You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
342 lines
9.4 KiB
342 lines
9.4 KiB
![]()
4 years ago
|
// algebra.cpp - originally written and placed in the public domain by Wei Dai
|
||
|
|
||
|
#include "pch.h"
|
||
|
|
||
|
#ifndef CRYPTOPP_ALGEBRA_CPP // SunCC workaround: compiler could cause this file to be included twice
|
||
|
#define CRYPTOPP_ALGEBRA_CPP
|
||
|
|
||
|
#include "algebra.h"
|
||
|
#include "integer.h"
|
||
|
|
||
|
#include <vector>
|
||
|
|
||
|
NAMESPACE_BEGIN(CryptoPP)
|
||
|
|
||
|
template <class T> const T& AbstractGroup<T>::Double(const Element &a) const
|
||
|
{
|
||
|
return this->Add(a, a);
|
||
|
}
|
||
|
|
||
|
template <class T> const T& AbstractGroup<T>::Subtract(const Element &a, const Element &b) const
|
||
|
{
|
||
|
// make copy of a in case Inverse() overwrites it
|
||
|
Element a1(a);
|
||
|
return this->Add(a1, Inverse(b));
|
||
|
}
|
||
|
|
||
|
template <class T> T& AbstractGroup<T>::Accumulate(Element &a, const Element &b) const
|
||
|
{
|
||
|
return a = this->Add(a, b);
|
||
|
}
|
||
|
|
||
|
template <class T> T& AbstractGroup<T>::Reduce(Element &a, const Element &b) const
|
||
|
{
|
||
|
return a = this->Subtract(a, b);
|
||
|
}
|
||
|
|
||
|
template <class T> const T& AbstractRing<T>::Square(const Element &a) const
|
||
|
{
|
||
|
return this->Multiply(a, a);
|
||
|
}
|
||
|
|
||
|
template <class T> const T& AbstractRing<T>::Divide(const Element &a, const Element &b) const
|
||
|
{
|
||
|
// make copy of a in case MultiplicativeInverse() overwrites it
|
||
|
Element a1(a);
|
||
|
return this->Multiply(a1, this->MultiplicativeInverse(b));
|
||
|
}
|
||
|
|
||
|
template <class T> const T& AbstractEuclideanDomain<T>::Mod(const Element &a, const Element &b) const
|
||
|
{
|
||
|
Element q;
|
||
|
this->DivisionAlgorithm(result, q, a, b);
|
||
|
return result;
|
||
|
}
|
||
|
|
||
|
template <class T> const T& AbstractEuclideanDomain<T>::Gcd(const Element &a, const Element &b) const
|
||
|
{
|
||
|
Element g[3]={b, a};
|
||
|
unsigned int i0=0, i1=1, i2=2;
|
||
|
|
||
|
while (!this->Equal(g[i1], this->Identity()))
|
||
|
{
|
||
|
g[i2] = this->Mod(g[i0], g[i1]);
|
||
|
unsigned int t = i0; i0 = i1; i1 = i2; i2 = t;
|
||
|
}
|
||
|
|
||
|
return result = g[i0];
|
||
|
}
|
||
|
|
||
|
template <class T> const typename QuotientRing<T>::Element& QuotientRing<T>::MultiplicativeInverse(const Element &a) const
|
||
|
{
|
||
|
Element g[3]={m_modulus, a};
|
||
|
Element v[3]={m_domain.Identity(), m_domain.MultiplicativeIdentity()};
|
||
|
Element y;
|
||
|
unsigned int i0=0, i1=1, i2=2;
|
||
|
|
||
|
while (!this->Equal(g[i1], this->Identity()))
|
||
|
{
|
||
|
// y = g[i0] / g[i1];
|
||
|
// g[i2] = g[i0] % g[i1];
|
||
|
m_domain.DivisionAlgorithm(g[i2], y, g[i0], g[i1]);
|
||
|
// v[i2] = v[i0] - (v[i1] * y);
