// ecp.cpp - originally written and placed in the public domain by Wei Dai

#include "pch.h"

#ifndef CRYPTOPP_IMPORTS

#include "ecp.h"

#include "asn.h"

#include "integer.h"

#include "nbtheory.h"

#include "modarith.h"

#include "filters.h"

#include "algebra.cpp"

ANONYMOUS_NAMESPACE_BEGIN

using CryptoPP::ECP;

using CryptoPP::Integer;

using CryptoPP::ModularArithmetic;

#if defined(HAVE_GCC_INIT_PRIORITY)

  #define INIT_ATTRIBUTE __attribute__ ((init_priority (CRYPTOPP_INIT_PRIORITY + 50)))

  const ECP::Point g_identity INIT_ATTRIBUTE = ECP::Point();

#elif defined(HAVE_MSC_INIT_PRIORITY)

  #pragma warning(disable: 4075)

  #pragma init_seg(".CRT$XCU")

  const ECP::Point g_identity;

  #pragma warning(default: 4075)

#elif defined(HAVE_XLC_INIT_PRIORITY)

  #pragma priority(290)

  const ECP::Point g_identity;

#endif

inline ECP::Point ToMontgomery(const ModularArithmetic &mr, const ECP::Point &P)

{

  return P.identity ? P : ECP::Point(mr.ConvertIn(P.x), mr.ConvertIn(P.y));

}

inline ECP::Point FromMontgomery(const ModularArithmetic &mr, const ECP::Point &P)

{

  return P.identity ? P : ECP::Point(mr.ConvertOut(P.x), mr.ConvertOut(P.y));

}

inline Integer IdentityToInteger(bool val)

{

  return val ? Integer::One() : Integer::Zero();

}

struct ProjectivePoint

{

  ProjectivePoint() {}

  ProjectivePoint(const Integer &x, const Integer &y, const Integer &z)

    : x(x), y(y), z(z)  {}

  Integer x, y, z;

};

ANONYMOUS_NAMESPACE_END

NAMESPACE_BEGIN(CryptoPP)

ECP::ECP(const ECP &ecp, bool convertToMontgomeryRepresentation)

{

  if (convertToMontgomeryRepresentation && !ecp.GetField().IsMontgomeryRepresentation())

  {

    m_fieldPtr.reset(new MontgomeryRepresentation(ecp.GetField().GetModulus()));

    m_a = GetField().ConvertIn(ecp.m_a);

    m_b = GetField().ConvertIn(ecp.m_b);

  }

  else

    operator=(ecp);

}

ECP::ECP(BufferedTransformation &bt)

  : m_fieldPtr(new Field(bt))

{

  BERSequenceDecoder seq(bt);

  GetField().BERDecodeElement(seq, m_a);

  GetField().BERDecodeElement(seq, m_b);

  // skip optional seed

  if (!seq.EndReached())

  {

    SecByteBlock seed;

    unsigned int unused;

    BERDecodeBitString(seq, seed, unused);

  }

  seq.MessageEnd();

}

void ECP::DEREncode(BufferedTransformation &bt) const

{

  GetField().DEREncode(bt);

  DERSequenceEncoder seq(bt);

  GetField().DEREncodeElement(seq, m_a);

  GetField().DEREncodeElement(seq, m_b);

  seq.MessageEnd();

}

bool ECP::DecodePoint(ECP::Point &P, const byte *encodedPoint, size_t encodedPointLen) const

{

  StringStore store(encodedPoint, encodedPointLen);

  return DecodePoint(P, store, encodedPointLen);

}

bool ECP::DecodePoint(ECP::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;

    // Check for p is prime due to GH #1249

    const Integer p = FieldSize();

    CRYPTOPP_ASSERT(IsPrime(p));

    if (!IsPrime(p))

      return false;

    P.identity = false;

    P.x.Decode(bt, GetField().MaxElementByteLength());

    P.y = ((P.x*P.x+m_a)*P.x+m_b) % p;

    if (Jacobi(P.y, p) !=1)

      return false;

    // Callers must ensure p is prime, GH #1249

    P.y = ModularSquareRoot(P.y, p);

    if ((type & 1) != P.y.GetBit(0))

