gf2n.cpp

// gf2n.cpp - originally written and placed in the public domain by Wei Dai
 
#include "pch.h"
#include "config.h"
 
#ifndef CRYPTOPP_IMPORTS
 
#include "cryptlib.h"
#include "algebra.h"
#include "randpool.h"
#include "filters.h"
#include "smartptr.h"
#include "words.h"
#include "misc.h"
#include "gf2n.h"
#include "oids.h"
#include "asn.h"
#include "cpu.h"
 
#include <iostream>
 
ANONYMOUS_NAMESPACE_BEGIN
 
using CryptoPP::PolynomialMod2;
 
#if defined(HAVE_GCC_INIT_PRIORITY)
  const PolynomialMod2 g_zero __attribute__ ((init_priority (CRYPTOPP_INIT_PRIORITY + 60))) = PolynomialMod2();
  const PolynomialMod2 g_one __attribute__ ((init_priority (CRYPTOPP_INIT_PRIORITY + 61))) = PolynomialMod2(1);
#elif defined(HAVE_MSC_INIT_PRIORITY)
  #pragma warning(disable: 4075)
  #pragma init_seg(".CRT$XCU")
  const PolynomialMod2 g_zero;
  const PolynomialMod2 g_one(1);
  #pragma warning(default: 4075)
#elif defined(HAVE_XLC_INIT_PRIORITY)
  #pragma priority(290)
  const PolynomialMod2 g_zero;
  const PolynomialMod2 g_one(1);
#endif
 
ANONYMOUS_NAMESPACE_END
 
NAMESPACE_BEGIN(CryptoPP)
 
#if (CRYPTOPP_CLMUL_AVAILABLE)
extern CRYPTOPP_DLL void GF2NT_233_Multiply_Reduce_CLMUL(const word* pA, const word* pB, word* pC);
extern CRYPTOPP_DLL void GF2NT_233_Square_Reduce_CLMUL(const word* pA, word* pC);
#endif
 
#if (CRYPTOPP_ARM_PMULL_AVAILABLE)
extern void GF2NT_233_Multiply_Reduce_ARMv8(const word* pA, const word* pB, word* pC);
extern void GF2NT_233_Square_Reduce_ARMv8(const word* pA, word* pC);
#endif
 
#if (CRYPTOPP_POWER8_VMULL_AVAILABLE) && 0
extern void GF2NT_233_Multiply_Reduce_POWER8(const word* pA, const word* pB, word* pC);
extern void GF2NT_233_Square_Reduce_POWER8(const word* pA, word* pC);
#endif
 
PolynomialMod2::PolynomialMod2()
{
}
 
PolynomialMod2::PolynomialMod2(word value, size_t bitLength)
        : reg(BitsToWords(bitLength))
{
        CRYPTOPP_ASSERT(value==0 || reg.size()>0);
 
        if (reg.size() > 0)
        {
                reg[0] = value;
                SetWords(reg+1, 0, reg.size()-1);
        }
}
 
PolynomialMod2::PolynomialMod2(const PolynomialMod2& t)
        : reg(t.reg.size())
{
        CopyWords(reg, t.reg, reg.size());
}
 
void PolynomialMod2::Randomize(RandomNumberGenerator &rng, size_t nbits)
{
        const size_t nbytes = nbits/8 + 1;
        SecByteBlock buf(nbytes);
        rng.GenerateBlock(buf, nbytes);
        buf[0] = (byte)Crop(buf[0], nbits % 8);
        Decode(buf, nbytes);
}
 
PolynomialMod2 PolynomialMod2::AllOnes(size_t bitLength)
{
        PolynomialMod2 result((word)0, bitLength);
        SetWords(result.reg, ~(word(0)), result.reg.size());
        if (bitLength%WORD_BITS)
                result.reg[result.reg.size()-1] = (word)Crop(result.reg[result.reg.size()-1], bitLength%WORD_BITS);
        return result;
}
 
void PolynomialMod2::SetBit(size_t n, int value)
{
        if (value)
        {
                reg.CleanGrow(n/WORD_BITS + 1);
                reg[n/WORD_BITS] |= (word(1) << (n%WORD_BITS));
        }
        else
        {
                if (n/WORD_BITS < reg.size())
                        reg[n/WORD_BITS] &= ~(word(1) << (n%WORD_BITS));
        }
}
 
byte PolynomialMod2::GetByte(size_t n) const
{
        if (n/WORD_SIZE >= reg.size())
                return 0;
        else
                return byte(reg[n/WORD_SIZE] >> ((n%WORD_SIZE)*8));
}
 
void PolynomialMod2::SetByte(size_t n, byte value)
{
        reg.CleanGrow(BytesToWords(n+1));
        reg[n/WORD_SIZE] &= ~(word(0xff) << 8*(n%WORD_SIZE));
        reg[n/WORD_SIZE] |= (word(value) << 8*(n%WORD_SIZE));
}
 