|
||
|
v[i2] = m_domain.Subtract(v[i0], m_domain.Multiply(v[i1], y));
|
||
|
unsigned int t = i0; i0 = i1; i1 = i2; i2 = t;
|
||
|
}
|
||
|
|
||
|
return m_domain.IsUnit(g[i0]) ? m_domain.Divide(v[i0], g[i0]) : m_domain.Identity();
|
||
|
}
|
||
|
|
||
|
template <class T> T AbstractGroup<T>::ScalarMultiply(const Element &base, const Integer &exponent) const
|
||
|
{
|
||
|
Element result;
|
||
|
this->SimultaneousMultiply(&result, base, &exponent, 1);
|
||
|
return result;
|
||
|
}
|
||
|
|
||
|
template <class T> T AbstractGroup<T>::CascadeScalarMultiply(const Element &x, const Integer &e1, const Element &y, const Integer &e2) const
|
||
|
{
|
||
|
const unsigned expLen = STDMAX(e1.BitCount(), e2.BitCount());
|
||
|
if (expLen==0)
|
||
|
return this->Identity();
|
||
|
|
||
|
const unsigned w = (expLen <= 46 ? 1 : (expLen <= 260 ? 2 : 3));
|
||
|
const unsigned tableSize = 1<<w;
|
||
|
std::vector<Element> powerTable(tableSize << w);
|
||
|
|
||
|
powerTable[1] = x;
|
||
|
powerTable[tableSize] = y;
|
||
|
if (w==1)
|
||
|
powerTable[3] = this->Add(x,y);
|
||
|
else
|
||
|
{
|
||
|
powerTable[2] = this->Double(x);
|
||
|
powerTable[2*tableSize] = this->Double(y);
|
||
|
|
||
|
unsigned i, j;
|
||
|
|
||
|
for (i=3; i<tableSize; i+=2)
|
||
|
powerTable[i] = Add(powerTable[i-2], powerTable[2]);
|
||
|
for (i=1; i<tableSize; i+=2)
|
||
|
for (j=i+tableSize; j<(tableSize<<w); j+=tableSize)
|
||
|
powerTable[j] = Add(powerTable[j-tableSize], y);
|
||
|
|
||
|
for (i=3*tableSize; i<(tableSize<<w); i+=2*tableSize)
|
||
|
powerTable[i] = Add(powerTable[i-2*tableSize], powerTable[2*tableSize]);
|
||
|
for (i=tableSize; i<(tableSize<<w); i+=2*tableSize)
|
||
|
for (j=i+2; j<i+tableSize; j+=2)
|
||
|
powerTable[j] = Add(powerTable[j-1], x);
|
||
|
}
|
||
|
|
||
|
Element result;
|
||
|
unsigned power1 = 0, power2 = 0, prevPosition = expLen-1;
|
||
|
bool firstTime = true;
|
||
|
|
||
|
for (int i = expLen-1; i>=0; i--)
|
||
|
{
|
||
|
power1 = 2*power1 + e1.GetBit(i);
|
||
|
power2 = 2*power2 + e2.GetBit(i);
|
||
|
|
||
|
if (i==0 || 2*power1 >= tableSize || 2*power2 >= tableSize)
|
||
|
{
|
||
|
unsigned squaresBefore = prevPosition-i;
|
||
|
unsigned squaresAfter = 0;
|
||
|
prevPosition = i;
|
||
|
while ((power1 || power2) && power1%2 == 0 && power2%2==0)
|
||
|
{
|
||
|
power1 /= 2;
|
||
|
power2 /= 2;
|
||
|
squaresBefore--;
|
||
|
squaresAfter++;
|
||
|
}
|
||
|
if (firstTime)
|
||
|
{
|
||
|
result = powerTable[(power2<<w) + power1];
|
||
|
firstTime = false;
|
||
|
}
|
||
|
else
|
||
|
{
|
||
|
while (squaresBefore--)
|
||
|
result = this->Double(result);
|
||
|
if (power1 || power2)
|
||
|
Accumulate(result, powerTable[(power2<<w) + power1]);
|
||
|
}
|
||
|
while (squaresAfter--)
|
||
|
result = this->Double(result);
|
||
|
power1 = power2 = 0;
|
||
|
}
|
||
