GroupParameters_GFP_DefaultSafePrime : public DL_GroupParameters_GFP
{
public:
    typedef NoCofactorMultiplication DefaultCofactorOption;
 
    virtual ~DL_GroupParameters_GFP_DefaultSafePrime() {}
 
protected:
    unsigned int GetDefaultSubgroupOrderSize(unsigned int modulusSize) const {return modulusSize-1;}
};
 
/// ElGamal encryption for safe interop
/// \sa <A HREF="https://eprint.iacr.org/2021/923.pdf">On the
///  (in)security of ElGamal in OpenPGP</A>,
///  <A HREF="https://github.com/weidai11/cryptopp/issues/1059">Issue 1059</A>,
///  <A HREF="https://nvd.nist.gov/vuln/detail/CVE-2021-40530">CVE-2021-40530</A>
/// \since Crypto++ 8.6
class CRYPTOPP_DLL DL_GroupParameters_ElGamal : public DL_GroupParameters_GFP_DefaultSafePrime
{
public:
    typedef NoCofactorMultiplication DefaultCofactorOption;
 
    virtual ~DL_GroupParameters_ElGamal() {}
 
    Integer GetMaxExponent() const
    {
        return GetSubgroupOrder()-1;
    }
};
 
/// \brief GDSA algorithm
/// \tparam T FieldElement type or class
/// \details FieldElement <tt>T</tt> can be Integer, ECP or EC2N.
template <class T>
class DL_Algorithm_GDSA : public DL_ElgamalLikeSignatureAlgorithm<T>
{
public:
    CRYPTOPP_STATIC_CONSTEXPR const char* CRYPTOPP_API StaticAlgorithmName() {return "DSA-1363";}
 
    virtual ~DL_Algorithm_GDSA() {}
 
    void Sign(const DL_GroupParameters<T> &params, const Integer &x, const Integer &k, const Integer &e, Integer &r, Integer &s) const
    {
        const Integer &q = params.GetSubgroupOrder();
        r %= q;
        Integer kInv = k.InverseMod(q);
        s = (kInv * (x*r + e)) % q;
        CRYPTOPP_ASSERT(!!r && !!s);
    }
 
    bool Verify(const DL_GroupParameters<T> &params, const DL_PublicKey<T> &publicKey, const Integer &e, const Integer &r, const Integer &s) const
    {
        const Integer &q = params.GetSubgroupOrder();
        if (r>=q || r<1 || s>=q || s<1)
            return false;
 
        Integer w = s.InverseMod(q);
        Integer u1 = (e * w) % q;
        Integer u2 = (r * w) % q;
        // verify r == (g^u1 * y^u2 mod p) mod q
        return r == params.ConvertElementToInteger(publicKey.CascadeExponentiateBaseAndPublicElement(u1, u2)) % q;
    }
};
 
/// \brief DSA signature algorithm based on RFC 6979
/// \tparam T FieldElement type or class
/// \tparam H HashTransformation derived class
/// \details FieldElement <tt>T</tt> can be Integer, ECP or EC2N.
/// \sa <a href="http://tools.ietf.org/rfc/rfc6979.txt">RFC 6979, Deterministic Usage of the
///  Digital Signature Algorithm (DSA) and Elliptic Curve Digital Signature Algorithm (ECDSA)</a>
/// \since Crypto++ 6.0
template <class T, class H>
class DL_Algorithm_DSA_RFC6979 : public DL_Algorithm_GDSA<T>, public DeterministicSignatureAlgorithm
{
public:
    CRYPTOPP_STATIC_CONSTEXPR const char* CRYPTOPP_API StaticAlgorithmName() {return "DSA-RFC6979";}
 
    virtual ~DL_Algorithm_DSA_RFC6979() {}
 
    bool IsProbabilistic() const
        {return false;}
    bool IsDeterministic() const
        {return true;}
 
    // Deterministic K
    Integer GenerateRandom(const Integer &x, const Integer &q, const Integer &e) const
    {
        static const byte zero = 0, one = 1;
        const size_t qlen = q.BitCount();
        const size_t rlen = BitsToBytes(qlen);
 
        // Step (a) - formatted E(m)
        SecByteBlock BH(e.MinEncodedSize());
        e.Encode(BH, BH.size());
        BH = bits2octets(BH, q);
 
        // Step (a) - private key to byte array
        SecByteBlock BX(STDMAX(rlen, x.MinEncodedSize()));
        x.Encode(BX, BX.size());
 