PolynomialMod2 PolynomialMod2::Monomial(size_t i)
{
        PolynomialMod2 r((word)0, i+1);
        r.SetBit(i);
        return r;
}
 
PolynomialMod2 PolynomialMod2::Trinomial(size_t t0, size_t t1, size_t t2)
{
        PolynomialMod2 r((word)0, t0+1);
        r.SetBit(t0);
        r.SetBit(t1);
        r.SetBit(t2);
        return r;
}
 
PolynomialMod2 PolynomialMod2::Pentanomial(size_t t0, size_t t1, size_t t2, size_t t3, size_t t4)
{
        PolynomialMod2 r((word)0, t0+1);
        r.SetBit(t0);
        r.SetBit(t1);
        r.SetBit(t2);
        r.SetBit(t3);
        r.SetBit(t4);
        return r;
}
 
template <word i>
struct NewPolynomialMod2
{
        PolynomialMod2 * operator()() const
        {
                return new PolynomialMod2(i);
        }
};
 
const PolynomialMod2 &PolynomialMod2::Zero()
{
#if defined(HAVE_GCC_INIT_PRIORITY) || defined(HAVE_MSC_INIT_PRIORITY) || defined(HAVE_XLC_INIT_PRIORITY)
        return g_zero;
#elif defined(CRYPTOPP_CXX11_STATIC_INIT)
        static const PolynomialMod2 g_zero;
        return g_zero;
#else
        return Singleton<PolynomialMod2>().Ref();
#endif
}
 
const PolynomialMod2 &PolynomialMod2::One()
{
#if defined(HAVE_GCC_INIT_PRIORITY) || defined(HAVE_MSC_INIT_PRIORITY) || defined(HAVE_XLC_INIT_PRIORITY)
        return g_one;
#elif defined(CRYPTOPP_CXX11_STATIC_INIT)
        static const PolynomialMod2 g_one(1);
        return g_one;
#else
        return Singleton<PolynomialMod2, NewPolynomialMod2<1> >().Ref();
#endif
}
 
void PolynomialMod2::Decode(const byte *input, size_t inputLen)
{
        StringStore store(input, inputLen);
        Decode(store, inputLen);
}
 
void PolynomialMod2::Encode(byte *output, size_t outputLen) const
{
        ArraySink sink(output, outputLen);
        Encode(sink, outputLen);
}
 
void PolynomialMod2::Decode(BufferedTransformation &bt, size_t inputLen)
{
        CRYPTOPP_ASSERT(bt.MaxRetrievable() >= inputLen);
        if (bt.MaxRetrievable() < inputLen)
                throw InvalidArgument("PolynomialMod2: input length is too small");
 
        reg.CleanNew(BytesToWords(inputLen));
 
        for (size_t i=inputLen; i > 0; i--)
        {
                byte b;
                (void)bt.Get(b);
                reg[(i-1)/WORD_SIZE] |= word(b) << ((i-1)%WORD_SIZE)*8;
        }
}
 
void PolynomialMod2::Encode(BufferedTransformation &bt, size_t outputLen) const
{
        for (size_t i=outputLen; i > 0; i--)
                bt.Put(GetByte(i-1));
}
 
void PolynomialMod2::DEREncodeAsOctetString(BufferedTransformation &bt, size_t length) const
{
        DERGeneralEncoder enc(bt, OCTET_STRING);
        Encode(enc, length);
        enc.MessageEnd();
}
 
void PolynomialMod2::BERDecodeAsOctetString(BufferedTransformation &bt, size_t length)
{
        BERGeneralDecoder dec(bt, OCTET_STRING);
        if (!dec.IsDefiniteLength() || dec.RemainingLength() != length)
                BERDecodeError();
        Decode(dec, length);
        dec.MessageEnd();
}
 
unsigned int PolynomialMod2::WordCount() const
{
        return (unsigned int)CountWords(reg, reg.size());
}
 
unsigned int PolynomialMod2::ByteCount() const
{
        unsigned wordCount = WordCount();
        if (wordCount)
                return (wordCount-1)*WORD_SIZE + BytePrecision(reg[wordCount-1]);
        else
                return 0;
}
 
unsigned int PolynomialMod2::BitCount() const
{
        unsigned wordCount = WordCount();
        if (wordCount)
                return (wordCount-1)*WORD_BITS + BitPrecision(reg[wordCount-1]);
        else
                return 0;
}
 
unsigned int PolynomialMod2::Parity() const
{
        unsigned i;
        word temp=0;
        for (i=0; i<reg.size(); i++)
                temp ^= reg[i];
        return CryptoPP::Parity(temp);
}
 