      P.y = p-P.y;

    return true;

  }

  case 4:

  {

    if (encodedPointLen != EncodedPointSize(false))

      return false;

    unsigned int len = GetField().MaxElementByteLength();

    P.identity = false;

    P.x.Decode(bt, len);

    P.y.Decode(bt, len);

    return true;

  }

  default:

    return false;

  }

}

void ECP::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.y.GetBit(0)));

    P.x.Encode(bt, GetField().MaxElementByteLength());

  }

  else

  {

    unsigned int len = GetField().MaxElementByteLength();

    bt.Put(4U); // uncompressed

    P.x.Encode(bt, len);

    P.y.Encode(bt, len);

  }

}

void ECP::EncodePoint(byte *encodedPoint, const Point &P, bool compressed) const

{

  ArraySink sink(encodedPoint, EncodedPointSize(compressed));

  EncodePoint(sink, P, compressed);

  CRYPTOPP_ASSERT(sink.TotalPutLength() == EncodedPointSize(compressed));

}

ECP::Point ECP::BERDecodePoint(BufferedTransformation &bt) const

{

  SecByteBlock str;

  BERDecodeOctetString(bt, str);

  Point P;

  if (!DecodePoint(P, str, str.size()))

    BERDecodeError();

  return P;

}

void ECP::DEREncodePoint(BufferedTransformation &bt, const Point &P, bool compressed) const

{

  SecByteBlock str(EncodedPointSize(compressed));

  EncodePoint(str, P, compressed);

  DEREncodeOctetString(bt, str);

}

bool ECP::ValidateParameters(RandomNumberGenerator &rng, unsigned int level) const

{

  Integer p = FieldSize();

  bool pass = p.IsOdd();

  pass = pass && !m_a.IsNegative() && m_a<p && !m_b.IsNegative() && m_b<p;

  if (level >= 1)

    pass = pass && ((4*m_a*m_a*m_a+27*m_b*m_b)%p).IsPositive();

  if (level >= 2)

    pass = pass && VerifyPrime(rng, p);

  return pass;

}

bool ECP::VerifyPoint(const Point &P) const

{

  const FieldElement &x = P.x, &y = P.y;

  Integer p = FieldSize();

  return P.identity ||

    (!x.IsNegative() && x<p && !y.IsNegative() && y<p

    && !(((x*x+m_a)*x+m_b-y*y)%p));

}

bool ECP::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 (GetField().Equal(P.x,Q.x) && GetField().Equal(P.y,Q.y));

}

const ECP::Point& ECP::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 ECP::Point g_identity;

  return g_identity;

#else

  return Singleton<Point>().Ref();

#endif

}

const ECP::Point& ECP::Inverse(const Point &P) const

{

  if (P.identity)

    return P;

  else

  {

    m_R.identity = false;

    m_R.x = P.x;

    m_R.y = GetField().Inverse(P.y);

    return m_R;

  }

}

const ECP::Point& ECP::Add(const Point &P, const Point &Q) const

{

  if (P.identity) return Q;

  if (Q.identity) return P;

  if (GetField().Equal(P.x, Q.x))

    return GetField().Equal(P.y, Q.y) ? Double(P) : Identity();

  FieldElement t = GetField().Subtract(Q.y, P.y);

  t = GetField().Divide(t, GetField().Subtract(Q.x, P.x));

  FieldElement x = GetField().Subtract(GetField().Subtract(GetField().Square(t), P.x), Q.x);

  m_R.y = GetField().Subtract(GetField().Multiply(t, GetField().Subtract(P.x, x)), P.y);

  m_R.x.swap(x);

  m_R.identity = false;

  return m_R;

}

const ECP::Point& ECP::Double(const Point &P) const

{

  if (P.identity || P.y==GetField().Identity()) return Identity();

  FieldElement t = GetField().Square(P.x);

  t = GetField().Add(GetField().Add(GetField().Double(t), t), m_a);

  t = GetField().Divide(t, GetField().Double(P.y));

  FieldElement x = GetField().Subtract(GetField().Subtract(GetField().Square(t), P.x), P.x);

  m_R.y = GetField().Subtract(GetField().Multiply(t, GetField().Subtract(P.x, x)), P.y);

  m_R.x.swap(x);

  m_R.identity = false;

  return m_R;