        // Step (b)
        SecByteBlock V(H::DIGESTSIZE);
        std::fill(V.begin(), V.begin()+H::DIGESTSIZE, one);
 
        // Step (c)
        SecByteBlock K(H::DIGESTSIZE);
        std::fill(K.begin(), K.begin()+H::DIGESTSIZE, zero);
 
        // Step (d)
        m_hmac.SetKey(K, K.size());
        m_hmac.Update(V, V.size());
        m_hmac.Update(&zero, 1);
        m_hmac.Update(BX, BX.size());
        m_hmac.Update(BH, BH.size());
        m_hmac.TruncatedFinal(K, K.size());
 
        // Step (e)
        m_hmac.SetKey(K, K.size());
        m_hmac.Update(V, V.size());
        m_hmac.TruncatedFinal(V, V.size());
 
        // Step (f)
        m_hmac.SetKey(K, K.size());
        m_hmac.Update(V, V.size());
        m_hmac.Update(&one, 1);
        m_hmac.Update(BX, BX.size());
        m_hmac.Update(BH, BH.size());
        m_hmac.TruncatedFinal(K, K.size());
 
        // Step (g)
        m_hmac.SetKey(K, K.size());
        m_hmac.Update(V, V.size());
        m_hmac.TruncatedFinal(V, V.size());
 
        Integer k;
        SecByteBlock temp(rlen);
        for (;;)
        {
            // We want qlen bits, but we support only hash functions with an output length
            //   multiple of 8; hence, we will gather rlen bits, i.e., rolen octets.
            size_t toff = 0;
            while (toff < rlen)
            {
                m_hmac.Update(V, V.size());
                m_hmac.TruncatedFinal(V, V.size());
 
                size_t cc = STDMIN(V.size(), temp.size() - toff);
                memcpy_s(temp+toff, temp.size() - toff, V, cc);
                toff += cc;
            }
 
            k = bits2int(temp, qlen);
            if (k > 0 && k < q)
                break;
 
            // k is not in the proper range; update K and V, and loop.
            m_hmac.Update(V, V.size());
            m_hmac.Update(&zero, 1);
            m_hmac.TruncatedFinal(K, K.size());
 
            m_hmac.SetKey(K, K.size());
            m_hmac.Update(V, V.size());
            m_hmac.TruncatedFinal(V, V.size());
        }
 
        return k;
    }
 
protected:
 
    Integer bits2int(const SecByteBlock& bits, size_t qlen) const
    {
        Integer ret(bits, bits.size());
        size_t blen = bits.size()*8;
 
        if (blen > qlen)
            ret >>= blen - qlen;
 
        return ret;
    }
 
    // RFC 6979 support function. Takes an integer and converts it into bytes that
    // are the same length as an elliptic curve's order.
    SecByteBlock int2octets(const Integer& val, size_t rlen) const
    {
        SecByteBlock block(val.MinEncodedSize());
        val.Encode(block, val.MinEncodedSize());
 
        if (block.size() == rlen)
            return block;
 
        // The least significant bytes are the ones we need to preserve.
        SecByteBlock t(rlen);
        if (block.size() > rlen)
        {
            size_t offset = block.size() - rlen;
            std::memcpy(t, block + offset, rlen);
        }
        else // block.size() < rlen
        {
            size_t offset = rlen - block.size();
            memset(t, '\x00', offset);
            std::memcpy(t + offset, block, rlen - offset);
        }
 
        return t;
    }
 
    // Turn a stream of bits into a set of bytes with the same length as an elliptic
    // curve's order.
    SecByteBlock bits2octets(const SecByteBlock& in, const Integer& q) const
    {
        Integer b2 = bits2int(in, q.BitCount());
        Integer b1 = b2 - q;
        return int2octets(b1.IsNegative() ? b2 : b1, q.ByteCount());
    }
 
private:
    mutable H m_hash;
    mutable HMAC<H> m_hmac;
};
 