PolynomialMod2& PolynomialMod2::operator=(const PolynomialMod2& t)
{
        reg.Assign(t.reg);
        return *this;
}
 
PolynomialMod2& PolynomialMod2::operator^=(const PolynomialMod2& t)
{
        reg.CleanGrow(t.reg.size());
        XorWords(reg, t.reg, t.reg.size());
        return *this;
}
 
PolynomialMod2 PolynomialMod2::Xor(const PolynomialMod2 &b) const
{
        if (b.reg.size() >= reg.size())
        {
                PolynomialMod2 result((word)0, b.reg.size()*WORD_BITS);
                XorWords(result.reg, reg, b.reg, reg.size());
                CopyWords(result.reg+reg.size(), b.reg+reg.size(), b.reg.size()-reg.size());
                return result;
        }
        else
        {
                PolynomialMod2 result((word)0, reg.size()*WORD_BITS);
                XorWords(result.reg, reg, b.reg, b.reg.size());
                CopyWords(result.reg+b.reg.size(), reg+b.reg.size(), reg.size()-b.reg.size());
                return result;
        }
}
 
PolynomialMod2 PolynomialMod2::And(const PolynomialMod2 &b) const
{
        PolynomialMod2 result((word)0, WORD_BITS*STDMIN(reg.size(), b.reg.size()));
        AndWords(result.reg, reg, b.reg, result.reg.size());
        return result;
}
 
PolynomialMod2 PolynomialMod2::Times(const PolynomialMod2 &b) const
{
        PolynomialMod2 result((word)0, BitCount() + b.BitCount());
 
        for (int i=b.Degree(); i>=0; i--)
        {
                result <<= 1;
                if (b[i])
                        XorWords(result.reg, reg, reg.size());
        }
        return result;
}
 
PolynomialMod2 PolynomialMod2::Squared() const
{
        static const word map[16] = {0, 1, 4, 5, 16, 17, 20, 21, 64, 65, 68, 69, 80, 81, 84, 85};
 
        PolynomialMod2 result((word)0, 2*reg.size()*WORD_BITS);
 
        for (unsigned i=0; i<reg.size(); i++)
        {
                unsigned j;
 
                for (j=0; j<WORD_BITS; j+=8)
                        result.reg[2*i] |= map[(reg[i] >> (j/2)) % 16] << j;
 
                for (j=0; j<WORD_BITS; j+=8)
                        result.reg[2*i+1] |= map[(reg[i] >> (j/2 + WORD_BITS/2)) % 16] << j;
        }
 
        return result;
}
 
void PolynomialMod2::Divide(PolynomialMod2 &remainder, PolynomialMod2 &quotient,
                                   const PolynomialMod2 &dividend, const PolynomialMod2 &divisor)
{
        if (!divisor)
                throw PolynomialMod2::DivideByZero();
 
        int degree = divisor.Degree();
        remainder.reg.CleanNew(BitsToWords(degree+1));
        if (dividend.BitCount() >= divisor.BitCount())
                quotient.reg.CleanNew(BitsToWords(dividend.BitCount() - divisor.BitCount() + 1));
        else
                quotient.reg.CleanNew(0);
 
        for (int i=dividend.Degree(); i>=0; i--)
        {
                remainder <<= 1;
                remainder.reg[0] |= dividend[i];
                if (remainder[degree])
                {
                        remainder -= divisor;
                        quotient.SetBit(i);
                }
        }
}
 
PolynomialMod2 PolynomialMod2::DividedBy(const PolynomialMod2 &b) const
{
        PolynomialMod2 remainder, quotient;
        PolynomialMod2::Divide(remainder, quotient, *this, b);
        return quotient;
}
 
PolynomialMod2 PolynomialMod2::Modulo(const PolynomialMod2 &b) const
{
        PolynomialMod2 remainder, quotient;
        PolynomialMod2::Divide(remainder, quotient, *this, b);
        return remainder;
}
 