}

template <class T, class Iterator> void ParallelInvert(const AbstractRing<T> &ring, Iterator begin, Iterator end)

{

  size_t n = end-begin;

  if (n == 1)

    *begin = ring.MultiplicativeInverse(*begin);

  else if (n > 1)

  {

    std::vector<T> vec((n+1)/2);

    unsigned int i;

    Iterator it;

    for (i=0, it=begin; i<n/2; i++, it+=2)

      vec[i] = ring.Multiply(*it, *(it+1));

    if (n%2 == 1)

      vec[n/2] = *it;

    ParallelInvert(ring, vec.begin(), vec.end());

    for (i=0, it=begin; i<n/2; i++, it+=2)

    {

      if (!vec[i])

      {

        *it = ring.MultiplicativeInverse(*it);

        *(it+1) = ring.MultiplicativeInverse(*(it+1));

      }

      else

      {

        std::swap(*it, *(it+1));

        *it = ring.Multiply(*it, vec[i]);

        *(it+1) = ring.Multiply(*(it+1), vec[i]);

      }

    }

    if (n%2 == 1)

      *it = vec[n/2];

  }

}

Unexecuted instantiation: void CryptoPP::ParallelInvert<CryptoPP::Integer, CryptoPP::ZIterator>(CryptoPP::AbstractRing<CryptoPP::Integer> const&, CryptoPP::ZIterator, CryptoPP::ZIterator)

Unexecuted instantiation: void CryptoPP::ParallelInvert<CryptoPP::Integer, std::__1::__wrap_iter<CryptoPP::Integer*> >(CryptoPP::AbstractRing<CryptoPP::Integer> const&, std::__1::__wrap_iter<CryptoPP::Integer*>, std::__1::__wrap_iter<CryptoPP::Integer*>)

class ProjectiveDoubling

{

public:

  ProjectiveDoubling(const ModularArithmetic &m_mr, const Integer &m_a, const Integer &m_b, const ECPPoint &Q)

    : mr(m_mr)

  {

    CRYPTOPP_UNUSED(m_b);

    if (Q.identity)

    {

      sixteenY4 = P.x = P.y = mr.MultiplicativeIdentity();

      aZ4 = P.z = mr.Identity();

    }

    else

    {

      P.x = Q.x;

      P.y = Q.y;

      sixteenY4 = P.z = mr.MultiplicativeIdentity();

      aZ4 = m_a;

    }

  }

  void Double()

  {

    twoY = mr.Double(P.y);

    P.z = mr.Multiply(P.z, twoY);

    fourY2 = mr.Square(twoY);

    S = mr.Multiply(fourY2, P.x);

    aZ4 = mr.Multiply(aZ4, sixteenY4);

    M = mr.Square(P.x);

    M = mr.Add(mr.Add(mr.Double(M), M), aZ4);

    P.x = mr.Square(M);

    mr.Reduce(P.x, S);

    mr.Reduce(P.x, S);

    mr.Reduce(S, P.x);

    P.y = mr.Multiply(M, S);

    sixteenY4 = mr.Square(fourY2);

    mr.Reduce(P.y, mr.Half(sixteenY4));

  }

  const ModularArithmetic &mr;

  ProjectivePoint P;

  Integer sixteenY4, aZ4, twoY, fourY2, S, M;

};

struct ZIterator

{

  ZIterator() {}

  ZIterator(std::vector<ProjectivePoint>::iterator it) : it(it) {}

  Integer& operator*() {return it->z;}

  int operator-(ZIterator it2) {return int(it-it2.it);}

  ZIterator operator+(int i) {return ZIterator(it+i);}

  ZIterator& operator+=(int i) {it+=i; return *this;}

  std::vector<ProjectivePoint>::iterator it;

};

ECP::Point ECP::ScalarMultiply(const Point &P, const Integer &k) const

{

  Element result;

  if (k.BitCount() <= 5)

    AbstractGroup<ECPPoint>::SimultaneousMultiply(&result, P, &k, 1);

  else

    ECP::SimultaneousMultiply(&result, P, &k, 1);

  return result;