/// \brief German Digital Signature Algorithm
/// \tparam T FieldElement type or class
/// \details FieldElement <tt>T</tt> can be Integer, ECP or EC2N.
/// \details The Digital Signature Scheme ECGDSA does not define the algorithm over integers. Rather, the
///  signature algorithm is only defined over elliptic curves. However, the library design is such that the
///  generic algorithm reside in <tt>gfpcrypt.h</tt>.
/// \sa Erwin Hess, Marcus Schafheutle, and Pascale Serf <A HREF="http://www.teletrust.de/fileadmin/files/oid/ecgdsa_final.pdf">
///  The Digital Signature Scheme ECGDSA (October 24, 2006)</A>
template <class T>
class DL_Algorithm_GDSA_ISO15946 : public DL_ElgamalLikeSignatureAlgorithm<T>
{
public:
    CRYPTOPP_STATIC_CONSTEXPR const char* CRYPTOPP_API StaticAlgorithmName() {return "GDSA-ISO15946";}
 
    virtual ~DL_Algorithm_GDSA_ISO15946() {}
 
    void Sign(const DL_GroupParameters<T> &params, const Integer &x, const Integer &k, const Integer &e, Integer &r, Integer &s) const
    {
        const Integer &q = params.GetSubgroupOrder();
        // r = x(k * G) mod q
        r = params.ConvertElementToInteger(params.ExponentiateBase(k)) % q;
        // s = (k * r - h(m)) * d_A mod q
        s = (k * r - e) * x % q;
        CRYPTOPP_ASSERT(!!r && !!s);
    }
 
    bool Verify(const DL_GroupParameters<T> &params, const DL_PublicKey<T> &publicKey, const Integer &e, const Integer &r, const Integer &s) const
    {
        const Integer &q = params.GetSubgroupOrder();
        if (r>=q || r<1 || s>=q || s<1)
            return false;
 
        const Integer& rInv = r.InverseMod(q);
        const Integer u1 = (rInv * e) % q;
        const Integer u2 = (rInv * s) % q;
        // verify x(G^u1 + P_A^u2) mod q
        return r == params.ConvertElementToInteger(publicKey.CascadeExponentiateBaseAndPublicElement(u1, u2)) % q;
    }
};
 
CRYPTOPP_DLL_TEMPLATE_CLASS DL_Algorithm_GDSA<Integer>;
CRYPTOPP_DLL_TEMPLATE_CLASS DL_Algorithm_DSA_RFC6979<Integer, SHA1>;
CRYPTOPP_DLL_TEMPLATE_CLASS DL_Algorithm_DSA_RFC6979<Integer, SHA224>;
CRYPTOPP_DLL_TEMPLATE_CLASS DL_Algorithm_DSA_RFC6979<Integer, SHA256>;
CRYPTOPP_DLL_TEMPLATE_CLASS DL_Algorithm_DSA_RFC6979<Integer, SHA384>;
CRYPTOPP_DLL_TEMPLATE_CLASS DL_Algorithm_DSA_RFC6979<Integer, SHA512>;
 
/// \brief NR algorithm
/// \tparam T FieldElement type or class
/// \details FieldElement <tt>T</tt> can be Integer, ECP or EC2N.
template <class T>
class DL_Algorithm_NR : public DL_ElgamalLikeSignatureAlgorithm<T>
{
public:
    CRYPTOPP_STATIC_CONSTEXPR const char* CRYPTOPP_API StaticAlgorithmName() {return "NR";}
 
    virtual ~DL_Algorithm_NR() {}
 
    void Sign(const DL_GroupParameters<T> &params, const Integer &x, const Integer &k, const Integer &e, Integer &r, Integer &s) const
    {
        const Integer &q = params.GetSubgroupOrder();
        r = (r + e) % q;
        s = (k - x*r) % q;
        CRYPTOPP_ASSERT(!!r);
    }
 
    bool Verify(const DL_GroupParameters<T> &params, const DL_PublicKey<T> &publicKey, const Integer &e, const Integer &r, const Integer &s) const
    {
        const Integer &q = params.GetSubgroupOrder();
        if (r>=q || r<1 || s>=q)
            return false;
 
        // check r == (m_g^s * m_y^r + m) mod m_q
        return r == (params.ConvertElementToInteger(publicKey.CascadeExponentiateBaseAndPublicElement(s, r)) + e) % q;
    }
};
 
/// \brief Discrete Log (DL) public key in GF(p) groups
/// \tparam GP GroupParameters derived class
/// \details DSA public key format is defined in 7.3.3 of RFC 2459. The    private key format is defined in 12.9 of PKCS #11 v2.10.
template <class GP>
class DL_PublicKey_GFP : public DL_PublicKeyImpl<GP>
{
public:
    virtual ~DL_PublicKey_GFP() {}
 
    /// \brief Initialize a public key over GF(p)
    /// \param params the group parameters
    /// \param y the public element
    void Initialize(const DL_GroupParameters_IntegerBased &params, const Integer &y)
        {this->AccessGroupParameters().Initialize(params); this->SetPublicElement(y);}
 