PolynomialMod2& PolynomialMod2::operator<<=(unsigned int n)
{
#if defined(CRYPTOPP_DEBUG)
        int x=0; CRYPTOPP_UNUSED(x);
        CRYPTOPP_ASSERT(SafeConvert(n,x));
#endif
 
        if (!reg.size())
                return *this;
 
        int i;
        word u;
        word carry=0;
        word *r=reg;
 
        if (n==1)       // special case code for most frequent case
        {
                i = (int)reg.size();
                while (i--)
                {
                        u = *r;
                        *r = (u << 1) | carry;
                        carry = u >> (WORD_BITS-1);
                        r++;
                }
 
                if (carry)
                {
                        reg.Grow(reg.size()+1);
                        reg[reg.size()-1] = carry;
                }
 
                return *this;
        }
 
        const int shiftWords = n / WORD_BITS;
        const int shiftBits = n % WORD_BITS;
 
        if (shiftBits)
        {
                i = (int)reg.size();
                while (i--)
                {
                        u = *r;
                        *r = (u << shiftBits) | carry;
                        carry = u >> (WORD_BITS-shiftBits);
                        r++;
                }
        }
 
        if (carry)
        {
                // Thanks to Apatryda, http://github.com/weidai11/cryptopp/issues/64
                const size_t carryIndex = reg.size();
                reg.Grow(reg.size()+shiftWords+!!shiftBits);
                reg[carryIndex] = carry;
        }
        else
                reg.Grow(reg.size()+shiftWords);
 
        if (shiftWords)
        {
                for (i = (int)reg.size()-1; i>=shiftWords; i--)
                        reg[i] = reg[i-shiftWords];
                for (; i>=0; i--)
                        reg[i] = 0;
        }
 
        return *this;
}
 
PolynomialMod2& PolynomialMod2::operator>>=(unsigned int n)
{
        if (!reg.size())
                return *this;
 
        int shiftWords = n / WORD_BITS;
        int shiftBits = n % WORD_BITS;
 
        size_t i;
        word u;
        word carry=0;
        word *r=reg+reg.size()-1;
 
        if (shiftBits)
        {
                i = reg.size();
                while (i--)
                {
                        u = *r;
                        *r = (u >> shiftBits) | carry;
                        carry = u << (WORD_BITS-shiftBits);
                        r--;
                }
        }
 
        if (shiftWords)
        {
                for (i=0; i<reg.size()-shiftWords; i++)
                        reg[i] = reg[i+shiftWords];
                for (; i<reg.size(); i++)
                        reg[i] = 0;
        }
 
        return *this;
}
 
PolynomialMod2 PolynomialMod2::operator<<(unsigned int n) const
{
        PolynomialMod2 result(*this);
        return result<<=n;
}
 
PolynomialMod2 PolynomialMod2::operator>>(unsigned int n) const
{
        PolynomialMod2 result(*this);
        return result>>=n;
}
 
bool PolynomialMod2::operator!() const
{
        for (unsigned i=0; i<reg.size(); i++)
                if (reg[i]) return false;
        return true;
}
 
bool PolynomialMod2::Equals(const PolynomialMod2 &rhs) const
{
        size_t i, smallerSize = STDMIN(reg.size(), rhs.reg.size());
 
        for (i=0; i<smallerSize; i++)
                if (reg[i] != rhs.reg[i]) return false;
 
        for (i=smallerSize; i<reg.size(); i++)
                if (reg[i] != 0) return false;
 
        for (i=smallerSize; i<rhs.reg.size(); i++)
                if (rhs.reg[i] != 0) return false;
 
        return true;
}
 
std::ostream& operator<<(std::ostream& out, const PolynomialMod2 &a)
{
        // Get relevant conversion specifications from ostream.
        long f = out.flags() & std::ios::basefield;     // Get base digits.
        int bits, block;
        char suffix;
        switch(f)
        {
        case std::ios::oct :
                bits = 3;
                block = 4;
                suffix = 'o';
                break;
        case std::ios::hex :
                bits = 4;
                block = 2;
                suffix = 'h';
                break;
        default :
                bits = 1;
                block = 8;
                suffix = 'b';
        }
 
        if (!a)
                return out << '0' << suffix;
 
