883 lines
18 KiB
C++
883 lines
18 KiB
C++
// gf2n.cpp - written and placed in the public domain by Wei Dai
|
|
|
|
#include "pch.h"
|
|
|
|
#ifndef CRYPTOPP_IMPORTS
|
|
|
|
#include "gf2n.h"
|
|
#include "algebra.h"
|
|
#include "words.h"
|
|
#include "randpool.h"
|
|
#include "asn.h"
|
|
#include "oids.h"
|
|
|
|
#include <iostream>
|
|
|
|
NAMESPACE_BEGIN(CryptoPP)
|
|
|
|
PolynomialMod2::PolynomialMod2()
|
|
{
|
|
}
|
|
|
|
PolynomialMod2::PolynomialMod2(word value, size_t bitLength)
|
|
: reg(BitsToWords(bitLength))
|
|
{
|
|
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()
|
|
{
|
|
return Singleton<PolynomialMod2>().Ref();
|
|
}
|
|
|
|
const PolynomialMod2 &PolynomialMod2::One()
|
|
{
|
|
return Singleton<PolynomialMod2, NewPolynomialMod2<1> >().Ref();
|
|
}
|
|
|
|
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)
|
|
{
|
|
reg.CleanNew(BytesToWords(inputLen));
|
|
|
|
for (size_t i=inputLen; i > 0; i--)
|
|
{
|
|
byte b;
|
|
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 "ient,
|
|
const PolynomialMod2 ÷nd, 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 (!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;
|
|
}
|
|
|
|
int shiftWords = n / WORD_BITS;
|
|
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)
|
|
{
|
|
reg.Grow(reg.size()+shiftWords+1);
|
|
reg[reg.size()-1] = 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* 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
|
|
{
|
|
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 t0, unsigned int t1, unsigned int t2)
|
|
: GF2NP(PolynomialMod2::Trinomial(t0, t1, t2))
|
|
, t0(t0), t1(t1)
|
|
, result((word)0, m)
|
|
{
|
|
assert(t0 > t1 && t1 > t2 && t2==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;
|
|
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++;
|
|
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++;
|
|
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++)
|
|
temp ^= ((temp >> j) & 1) << (t1 + j);
|
|
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++)
|
|
temp ^= ((temp >> j) & 1) << (t1 + j);
|
|
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
|
|
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)
|
|
{
|
|
// VC60 workaround: auto_ptr lacks reset()
|
|
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 NULL;
|
|
}
|
|
parameters.MessageEnd();
|
|
seq.MessageEnd();
|
|
|
|
return result.release();
|
|
}
|
|
|
|
NAMESPACE_END
|
|
|
|
#endif
|