    /// \brief Initialize a public key over GF(p)
    /// \param p the modulus
    /// \param g the generator
    /// \param y the public element
    void Initialize(const Integer &p, const Integer &g, const Integer &y)
        {this->AccessGroupParameters().Initialize(p, g); this->SetPublicElement(y);}
 
    /// \brief Initialize a public key over GF(p)
    /// \param p the modulus
    /// \param q the subgroup order
    /// \param g the generator
    /// \param y the public element
    void Initialize(const Integer &p, const Integer &q, const Integer &g, const Integer &y)
        {this->AccessGroupParameters().Initialize(p, q, g); this->SetPublicElement(y);}
 
    // X509PublicKey
    void BERDecodePublicKey(BufferedTransformation &bt, bool, size_t)
        {this->SetPublicElement(Integer(bt));}
    void DEREncodePublicKey(BufferedTransformation &bt) const
        {this->GetPublicElement().DEREncode(bt);}
};
 
/// \brief Discrete Log (DL) private key in GF(p) groups
/// \tparam GP GroupParameters derived class
template <class GP>
class DL_PrivateKey_GFP : public DL_PrivateKeyImpl<GP>
{
public:
    virtual ~DL_PrivateKey_GFP();
 
    /// \brief Create a private key
    /// \param rng a RandomNumberGenerator derived class
    /// \param modulusBits the size of the modulus, in bits
    /// \details This function overload of Initialize() creates a new private key 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)
        {this->GenerateRandomWithKeySize(rng, modulusBits);}
 
    /// \brief Create a private key
    /// \param rng a RandomNumberGenerator derived class
    /// \param p the modulus
    /// \param g the generator
    /// \details This function overload of Initialize() creates a new private key 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, const Integer &p, const Integer &g)
        {this->GenerateRandom(rng, MakeParameters("Modulus", p)("SubgroupGenerator", g));}
 
    /// \brief Create a private key
    /// \param rng a RandomNumberGenerator derived class
    /// \param p the modulus
    /// \param q the subgroup order
    /// \param g the generator
    /// \details This function overload of Initialize() creates a new private key 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, const Integer &p, const Integer &q, const Integer &g)
        {this->GenerateRandom(rng, MakeParameters("Modulus", p)("SubgroupOrder", q)("SubgroupGenerator", g));}
 
    /// \brief Initialize a private key over GF(p)
    /// \param params the group parameters
    /// \param x the private exponent
    void Initialize(const DL_GroupParameters_IntegerBased &params, const Integer &x)
        {this->AccessGroupParameters().Initialize(params); this->SetPrivateExponent(x);}
 
    /// \brief Initialize a private key over GF(p)
    /// \param p the modulus
    /// \param g the generator
    /// \param x the private exponent
    void Initialize(const Integer &p, const Integer &g, const Integer &x)
        {this->AccessGroupParameters().Initialize(p, g); this->SetPrivateExponent(x);}
 
    /// \brief Initialize a private key over GF(p)
    /// \param p the modulus
    /// \param q the subgroup order
    /// \param g the generator
    /// \param x the private exponent
    void Initialize(const Integer &p, const Integer &q, const Integer &g, const Integer &x)
        {this->AccessGroupParameters().Initialize(p, q, g); this->SetPrivateExponent(x);}
};
 
// Out-of-line dtor due to AIX and GCC, http://github.com/weidai11/cryptopp/issues/499
template <class GP>
DL_PrivateKey_GFP<GP>::~DL_PrivateKey_GFP() {}
 
/// \brief Discrete Log (DL) signing/verification keys in GF(p) groups
struct DL_SignatureKeys_GFP
{
    typedef DL_GroupParameters_GFP GroupParameters;
    typedef DL_PublicKey_GFP<GroupParameters> PublicKey;
    typedef DL_PrivateKey_GFP<GroupParameters> PrivateKey;
};
 
/// \brief Discrete Log (DL) encryption/decryption keys in GF(p) groups
struct DL_CryptoKeys_GFP
{
    typedef DL_GroupParameters_GFP_DefaultSafePrime GroupParameters;
    typedef DL_PublicKey_GFP<GroupParameters> PublicKey;
    typedef DL_PrivateKey_GFP<GroupParameters> PrivateKey;
};
 