        SecBlock<char> s(a.BitCount()/bits+1);
        unsigned i;
 
        static const char upper[]="0123456789ABCDEF";
        static const char lower[]="0123456789abcdef";
        const char* const vec = (out.flags() & std::ios::uppercase) ? upper : lower;
 
        for (i=0; i*bits < a.BitCount(); i++)
        {
                int digit=0;
                for (int j=0; j<bits; j++)
                        digit |= a[i*bits+j] << j;
                s[i]=vec[digit];
        }
 
        while (i--)
        {
                out << s[i];
                if (i && (i%block)==0)
                        out << ',';
        }
 
        return out << suffix;
}
 
PolynomialMod2 PolynomialMod2::Gcd(const PolynomialMod2 &a, const PolynomialMod2 &b)
{
        return EuclideanDomainOf<PolynomialMod2>().Gcd(a, b);
}
 
PolynomialMod2 PolynomialMod2::InverseMod(const PolynomialMod2 &modulus) const
{
        typedef EuclideanDomainOf<PolynomialMod2> Domain;
        return QuotientRing<Domain>(Domain(), modulus).MultiplicativeInverse(*this);
}
 
bool PolynomialMod2::IsIrreducible() const
{
        signed int d = Degree();
        if (d <= 0)
                return false;
 
        PolynomialMod2 t(2), u(t);
        for (int i=1; i<=d/2; i++)
        {
                u = u.Squared()%(*this);
                if (!Gcd(u+t, *this).IsUnit())
                        return false;
        }
        return true;
}
 
// ********************************************************
 
GF2NP::GF2NP(const PolynomialMod2 &modulus)
        : QuotientRing<EuclideanDomainOf<PolynomialMod2> >(EuclideanDomainOf<PolynomialMod2>(), modulus), m(modulus.Degree())
{
}
 
GF2NP::Element GF2NP::SquareRoot(const Element &a) const
{
        Element r = a;
        for (unsigned int i=1; i<m; i++)
                r = Square(r);
        return r;
}
 
GF2NP::Element GF2NP::HalfTrace(const Element &a) const
{
        CRYPTOPP_ASSERT(m%2 == 1);
        Element h = a;
        for (unsigned int i=1; i<=(m-1)/2; i++)
                h = Add(Square(Square(h)), a);
        return h;
}
 
GF2NP::Element GF2NP::SolveQuadraticEquation(const Element &a) const
{
        if (m%2 == 0)
        {
                Element z, w;
                RandomPool rng;
                do
                {
                        Element p((RandomNumberGenerator &)rng, m);
                        z = PolynomialMod2::Zero();
                        w = p;
                        for (unsigned int i=1; i<=m-1; i++)
                        {
                                w = Square(w);
                                z = Square(z);
                                Accumulate(z, Multiply(w, a));
                                Accumulate(w, p);
                        }
                } while (w.IsZero());
                return z;
        }
        else
                return HalfTrace(a);
}
 
// ********************************************************
 
GF2NT::GF2NT(unsigned int c0, unsigned int c1, unsigned int c2)
        : GF2NP(PolynomialMod2::Trinomial(c0, c1, c2))
        , t0(c0), t1(c1)
        , result((word)0, m)
{
        CRYPTOPP_ASSERT(c0 > c1 && c1 > c2 && c2==0);
}
 
const GF2NT::Element& GF2NT::MultiplicativeInverse(const Element &a) const
{
        if (t0-t1 < WORD_BITS)
                return GF2NP::MultiplicativeInverse(a);
 
        SecWordBlock T(m_modulus.reg.size() * 4);
        word *b = T;
        word *c = T+m_modulus.reg.size();
        word *f = T+2*m_modulus.reg.size();
        word *g = T+3*m_modulus.reg.size();
        size_t bcLen=1, fgLen=m_modulus.reg.size();
        unsigned int k=0;
 
        SetWords(T, 0, 3*m_modulus.reg.size());
        b[0]=1;
        CRYPTOPP_ASSERT(a.reg.size() <= m_modulus.reg.size());
        CopyWords(f, a.reg, a.reg.size());
        CopyWords(g, m_modulus.reg, m_modulus.reg.size());
 
        while (1)
        {
                word t=f[0];
                while (!t)
                {
                        ShiftWordsRightByWords(f, fgLen, 1);
                        if (c[bcLen-1])
                                bcLen++;
                        CRYPTOPP_ASSERT(bcLen <= m_modulus.reg.size());
                        ShiftWordsLeftByWords(c, bcLen, 1);
                        k+=WORD_BITS;
                        t=f[0];
                }
 
                unsigned int i=0;
                while (t%2 == 0)
                {
                        t>>=1;
                        i++;
                }
                k+=i;
 
                if (t==1 && CountWords(f, fgLen)==1)
                        break;
 