|
}
|
||
|
return result;
|
||
|
}
|
||
|
|
||
|
template <class Element, class Iterator> Element GeneralCascadeMultiplication(const AbstractGroup<Element> &group, Iterator begin, Iterator end)
|
||
|
{
|
||
|
if (end-begin == 1)
|
||
|
return group.ScalarMultiply(begin->base, begin->exponent);
|
||
|
else if (end-begin == 2)
|
||
|
return group.CascadeScalarMultiply(begin->base, begin->exponent, (begin+1)->base, (begin+1)->exponent);
|
||
|
else
|
||
|
{
|
||
|
Integer q, t;
|
||
|
Iterator last = end;
|
||
|
--last;
|
||
|
|
||
|
std::make_heap(begin, end);
|
||
|
std::pop_heap(begin, end);
|
||
|
|
||
|
while (!!begin->exponent)
|
||
|
{
|
||
|
// last->exponent is largest exponent, begin->exponent is next largest
|
||
|
t = last->exponent;
|
||
|
Integer::Divide(last->exponent, q, t, begin->exponent);
|
||
|
|
||
|
if (q == Integer::One())
|
||
|
group.Accumulate(begin->base, last->base); // avoid overhead of ScalarMultiply()
|
||
|
else
|
||
|
group.Accumulate(begin->base, group.ScalarMultiply(last->base, q));
|
||
|
|
||
|
std::push_heap(begin, end);
|
||
|
std::pop_heap(begin, end);
|
||
|
}
|
||
|
|
||
|
return group.ScalarMultiply(last->base, last->exponent);
|
||
|
}
|
||
|
}
|
||
|
|
||
|
struct WindowSlider
|
||
|
{
|
||
|
WindowSlider(const Integer &expIn, bool fastNegate, unsigned int windowSizeIn=0)
|
||
|
: exp(expIn), windowModulus(Integer::One()), windowSize(windowSizeIn), windowBegin(0), expWindow(0)
|
||
|
, fastNegate(fastNegate), negateNext(false), firstTime(true), finished(false)
|
||
|
{
|
||
|
if (windowSize == 0)
|
||
|
{
|
||
|
unsigned int expLen = exp.BitCount();
|
||
|
windowSize = expLen <= 17 ? 1 : (expLen <= 24 ? 2 : (expLen <= 70 ? 3 : (expLen <= 197 ? 4 : (expLen <= 539 ? 5 : (expLen <= 1434 ? 6 : 7)))));
|
||
|
}
|
||
|
windowModulus <<= windowSize;
|
||
|
}
|
||
|
|
||
|
void FindNextWindow()
|
||
|
{
|
||
|
unsigned int expLen = exp.WordCount() * WORD_BITS;
|
||
|
unsigned int skipCount = firstTime ? 0 : windowSize;
|
||
|
firstTime = false;
|
||
|
while (!exp.GetBit(skipCount))
|
||
|
{
|
||
|
if (skipCount >= expLen)
|
||
|
{
|
||
|
finished = true;
|
||
|
return;
|
||
|
}
|
||
|
skipCount++;
|
||
|
}
|
||
|
|
||
|
exp >>= skipCount;
|
||
|
windowBegin += skipCount;
|
||
|
expWindow = word32(exp % (word(1) << windowSize));
|
||
|
|
||
|
if (fastNegate && exp.GetBit(windowSize))
|
||
|
{
|
||
|
negateNext = true;
|
||
|
expWindow = (word32(1) << windowSize) - expWindow;
|
||
|
exp += windowModulus;
|
||
|
}
|
||
|
else
|
||
|
negateNext = false;
|
||
|
}
|
||
|
|
||
|
Integer exp, windowModulus;
|
||
|
unsigned int windowSize, windowBegin;
|
||
|
word32 expWindow;
|
||
|
bool fastNegate, negateNext, firstTime, finished;
|
||
|
};
|
||
|
|
||
|
template <class T>
|
||
|
