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Diffstat (limited to 'plugins/CryptoPP/crypto/algebra.cpp')
| -rw-r--r-- | plugins/CryptoPP/crypto/algebra.cpp | 340 |
1 files changed, 340 insertions, 0 deletions
diff --git a/plugins/CryptoPP/crypto/algebra.cpp b/plugins/CryptoPP/crypto/algebra.cpp new file mode 100644 index 0000000000..5d7e2134fc --- /dev/null +++ b/plugins/CryptoPP/crypto/algebra.cpp @@ -0,0 +1,340 @@ +// algebra.cpp - 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 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 Add(a1, Inverse(b));
+}
+
+template <class T> T& AbstractGroup<T>::Accumulate(Element &a, const Element &b) const
+{
+ return a = Add(a, b);
+}
+
+template <class T> T& AbstractGroup<T>::Reduce(Element &a, const Element &b) const
+{
+ return a = Subtract(a, b);
+}
+
+template <class T> const T& AbstractRing<T>::Square(const Element &a) const
+{
+ return 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 Multiply(a1, MultiplicativeInverse(b));
+}
+
+template <class T> const T& AbstractEuclideanDomain<T>::Mod(const Element &a, const Element &b) const
+{
+ Element q;
+ 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 (!Equal(g[i1], this->Identity()))
+ {
+ g[i2] = 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 (!Equal(g[i1], 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;
+ 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 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] = Add(x,y);
+ else
+ {
+ powerTable[2] = Double(x);
+ powerTable[2*tableSize] = 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 = Double(result);
+ if (power1 || power2)
+ Accumulate(result, powerTable[(power2<<w) + power1]);
+ }
+ while (squaresAfter--)
+ result = 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), fastNegate(fastNegate), 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; i<expCount; i++)
+ {
+ assert(expBegin->NotNegative());
+ exponents.push_back(WindowSlider(*expBegin++, InversionIsFast(), 0));
+ exponents[i].FindNextWindow();
+ buckets[i].resize(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
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