/// ElGamal encryption keys for safe interop
/// \sa <A HREF="https://eprint.iacr.org/2021/923.pdf">On the
///  (in)security of ElGamal in OpenPGP</A>,
///  <A HREF="https://github.com/weidai11/cryptopp/issues/1059">Issue 1059</A>,
///  <A HREF="https://nvd.nist.gov/vuln/detail/CVE-2021-40530">CVE-2021-40530</A>
/// \since Crypto++ 8.6
struct DL_CryptoKeys_ElGamal
{
    typedef DL_GroupParameters_ElGamal GroupParameters;
    typedef DL_PublicKey_GFP<GroupParameters> PublicKey;
    typedef DL_PrivateKey_GFP<GroupParameters> PrivateKey;
};
 
/// \brief DSA signature scheme
/// \tparam H HashTransformation derived class
/// \sa <a href="http://www.weidai.com/scan-mirror/sig.html#DSA-1363">DSA-1363</a>
/// \since Crypto++ 1.0 for DSA, Crypto++ 5.6.2 for DSA2
template <class H>
struct GDSA : public DL_SS<
    DL_SignatureKeys_GFP,
    DL_Algorithm_GDSA<Integer>,
    DL_SignatureMessageEncodingMethod_DSA,
    H>
{
};
 
/// \brief NR signature scheme
/// \tparam H HashTransformation derived class
/// \sa <a href="http://www.weidai.com/scan-mirror/sig.html#NR">NR</a>
template <class H>
struct NR : public DL_SS<
    DL_SignatureKeys_GFP,
    DL_Algorithm_NR<Integer>,
    DL_SignatureMessageEncodingMethod_NR,
    H>
{
};
 
/// \brief DSA group parameters
/// \details These are GF(p) group parameters that are allowed by the DSA standard
/// \sa DL_Keys_DSA
/// \since Crypto++ 1.0
class CRYPTOPP_DLL DL_GroupParameters_DSA : public DL_GroupParameters_GFP
{
public:
    virtual ~DL_GroupParameters_DSA() {}
 
    /// \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 ValidateGroup() also checks that the lengths of p and q are allowed
    ///  by the DSA standard.
    /// \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.
    bool ValidateGroup(RandomNumberGenerator &rng, unsigned int level) const;
 
    /// \brief Generate a random key or crypto parameters
    /// \param rng a RandomNumberGenerator to produce keying material
    /// \param alg additional initialization parameters
    /// \details NameValuePairs can be ModulusSize alone; or Modulus, SubgroupOrder, and
    ///  SubgroupGenerator. ModulusSize must be between <tt>DSA::MIN_PRIME_LENGTH</tt> and
    ///  <tt>DSA::MAX_PRIME_LENGTH</tt>, and divisible by <tt>DSA::PRIME_LENGTH_MULTIPLE</tt>.
    /// \details An example of changing the modulus size using NameValuePairs is shown below.
    /// <pre>
    ///  AlgorithmParameters params = MakeParameters
    ///    (Name::ModulusSize(), 2048);
    ///
    ///  DL_GroupParameters_DSA groupParams;
    ///  groupParams.GenerateRandom(prng, params);
    /// </pre>
    /// \throw KeyingErr if a key can't be generated or algorithm parameters are invalid.
    void GenerateRandom(RandomNumberGenerator &rng, const NameValuePairs &alg);
 
    /// \brief Check the prime length for errors
    /// \param pbits number of bits in the prime number
    /// \return true if the tests succeed, false otherwise
    static bool CRYPTOPP_API IsValidPrimeLength(unsigned int pbits)
        {return pbits >= MIN_PRIME_LENGTH && pbits <= MAX_PRIME_LENGTH && pbits % PRIME_LENGTH_MULTIPLE == 0;}
 
    /// \brief DSA prime length
    enum {
        /// \brief Minimum prime length
        MIN_PRIME_LENGTH = 1024,
        /// \brief Maximum prime length
        MAX_PRIME_LENGTH = 3072,
        /// \brief Prime length multiple
        PRIME_LENGTH_MULTIPLE = 1024
    };
};
 
template <class H>
class DSA2;
 
/// \brief DSA keys
/// \sa DL_GroupParameters_DSA
/// \since Crypto++ 1.0
struct DL_Keys_DSA
{
    typedef DL_PublicKey_GFP<DL_GroupParameters_DSA> PublicKey;
    typedef DL_PrivateKey_WithSignaturePairwiseConsistencyTest<DL_PrivateKey_GFP<DL_GroupParameters_DSA>, DSA2<SHA1> > PrivateKey;
};
 
