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