                if (i==1)
                {
                        ShiftWordsRightByBits(f, fgLen, 1);
                        t=ShiftWordsLeftByBits(c, bcLen, 1);
                }
                else
                {
                        ShiftWordsRightByBits(f, fgLen, i);
                        t=ShiftWordsLeftByBits(c, bcLen, i);
                }
                if (t)
                {
                        c[bcLen] = t;
                        bcLen++;
                        CRYPTOPP_ASSERT(bcLen <= m_modulus.reg.size());
                }
 
                if (f[fgLen-1]==0 && g[fgLen-1]==0)
                        fgLen--;
 
                if (f[fgLen-1] < g[fgLen-1])
                {
                        std::swap(f, g);
                        std::swap(b, c);
                }
 
                XorWords(f, g, fgLen);
                XorWords(b, c, bcLen);
        }
 
        while (k >= WORD_BITS)
        {
                word temp = b[0];
                // right shift b
                for (unsigned i=0; i+1<BitsToWords(m); i++)
                        b[i] = b[i+1];
                b[BitsToWords(m)-1] = 0;
 
                if (t1 < WORD_BITS)
                        for (unsigned int j=0; j<WORD_BITS-t1; j++)
                        {
                                // Coverity finding on shift amount of 'word x << (t1+j)'.
                                //   temp ^= ((temp >> j) & 1) << (t1 + j);
                                const unsigned int shift = t1 + j;
                                CRYPTOPP_ASSERT(shift < WORD_BITS);
                                temp ^= (shift < WORD_BITS) ? (((temp >> j) & 1) << shift) : 0;
                        }
                else
                        b[t1/WORD_BITS-1] ^= temp << t1%WORD_BITS;
 
                if (t1 % WORD_BITS)
                        b[t1/WORD_BITS] ^= temp >> (WORD_BITS - t1%WORD_BITS);
 
                if (t0%WORD_BITS)
                {
                        b[t0/WORD_BITS-1] ^= temp << t0%WORD_BITS;
                        b[t0/WORD_BITS] ^= temp >> (WORD_BITS - t0%WORD_BITS);
                }
                else
                        b[t0/WORD_BITS-1] ^= temp;
 
                k -= WORD_BITS;
        }
 
        if (k)
        {
                word temp = b[0] << (WORD_BITS - k);
                ShiftWordsRightByBits(b, BitsToWords(m), k);
 
                if (t1 < WORD_BITS)
                {
                        for (unsigned int j=0; j<WORD_BITS-t1; j++)
                        {
                                // Coverity finding on shift amount of 'word x << (t1+j)'.
                                //   temp ^= ((temp >> j) & 1) << (t1 + j);
                                const unsigned int shift = t1 + j;
                                CRYPTOPP_ASSERT(shift < WORD_BITS);
                                temp ^= (shift < WORD_BITS) ? (((temp >> j) & 1) << shift) : 0;
                        }
                }
                else
                {
                        b[t1/WORD_BITS-1] ^= temp << t1%WORD_BITS;
                }
 
                if (t1 % WORD_BITS)
                        b[t1/WORD_BITS] ^= temp >> (WORD_BITS - t1%WORD_BITS);
 
                if (t0%WORD_BITS)
                {
                        b[t0/WORD_BITS-1] ^= temp << t0%WORD_BITS;
                        b[t0/WORD_BITS] ^= temp >> (WORD_BITS - t0%WORD_BITS);
                }
                else
                        b[t0/WORD_BITS-1] ^= temp;
        }
 
        CopyWords(result.reg.begin(), b, result.reg.size());
        return result;
}
 
const GF2NT::Element& GF2NT::Multiply(const Element &a, const Element &b) const
{
        size_t aSize = STDMIN(a.reg.size(), result.reg.size());
        Element r((word)0, m);
 
        for (int i=m-1; i>=0; i--)
        {
                if (r[m-1])
                {
                        ShiftWordsLeftByBits(r.reg.begin(), r.reg.size(), 1);
                        XorWords(r.reg.begin(), m_modulus.reg, r.reg.size());
                }
                else
                        ShiftWordsLeftByBits(r.reg.begin(), r.reg.size(), 1);
 
                if (b[i])
                        XorWords(r.reg.begin(), a.reg, aSize);
        }
 
        if (m%WORD_BITS)
                r.reg.begin()[r.reg.size()-1] = (word)Crop(r.reg[r.reg.size()-1], m%WORD_BITS);
 
