ec2n.cpp

// ec2n.cpp - originally written and placed in the public domain by Wei Dai
 
#include "pch.h"
 
#ifndef CRYPTOPP_IMPORTS
 
#include "ec2n.h"
#include "asn.h"
#include "integer.h"
#include "filters.h"
#include "algebra.cpp"
#include "eprecomp.cpp"
 
ANONYMOUS_NAMESPACE_BEGIN
 
using CryptoPP::EC2N;
 
#if defined(HAVE_GCC_INIT_PRIORITY)
    #define INIT_ATTRIBUTE __attribute__ ((init_priority (CRYPTOPP_INIT_PRIORITY + 51)))
    const EC2N::Point g_identity INIT_ATTRIBUTE = EC2N::Point();
#elif defined(HAVE_MSC_INIT_PRIORITY)
    #pragma warning(disable: 4075)
    #pragma init_seg(".CRT$XCU")
    const EC2N::Point g_identity;
    #pragma warning(default: 4075)
#elif defined(HAVE_XLC_INIT_PRIORITY)
    #pragma priority(290)
    const EC2N::Point g_identity;
#endif
 
ANONYMOUS_NAMESPACE_END
 
NAMESPACE_BEGIN(CryptoPP)
 
EC2N::EC2N(BufferedTransformation &bt)
    : m_field(BERDecodeGF2NP(bt))
{
    BERSequenceDecoder seq(bt);
    m_field->BERDecodeElement(seq, m_a);
    m_field->BERDecodeElement(seq, m_b);
    // skip optional seed
    if (!seq.EndReached())
    {
        SecByteBlock seed;
        unsigned int unused;
        BERDecodeBitString(seq, seed, unused);
    }
    seq.MessageEnd();
}
 
void EC2N::DEREncode(BufferedTransformation &bt) const
{
    m_field->DEREncode(bt);
    DERSequenceEncoder seq(bt);
       m_field->DEREncodeElement(seq, m_a);
       m_field->DEREncodeElement(seq, m_b);
    seq.MessageEnd();
}
 
bool EC2N::DecodePoint(EC2N::Point &P, const byte *encodedPoint, size_t encodedPointLen) const
{
    StringStore store(encodedPoint, encodedPointLen);
    return DecodePoint(P, store, encodedPointLen);
}
 
bool EC2N::DecodePoint(EC2N::Point &P, BufferedTransformation &bt, size_t encodedPointLen) const
{
    byte type;
    if (encodedPointLen < 1 || !bt.Get(type))
        return false;
 
    switch (type)
    {
    case 0:
        P.identity = true;
        return true;
    case 2:
    case 3:
    {
        if (encodedPointLen != EncodedPointSize(true))
            return false;
 
        P.identity = false;
        P.x.Decode(bt, m_field->MaxElementByteLength());
 
        if (P.x.IsZero())
        {
            P.y = m_field->SquareRoot(m_b);
            return true;
        }
 
        FieldElement z = m_field->Square(P.x);
        CRYPTOPP_ASSERT(P.x == m_field->SquareRoot(z));
        P.y = m_field->Divide(m_field->Add(m_field->Multiply(z, m_field->Add(P.x, m_a)), m_b), z);
        CRYPTOPP_ASSERT(P.x == m_field->Subtract(m_field->Divide(m_field->Subtract(m_field->Multiply(P.y, z), m_b), z), m_a));
        z = m_field->SolveQuadraticEquation(P.y);
        CRYPTOPP_ASSERT(m_field->Add(m_field->Square(z), z) == P.y);
        z.SetCoefficient(0, type & 1);
 
        P.y = m_field->Multiply(z, P.x);
        return true;
    }
    case 4:
    {
        if (encodedPointLen != EncodedPointSize(false))
            return false;
 
        unsigned int len = m_field->MaxElementByteLength();
        P.identity = false;
        P.x.Decode(bt, len);
        P.y.Decode(bt, len);
        return true;
    }
    default:
        return false;
    }
}
 
void EC2N::EncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const
{
    if (P.identity)
        NullStore().TransferTo(bt, EncodedPointSize(compressed));
    else if (compressed)
    {
        bt.Put((byte)(2U + (!P.x ? 0U : m_field->Divide(P.y, P.x).GetBit(0))));
        P.x.Encode(bt, m_field->MaxElementByteLength());
    }
    else
    {
        unsigned int len = m_field->MaxElementByteLength();
        bt.Put(4);  // uncompressed
        P.x.Encode(bt, len);
        P.y.Encode(bt, len);
    }
}
 
void EC2N::EncodePoint(byte *encodedPoint, const Point &P, bool compressed) const
{
    ArraySink sink(encodedPoint, EncodedPointSize(compressed));
    EncodePoint(sink, P, compressed);
    CRYPTOPP_ASSERT(sink.TotalPutLength() == EncodedPointSize(compressed));
}
 