/// \brief DSA signature scheme
/// \tparam H HashTransformation derived class
/// \details The class is named DSA2 instead of DSA for backwards compatibility because
///  DSA was a non-template class.
/// \details DSA default method GenerateRandom uses a 2048-bit modulus and a 224-bit subgoup by default.
///  The modulus can be changed using the following code:
/// <pre>
///  DSA::PrivateKey privateKey;
///  privateKey.GenerateRandomWithKeySize(prng, 2048);
/// </pre>
/// \details The subgroup order can be changed using the following code:
/// <pre>
///  AlgorithmParameters params = MakeParameters
///    (Name::ModulusSize(), 2048)
///    (Name::SubgroupOrderSize(), 256);
///
///  DSA::PrivateKey privateKey;
///  privateKey.GenerateRandom(prng, params);
/// </pre>
/// \sa <a href="http://en.wikipedia.org/wiki/Digital_Signature_Algorithm">DSA</a>, as specified in FIPS 186-3,
///  <a href="https://www.cryptopp.com/wiki/Digital_Signature_Algorithm">Digital Signature Algorithm</a> on the wiki, and
///  <a href="https://www.cryptopp.com/wiki/NameValuePairs">NameValuePairs</a> on the wiki.
/// \since Crypto++ 1.0 for DSA, Crypto++ 5.6.2 for DSA2, Crypto++ 6.1 for 2048-bit modulus.
template <class H>
class DSA2 : public DL_SS<
    DL_Keys_DSA,
    DL_Algorithm_GDSA<Integer>,
    DL_SignatureMessageEncodingMethod_DSA,
    H,
    DSA2<H> >
{
public:
    static std::string CRYPTOPP_API StaticAlgorithmName() {return "DSA/" + (std::string)H::StaticAlgorithmName();}
};
 
/// \brief DSA deterministic signature scheme
/// \tparam H HashTransformation derived class
/// \sa <a href="http://www.weidai.com/scan-mirror/sig.html#DSA-1363">DSA-1363</a>
/// \since Crypto++ 1.0 for DSA, Crypto++ 5.6.2 for DSA2
template <class H>
struct DSA_RFC6979 : public DL_SS<
    DL_SignatureKeys_GFP,
    DL_Algorithm_DSA_RFC6979<Integer, H>,
    DL_SignatureMessageEncodingMethod_DSA,
    H,
    DSA_RFC6979<H> >
{
    static std::string CRYPTOPP_API StaticAlgorithmName() {return std::string("DSA-RFC6979/") + H::StaticAlgorithmName();}
};
 
/// DSA with SHA-1, typedef'd for backwards compatibility
typedef DSA2<SHA1> DSA;
 
CRYPTOPP_DLL_TEMPLATE_CLASS DL_PublicKey_GFP<DL_GroupParameters_DSA>;
CRYPTOPP_DLL_TEMPLATE_CLASS DL_PrivateKey_GFP<DL_GroupParameters_DSA>;
CRYPTOPP_DLL_TEMPLATE_CLASS DL_PrivateKey_WithSignaturePairwiseConsistencyTest<DL_PrivateKey_GFP<DL_GroupParameters_DSA>, DSA2<SHA1> >;
 
/// \brief P1363 based XOR Encryption Method
/// \tparam MAC MessageAuthenticationCode derived class used for MAC computation
/// \tparam DHAES_MODE flag indicating DHAES mode
/// \tparam LABEL_OCTETS flag indicating the label is octet count
/// \details DL_EncryptionAlgorithm_Xor is based on an early P1363 draft, which itself appears to be based on an
///  early Certicom SEC-1 draft (or an early SEC-1 draft was based on a P1363 draft). Crypto++ 4.2 used it in its Integrated
///  Ecryption Schemes with <tt>NoCofactorMultiplication</tt>, <tt>DHAES_MODE=false</tt> and <tt>LABEL_OCTETS=true</tt>.
/// \details If you need this method for Crypto++ 4.2 compatibility, then use the ECIES template class with
///  <tt>NoCofactorMultiplication</tt>, <tt>DHAES_MODE=false</tt> and <tt>LABEL_OCTETS=true</tt>.
/// \details If you need this method for Bouncy Castle 1.54 and Botan 1.11 compatibility, then use the ECIES template class with
///  <tt>NoCofactorMultiplication</tt>, <tt>DHAES_MODE=true</tt> and <tt>LABEL_OCTETS=false</tt>.
/// \details Bouncy Castle 1.54 and Botan 1.11 compatibility are the default template parameters.
/// \since Crypto++ 4.0
template <class MAC, bool DHAES_MODE, bool LABEL_OCTETS=false>
class DL_EncryptionAlgorithm_Xor : public DL_SymmetricEncryptionAlgorithm
{
public:
    virtual ~DL_EncryptionAlgorithm_Xor() {}
 