        CopyWords(result.reg.begin(), r.reg.begin(), result.reg.size());
        return result;
}
 
const GF2NT::Element& GF2NT::Reduced(const Element &a) const
{
        if (t0-t1 < WORD_BITS)
                return m_domain.Mod(a, m_modulus);
 
        SecWordBlock b(a.reg);
 
        size_t i;
        for (i=b.size()-1; i>=BitsToWords(t0); i--)
        {
                word temp = b[i];
 
                if (t0%WORD_BITS)
                {
                        b[i-t0/WORD_BITS] ^= temp >> t0%WORD_BITS;
                        b[i-t0/WORD_BITS-1] ^= temp << (WORD_BITS - t0%WORD_BITS);
                }
                else
                        b[i-t0/WORD_BITS] ^= temp;
 
                if ((t0-t1)%WORD_BITS)
                {
                        b[i-(t0-t1)/WORD_BITS] ^= temp >> (t0-t1)%WORD_BITS;
                        b[i-(t0-t1)/WORD_BITS-1] ^= temp << (WORD_BITS - (t0-t1)%WORD_BITS);
                }
                else
                        b[i-(t0-t1)/WORD_BITS] ^= temp;
        }
 
        if (i==BitsToWords(t0)-1 && t0%WORD_BITS)
        {
                word mask = ((word)1<<(t0%WORD_BITS))-1;
                word temp = b[i] & ~mask;
                b[i] &= mask;
 
                b[i-t0/WORD_BITS] ^= temp >> t0%WORD_BITS;
 
                if ((t0-t1)%WORD_BITS)
                {
                        b[i-(t0-t1)/WORD_BITS] ^= temp >> (t0-t1)%WORD_BITS;
                        if ((t0-t1)%WORD_BITS > t0%WORD_BITS)
                                b[i-(t0-t1)/WORD_BITS-1] ^= temp << (WORD_BITS - (t0-t1)%WORD_BITS);
                        else
                                CRYPTOPP_ASSERT(temp << (WORD_BITS - (t0-t1)%WORD_BITS) == 0);
                }
                else
                        b[i-(t0-t1)/WORD_BITS] ^= temp;
        }
 
        SetWords(result.reg.begin(), 0, result.reg.size());
        CopyWords(result.reg.begin(), b, STDMIN(b.size(), result.reg.size()));
        return result;
}
 
void GF2NP::DEREncodeElement(BufferedTransformation &out, const Element &a) const
{
        a.DEREncodeAsOctetString(out, MaxElementByteLength());
}
 
void GF2NP::BERDecodeElement(BufferedTransformation &in, Element &a) const
{
        a.BERDecodeAsOctetString(in, MaxElementByteLength());
}
 
void GF2NT::DEREncode(BufferedTransformation &bt) const
{
        DERSequenceEncoder seq(bt);
                ASN1::characteristic_two_field().DEREncode(seq);
                DERSequenceEncoder parameters(seq);
                        DEREncodeUnsigned(parameters, m);
                        ASN1::tpBasis().DEREncode(parameters);
                        DEREncodeUnsigned(parameters, t1);
                parameters.MessageEnd();
        seq.MessageEnd();
}
 
void GF2NPP::DEREncode(BufferedTransformation &bt) const
{
        DERSequenceEncoder seq(bt);
                ASN1::characteristic_two_field().DEREncode(seq);
                DERSequenceEncoder parameters(seq);
                        DEREncodeUnsigned(parameters, m);
                        ASN1::ppBasis().DEREncode(parameters);
                        DERSequenceEncoder pentanomial(parameters);
                                DEREncodeUnsigned(pentanomial, t3);
                                DEREncodeUnsigned(pentanomial, t2);
                                DEREncodeUnsigned(pentanomial, t1);
                        pentanomial.MessageEnd();
                parameters.MessageEnd();
        seq.MessageEnd();
}
 
GF2NP * BERDecodeGF2NP(BufferedTransformation &bt)
{
        member_ptr<GF2NP> result;
 