EC2N::Point EC2N::BERDecodePoint(BufferedTransformation &bt) const
{
    SecByteBlock str;
    BERDecodeOctetString(bt, str);
    Point P;
    if (!DecodePoint(P, str, str.size()))
        BERDecodeError();
    return P;
}
 
void EC2N::DEREncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const
{
    SecByteBlock str(EncodedPointSize(compressed));
    EncodePoint(str, P, compressed);
    DEREncodeOctetString(bt, str);
}
 
bool EC2N::ValidateParameters(RandomNumberGenerator &rng, unsigned int level) const
{
    CRYPTOPP_UNUSED(rng);
    bool pass = !!m_b;
    pass = pass && m_a.CoefficientCount() <= m_field->MaxElementBitLength();
    pass = pass && m_b.CoefficientCount() <= m_field->MaxElementBitLength();
 
    if (level >= 1)
        pass = pass && m_field->GetModulus().IsIrreducible();
 
    return pass;
}
 
bool EC2N::VerifyPoint(const Point &P) const
{
    const FieldElement &x = P.x, &y = P.y;
    return P.identity ||
        (x.CoefficientCount() <= m_field->MaxElementBitLength()
        && y.CoefficientCount() <= m_field->MaxElementBitLength()
        && !(((x+m_a)*x*x+m_b-(x+y)*y)%m_field->GetModulus()));
}
 
bool EC2N::Equal(const Point &P, const Point &Q) const
{
    if (P.identity && Q.identity)
        return true;
 
    if (P.identity && !Q.identity)
        return false;
 
    if (!P.identity && Q.identity)
        return false;
 
    return (m_field->Equal(P.x,Q.x) && m_field->Equal(P.y,Q.y));
}
 
const EC2N::Point& EC2N::Identity() const
{
#if defined(HAVE_GCC_INIT_PRIORITY) || defined(HAVE_MSC_INIT_PRIORITY) || defined(HAVE_XLC_INIT_PRIORITY)
    return g_identity;
#elif defined(CRYPTOPP_CXX11_STATIC_INIT)
    static const EC2N::Point g_identity;
    return g_identity;
#else
    return Singleton<Point>().Ref();
#endif
}
 
const EC2N::Point& EC2N::Inverse(const Point &P) const
{
    if (P.identity)
        return P;
    else
    {
        m_R.identity = false;
        m_R.y = m_field->Add(P.x, P.y);
        m_R.x = P.x;
        return m_R;
    }
}
 
const EC2N::Point& EC2N::Add(const Point &P, const Point &Q) const
{
    if (P.identity) return Q;
    if (Q.identity) return P;
    if (Equal(P, Q)) return Double(P);
    if (m_field->Equal(P.x, Q.x) && m_field->Equal(P.y, m_field->Add(Q.x, Q.y))) return Identity();
 
    FieldElement t = m_field->Add(P.y, Q.y);
    t = m_field->Divide(t, m_field->Add(P.x, Q.x));
    FieldElement x = m_field->Square(t);
    m_field->Accumulate(x, t);
    m_field->Accumulate(x, Q.x);
    m_field->Accumulate(x, m_a);
    m_R.y = m_field->Add(P.y, m_field->Multiply(t, x));
    m_field->Accumulate(x, P.x);
    m_field->Accumulate(m_R.y, x);
 
    m_R.x.swap(x);
    m_R.identity = false;
    return m_R;
}
 
const EC2N::Point& EC2N::Double(const Point &P) const
{
    if (P.identity) return P;
    if (!m_field->IsUnit(P.x)) return Identity();
 
    FieldElement t = m_field->Divide(P.y, P.x);
    m_field->Accumulate(t, P.x);
    m_R.y = m_field->Square(P.x);
    m_R.x = m_field->Square(t);
    m_field->Accumulate(m_R.x, t);
    m_field->Accumulate(m_R.x, m_a);
    m_field->Accumulate(m_R.y, m_field->Multiply(t, m_R.x));
    m_field->Accumulate(m_R.y, m_R.x);
 
    m_R.identity = false;
    return m_R;
}
 
// ********************************************************
 
#if 0
EcPrecomputation<EC2N>& EcPrecomputation<EC2N>::operator=(const EcPrecomputation<EC2N> &rhs)
{
    m_ec = rhs.m_ec;
    m_ep = rhs.m_ep;
    m_ep.m_group = m_ec.get();
    return *this;
}
 
void EcPrecomputation<EC2N>::SetCurveAndBase(const EC2N &ec, const EC2N::Point &base)
{
    m_ec.reset(new EC2N(ec));
    m_ep.SetGroupAndBase(*m_ec, base);
}
 
void EcPrecomputation<EC2N>::Precompute(unsigned int maxExpBits, unsigned int storage)
{
    m_ep.Precompute(maxExpBits, storage);
}
 
void EcPrecomputation<EC2N>::Load(BufferedTransformation &bt)
{
    BERSequenceDecoder seq(bt);
    word32 version;
    BERDecodeUnsigned<word32>(seq, version, INTEGER, 1, 1);
    m_ep.m_exponentBase.BERDecode(seq);
    m_ep.m_windowSize = m_ep.m_exponentBase.BitCount() - 1;
    m_ep.m_bases.clear();
    while (!seq.EndReached())
        m_ep.m_bases.push_back(m_ec->BERDecodePoint(seq));
    seq.MessageEnd();
}
 
void EcPrecomputation<EC2N>::Save(BufferedTransformation &bt) const
{
    DERSequenceEncoder seq(bt);
    DEREncodeUnsigned<word32>(seq, 1);  // version
    m_ep.m_exponentBase.DEREncode(seq);
    for (unsigned i=0; i<m_ep.m_bases.size(); i++)
        m_ec->DEREncodePoint(seq, m_ep.m_bases[i]);
    seq.MessageEnd();
}
 
EC2N::Point EcPrecomputation<EC2N>::Exponentiate(const Integer &exponent) const
{
    return m_ep.Exponentiate(exponent);
}
 
EC2N::Point EcPrecomputation<EC2N>::CascadeExponentiate(const Integer &exponent, const DL_FixedBasePrecomputation<Element> &pc2, const Integer &exponent2) const
{
    return m_ep.CascadeExponentiate(exponent, static_cast<const EcPrecomputation<EC2N> &>(pc2).m_ep, exponent2);
}
#endif
 
NAMESPACE_END
 
#endif