    bool ParameterSupported(const char *name) const {return strcmp(name, Name::EncodingParameters()) == 0;}
    size_t GetSymmetricKeyLength(size_t plaintextLength) const
        {return plaintextLength + static_cast<size_t>(MAC::DEFAULT_KEYLENGTH);}
    size_t GetSymmetricCiphertextLength(size_t plaintextLength) const
        {return plaintextLength + static_cast<size_t>(MAC::DIGESTSIZE);}
    size_t GetMaxSymmetricPlaintextLength(size_t ciphertextLength) const
        {return SaturatingSubtract(ciphertextLength, static_cast<size_t>(MAC::DIGESTSIZE));}
    void SymmetricEncrypt(RandomNumberGenerator &rng, const byte *key, const byte *plaintext, size_t plaintextLength, byte *ciphertext, const NameValuePairs &parameters) const
    {
        CRYPTOPP_UNUSED(rng);
        const byte *cipherKey = NULLPTR, *macKey = NULLPTR;
        if (DHAES_MODE)
        {
            macKey = key;
            cipherKey = key + MAC::DEFAULT_KEYLENGTH;
        }
        else
        {
            cipherKey = key;
            macKey = key + plaintextLength;
        }
 
        ConstByteArrayParameter encodingParameters;
        parameters.GetValue(Name::EncodingParameters(), encodingParameters);
 
        if (plaintextLength)    // Coverity finding
            xorbuf(ciphertext, plaintext, cipherKey, plaintextLength);
 
        MAC mac(macKey);
        mac.Update(ciphertext, plaintextLength);
        mac.Update(encodingParameters.begin(), encodingParameters.size());
        if (DHAES_MODE)
        {
            byte L[8];
            PutWord(false, BIG_ENDIAN_ORDER, L, (LABEL_OCTETS ? word64(encodingParameters.size()) : 8 * word64(encodingParameters.size())));
            mac.Update(L, 8);
        }
        mac.Final(ciphertext + plaintextLength);
    }
    DecodingResult SymmetricDecrypt(const byte *key, const byte *ciphertext, size_t ciphertextLength, byte *plaintext, const NameValuePairs &parameters) const
    {
        size_t plaintextLength = GetMaxSymmetricPlaintextLength(ciphertextLength);
        const byte *cipherKey, *macKey;
        if (DHAES_MODE)
        {
            macKey = key;
            cipherKey = key + MAC::DEFAULT_KEYLENGTH;
        }
        else
        {
            cipherKey = key;
            macKey = key + plaintextLength;
        }
 
        ConstByteArrayParameter encodingParameters;
        parameters.GetValue(Name::EncodingParameters(), encodingParameters);
 
        MAC mac(macKey);
        mac.Update(ciphertext, plaintextLength);
        mac.Update(encodingParameters.begin(), encodingParameters.size());
        if (DHAES_MODE)
        {
            byte L[8];
            PutWord(false, BIG_ENDIAN_ORDER, L, (LABEL_OCTETS ? word64(encodingParameters.size()) : 8 * word64(encodingParameters.size())));
            mac.Update(L, 8);
        }
        if (!mac.Verify(ciphertext + plaintextLength))
            return DecodingResult();
 
        if (plaintextLength)    // Coverity finding
            xorbuf(plaintext, ciphertext, cipherKey, plaintextLength);
 
        return DecodingResult(plaintextLength);
    }
};
 
/// \brief P1363 based Key Derivation Method
/// \tparam T FieldElement type or class
/// \tparam DHAES_MODE flag indicating DHAES mode
/// \tparam KDF key derivation function
/// \details FieldElement <tt>T</tt> can be Integer, ECP or EC2N.
template <class T, bool DHAES_MODE, class KDF>
class DL_KeyDerivationAlgorithm_P1363 : public DL_KeyDerivationAlgorithm<T>
{
public:
    virtual ~DL_KeyDerivationAlgorithm_P1363() {}
 
    bool ParameterSupported(const char *name) const {return strcmp(name, Name::KeyDerivationParameters()) == 0;}
    void Derive(const DL_GroupParameters<T> &params, byte *derivedKey, size_t derivedLength, const T &agreedElement, const T &ephemeralPublicKey, const NameValuePairs &parameters) const
    {
        SecByteBlock agreedSecret;
        if (DHAES_MODE)
        {
            agreedSecret.New(params.GetEncodedElementSize(true) + params.GetEncodedElementSize(false));
            params.EncodeElement(true, ephemeralPublicKey, agreedSecret);
            params.EncodeElement(false, agreedElement, agreedSecret + params.GetEncodedElementSize(true));
        }
        else
        {
            agreedSecret.New(params.GetEncodedElementSize(false));
            params.EncodeElement(false, agreedElement, agreedSecret);
        }
 