        BERSequenceDecoder seq(bt);
                if (OID(seq) != ASN1::characteristic_two_field())
                        BERDecodeError();
                BERSequenceDecoder parameters(seq);
                        unsigned int m;
                        BERDecodeUnsigned(parameters, m);
                        OID oid(parameters);
                        if (oid == ASN1::tpBasis())
                        {
                                unsigned int t1;
                                BERDecodeUnsigned(parameters, t1);
                                result.reset(new GF2NT(m, t1, 0));
                        }
                        else if (oid == ASN1::ppBasis())
                        {
                                unsigned int t1, t2, t3;
                                BERSequenceDecoder pentanomial(parameters);
                                BERDecodeUnsigned(pentanomial, t3);
                                BERDecodeUnsigned(pentanomial, t2);
                                BERDecodeUnsigned(pentanomial, t1);
                                pentanomial.MessageEnd();
                                result.reset(new GF2NPP(m, t3, t2, t1, 0));
                        }
                        else
                        {
                                BERDecodeError();
                                return NULLPTR;
                        }
                parameters.MessageEnd();
        seq.MessageEnd();
 
        return result.release();
}
 
// ********************************************************
 
GF2NT233::GF2NT233(unsigned int c0, unsigned int c1, unsigned int c2)
        : GF2NT(c0, c1, c2)
{
        CRYPTOPP_ASSERT(c0 > c1 && c1 > c2 && c2==0);
}
 
const GF2NT::Element& GF2NT233::Multiply(const Element &a, const Element &b) const
{
#if (CRYPTOPP_CLMUL_AVAILABLE)
        if (HasCLMUL())
        {
                CRYPTOPP_ASSERT(a.reg.size()*WORD_BITS == 256);
                CRYPTOPP_ASSERT(b.reg.size()*WORD_BITS == 256);
                CRYPTOPP_ASSERT(result.reg.size()*WORD_BITS == 256);
 
                const word* pA = a.reg.begin();
                const word* pB = b.reg.begin();
                word* pR = result.reg.begin();
 
                GF2NT_233_Multiply_Reduce_CLMUL(pA, pB, pR);
                return result;
        }
        else
#elif (CRYPTOPP_ARM_PMULL_AVAILABLE)
        if (HasPMULL())
        {
                CRYPTOPP_ASSERT(a.reg.size()*WORD_BITS == 256);
                CRYPTOPP_ASSERT(b.reg.size()*WORD_BITS == 256);
                CRYPTOPP_ASSERT(result.reg.size()*WORD_BITS == 256);
 
                const word* pA = a.reg.begin();
                const word* pB = b.reg.begin();
                word* pR = result.reg.begin();
 
                GF2NT_233_Multiply_Reduce_ARMv8(pA, pB, pR);
                return result;
        }
        else
#elif (CRYPTOPP_POWER8_VMULL_AVAILABLE) && 0
        if (HasPMULL())
        {
                CRYPTOPP_ASSERT(a.reg.size()*WORD_BITS == 256);
                CRYPTOPP_ASSERT(b.reg.size()*WORD_BITS == 256);
                CRYPTOPP_ASSERT(result.reg.size()*WORD_BITS == 256);
 
                const word* pA = a.reg.begin();
                const word* pB = b.reg.begin();
                word* pR = result.reg.begin();
 
                GF2NT_233_Multiply_Reduce_POWER8(pA, pB, pR);
                return result;
        }
        else
#endif
 
        return GF2NT::Multiply(a, b);
}
 
const GF2NT::Element& GF2NT233::Square(const Element &a) const
{
#if (CRYPTOPP_CLMUL_AVAILABLE)
        if (HasCLMUL())
        {
                CRYPTOPP_ASSERT(a.reg.size()*WORD_BITS == 256);
                CRYPTOPP_ASSERT(result.reg.size()*WORD_BITS == 256);
 
                const word* pA = a.reg.begin();
                word* pR = result.reg.begin();
 
                GF2NT_233_Square_Reduce_CLMUL(pA, pR);
                return result;
        }
        else
#elif (CRYPTOPP_ARM_PMULL_AVAILABLE)
        if (HasPMULL())
        {
                CRYPTOPP_ASSERT(a.reg.size()*WORD_BITS == 256);
                CRYPTOPP_ASSERT(result.reg.size()*WORD_BITS == 256);
 
                const word* pA = a.reg.begin();
                word* pR = result.reg.begin();
 
                GF2NT_233_Square_Reduce_ARMv8(pA, pR);
                return result;
        }
        else
#elif (CRYPTOPP_POWER8_VMULL_AVAILABLE) && 0
        if (HasPMULL())
        {
                CRYPTOPP_ASSERT(a.reg.size()*WORD_BITS == 256);
                CRYPTOPP_ASSERT(result.reg.size()*WORD_BITS == 256);
 
                const word* pA = a.reg.begin();
                word* pR = result.reg.begin();
 
                GF2NT_233_Square_Reduce_POWER8(pA, pR);
                return result;
        }
        else
#endif
 
        return GF2NT::Square(a);
}
 
NAMESPACE_END
 
#endif