}

void ECP::SimultaneousMultiply(ECP::Point *results, const ECP::Point &P, const Integer *expBegin, unsigned int expCount) const

{

  if (!GetField().IsMontgomeryRepresentation())

  {

    ECP ecpmr(*this, true);

    const ModularArithmetic &mr = ecpmr.GetField();

    ecpmr.SimultaneousMultiply(results, ToMontgomery(mr, P), expBegin, expCount);

    for (unsigned int i=0; i<expCount; i++)

      results[i] = FromMontgomery(mr, results[i]);

    return;

  }

  ProjectiveDoubling rd(GetField(), m_a, m_b, P);

  std::vector<ProjectivePoint> bases;

  std::vector<WindowSlider> exponents;

  exponents.reserve(expCount);

  std::vector<std::vector<word32> > baseIndices(expCount);

  std::vector<std::vector<bool> > negateBase(expCount);

  std::vector<std::vector<word32> > exponentWindows(expCount);

  unsigned int i;

  for (i=0; i<expCount; i++)

  {

    CRYPTOPP_ASSERT(expBegin->NotNegative());

    exponents.push_back(WindowSlider(*expBegin++, InversionIsFast(), 5));

    exponents[i].FindNextWindow();

  }

  unsigned int expBitPosition = 0;

  bool notDone = true;

  while (notDone)

  {

    notDone = false;

    bool baseAdded = false;

    for (i=0; i<expCount; i++)

    {

      if (!exponents[i].finished && expBitPosition == exponents[i].windowBegin)

      {

        if (!baseAdded)

        {

          bases.push_back(rd.P);

          baseAdded =true;

        }

        exponentWindows[i].push_back(exponents[i].expWindow);

        baseIndices[i].push_back((word32)bases.size()-1);

        negateBase[i].push_back(exponents[i].negateNext);

        exponents[i].FindNextWindow();

      }

      notDone = notDone || !exponents[i].finished;

    }

    if (notDone)

    {

      rd.Double();

      expBitPosition++;

    }

  }

  // convert from projective to affine coordinates

  ParallelInvert(GetField(), ZIterator(bases.begin()), ZIterator(bases.end()));

  for (i=0; i<bases.size(); i++)

  {

    if (bases[i].z.NotZero())

    {

      bases[i].y = GetField().Multiply(bases[i].y, bases[i].z);

      bases[i].z = GetField().Square(bases[i].z);

      bases[i].x = GetField().Multiply(bases[i].x, bases[i].z);

      bases[i].y = GetField().Multiply(bases[i].y, bases[i].z);

    }

  }

  std::vector<BaseAndExponent<Point, Integer> > finalCascade;

  for (i=0; i<expCount; i++)

  {

    finalCascade.resize(baseIndices[i].size());

    for (unsigned int j=0; j<baseIndices[i].size(); j++)

    {

      ProjectivePoint &base = bases[baseIndices[i][j]];

      if (base.z.IsZero())

        finalCascade[j].base.identity = true;

      else

      {

        finalCascade[j].base.identity = false;

        finalCascade[j].base.x = base.x;

        if (negateBase[i][j])

          finalCascade[j].base.y = GetField().Inverse(base.y);

        else

          finalCascade[j].base.y = base.y;

      }

      finalCascade[j].exponent = Integer(Integer::POSITIVE, 0, exponentWindows[i][j]);

    }

    results[i] = GeneralCascadeMultiplication(*this, finalCascade.begin(), finalCascade.end());

  }

}

ECP::Point ECP::CascadeScalarMultiply(const Point &P, const Integer &k1, const Point &Q, const Integer &k2) const

{

  if (!GetField().IsMontgomeryRepresentation())

  {

    ECP ecpmr(*this, true);

    const ModularArithmetic &mr = ecpmr.GetField();

    return FromMontgomery(mr, ecpmr.CascadeScalarMultiply(ToMontgomery(mr, P), k1, ToMontgomery(mr, Q), k2));

  }

  else

    return AbstractGroup<Point>::CascadeScalarMultiply(P, k1, Q, k2);

}

NAMESPACE_END

#endif