void AbstractGroup<T>::SimultaneousMultiply(T *results, const T &base, const Integer *expBegin, unsigned int expCount) const
|
||
|
{
|
||
|
std::vector<std::vector<Element> > buckets(expCount);
|
||
|
std::vector<WindowSlider> exponents;
|
||
|
exponents.reserve(expCount);
|
||
|
unsigned int i;
|
||
|
|
||
|
for (i=0; expBegin && i<expCount; i++)
|
||
|
{
|
||
|
CRYPTOPP_ASSERT(expBegin->NotNegative());
|
||
|
exponents.push_back(WindowSlider(*expBegin++, InversionIsFast(), 0));
|
||
|
exponents[i].FindNextWindow();
|
||
|
buckets[i].resize(((size_t) 1) << (exponents[i].windowSize-1), Identity());
|
||
|
}
|
||
|
|
||
|
unsigned int expBitPosition = 0;
|
||
|
Element g = base;
|
||
|
bool notDone = true;
|
||
|
|
||
|
while (notDone)
|
||
|
{
|
||
|
notDone = false;
|
||
|
for (i=0; i<expCount; i++)
|
||
|
{
|
||
|
if (!exponents[i].finished && expBitPosition == exponents[i].windowBegin)
|
||
|
{
|
||
|
Element &bucket = buckets[i][exponents[i].expWindow/2];
|
||
|
if (exponents[i].negateNext)
|
||
|
Accumulate(bucket, Inverse(g));
|
||
|
else
|
||
|
Accumulate(bucket, g);
|
||
|
exponents[i].FindNextWindow();
|
||
|
}
|
||
|
notDone = notDone || !exponents[i].finished;
|
||
|
}
|
||
|
|
||
|
if (notDone)
|
||
|
{
|
||
|
g = Double(g);
|
||
|
expBitPosition++;
|
||
|
}
|
||
|
}
|
||
|
|
||
|
for (i=0; i<expCount; i++)
|
||
|
{
|
||
|
Element &r = *results++;
|
||
|
r = buckets[i][buckets[i].size()-1];
|
||
|
if (buckets[i].size() > 1)
|
||
|
{
|
||
|
for (int j = (int)buckets[i].size()-2; j >= 1; j--)
|
||
|
{
|
||
|
Accumulate(buckets[i][j], buckets[i][j+1]);
|
||
|
Accumulate(r, buckets[i][j]);
|
||
|
}
|
||
|
Accumulate(buckets[i][0], buckets[i][1]);
|
||
|
r = Add(Double(r), buckets[i][0]);
|
||
|
}
|
||
|
}
|
||
|
}
|
||
|
|
||
|
template <class T> T AbstractRing<T>::Exponentiate(const Element &base, const Integer &exponent) const
|
||
|
{
|
||
|
Element result;
|
||
|
SimultaneousExponentiate(&result, base, &exponent, 1);
|
||
|
return result;
|
||
|
}
|
||
|
|
||
|
template <class T> T AbstractRing<T>::CascadeExponentiate(const Element &x, const Integer &e1, const Element &y, const Integer &e2) const
|
||
|
{
|
||
|
return MultiplicativeGroup().AbstractGroup<T>::CascadeScalarMultiply(x, e1, y, e2);
|
||
|
}
|
||
|
|
||
|
template <class Element, class Iterator> Element GeneralCascadeExponentiation(const AbstractRing<Element> &ring, Iterator begin, Iterator end)
|
||
|
{
|
||
|
return GeneralCascadeMultiplication<Element>(ring.MultiplicativeGroup(), begin, end);
|
||
|
}
|
||
|
|
||
|
template <class T>
|
||
|
void AbstractRing<T>::SimultaneousExponentiate(T *results, const T &base, const Integer *exponents, unsigned int expCount) const
|
||
|
{
|
||
|
MultiplicativeGroup().AbstractGroup<T>::SimultaneousMultiply(results, base, exponents, expCount);
|
||
|
}
|
||
|
|
||
|
NAMESPACE_END
|
||
|
|
||
|
#endif
|