        ConstByteArrayParameter derivationParameters;
        parameters.GetValue(Name::KeyDerivationParameters(), derivationParameters);
        KDF::DeriveKey(derivedKey, derivedLength, agreedSecret, agreedSecret.size(), derivationParameters.begin(), derivationParameters.size());
    }
};
 
/// \brief Discrete Log 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 addition context parameters such as the label
/// \tparam LABEL_OCTETS flag indicating if the label size is specified in octets or bits
/// \details DLIES is an Integer based Integrated Encryption Scheme (IES). The scheme combines a Key Encapsulation Method (KEM)
///  with a Data Encapsulation Method (DEM) and a MAC tag. The scheme is
///  <A HREF="http://en.wikipedia.org/wiki/ciphertext_indistinguishability">IND-CCA2</A>, which is a strong notion of security.
///  You should prefer an Integrated Encryption Scheme over homegrown schemes.
/// \details The library's original implementation is based on an early P1363 draft, which itself appears to be based on an early Certicom
///  SEC-1 draft (or an early SEC-1 draft was based on a P1363 draft). Crypto++ 4.2 used the early draft in its Integrated Ecryption
///  Schemes with <tt>NoCofactorMultiplication</tt>, <tt>DHAES_MODE=false</tt> and <tt>LABEL_OCTETS=true</tt>.
/// \details If you desire an Integrated Encryption Scheme with Crypto++ 4.2 compatibility, then use the DLIES template class with
///  <tt>NoCofactorMultiplication</tt>, <tt>DHAES_MODE=false</tt> and <tt>LABEL_OCTETS=true</tt>.
/// \details If you desire an Integrated Encryption Scheme with Bouncy Castle 1.54 and Botan 1.11 compatibility, then use the DLIES
///  template class with <tt>NoCofactorMultiplication</tt>, <tt>DHAES_MODE=true</tt> and <tt>LABEL_OCTETS=false</tt>.
/// \details The default template parameters ensure compatibility with Bouncy Castle 1.54 and Botan 1.11. The combination of
///  <tt>IncompatibleCofactorMultiplication</tt> and <tt>DHAES_MODE=true</tt> is recommended for best efficiency and security.
///  SHA1 is used for compatibility reasons, but it can be changed if desired. SHA-256 or another hash will likely improve the
///  security provided by the MAC. The hash is also used in the key derivation function as a PRF.
/// \details Below is an example of constructing a Crypto++ 4.2 compatible DLIES encryptor and decryptor.
/// <pre>
///    AutoSeededRandomPool prng;
///    DL_PrivateKey_GFP<DL_GroupParameters_GFP> key;
///    key.Initialize(prng, 2048);
///
///    DLIES<SHA1,NoCofactorMultiplication,true,true>::Decryptor decryptor(key);
///    DLIES<SHA1,NoCofactorMultiplication,true,true>::Encryptor encryptor(decryptor);
/// </pre>
/// \sa ECIES, <a href="http://www.weidai.com/scan-mirror/ca.html#DLIES">Discrete Log Integrated Encryption Scheme (DLIES)</a>,
///  Martínez, Encinas, and Ávila's <A HREF="http://digital.csic.es/bitstream/10261/32671/1/V2-I2-P7-13.pdf">A Survey of the Elliptic
///  Curve Integrated Encryption Schemes</A>
/// \since Crypto++ 4.0, 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 DLIES
    : public DL_ES<
        DL_CryptoKeys_GFP,
        DL_KeyAgreementAlgorithm_DH<Integer, COFACTOR_OPTION>,
        DL_KeyDerivationAlgorithm_P1363<Integer, DHAES_MODE, P1363_KDF2<HASH> >,
        DL_EncryptionAlgorithm_Xor<HMAC<HASH>, DHAES_MODE, LABEL_OCTETS>,
        DLIES<> >
{
    static std::string CRYPTOPP_API StaticAlgorithmName() {return "DLIES";}    // TODO: fix this after name is standardized
};
 
NAMESPACE_END
 
#if CRYPTOPP_MSC_VERSION
# pragma warning(pop)
#endif
 
#endif