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Diffstat (limited to 'CryptoPP/polynomi.cpp')
| -rw-r--r-- | CryptoPP/polynomi.cpp | 577 |
1 files changed, 0 insertions, 577 deletions
diff --git a/CryptoPP/polynomi.cpp b/CryptoPP/polynomi.cpp deleted file mode 100644 index 734cae926..000000000 --- a/CryptoPP/polynomi.cpp +++ /dev/null @@ -1,577 +0,0 @@ -// polynomi.cpp - written and placed in the public domain by Wei Dai - -// Part of the code for polynomial evaluation and interpolation -// originally came from Hal Finney's public domain secsplit.c. - -#include "pch.h" -#include "polynomi.h" -#include "secblock.h" - -#include <sstream> -#include <iostream> - -NAMESPACE_BEGIN(CryptoPP) - -template <class T> -void PolynomialOver<T>::Randomize(RandomNumberGenerator &rng, const RandomizationParameter ¶meter, const Ring &ring) -{ - m_coefficients.resize(parameter.m_coefficientCount); - for (unsigned int i=0; i<m_coefficients.size(); ++i) - m_coefficients[i] = ring.RandomElement(rng, parameter.m_coefficientParameter); -} - -template <class T> -void PolynomialOver<T>::FromStr(const char *str, const Ring &ring) -{ - std::istringstream in((char *)str); - bool positive = true; - CoefficientType coef; - unsigned int power; - - while (in) - { - std::ws(in); - if (in.peek() == 'x') - coef = ring.MultiplicativeIdentity(); - else - in >> coef; - - std::ws(in); - if (in.peek() == 'x') - { - in.get(); - std::ws(in); - if (in.peek() == '^') - { - in.get(); - in >> power; - } - else - power = 1; - } - else - power = 0; - - if (!positive) - coef = ring.Inverse(coef); - - SetCoefficient(power, coef, ring); - - std::ws(in); - switch (in.get()) - { - case '+': - positive = true; - break; - case '-': - positive = false; - break; - default: - return; // something's wrong with the input string - } - } -} - -template <class T> -unsigned int PolynomialOver<T>::CoefficientCount(const Ring &ring) const -{ - unsigned count = m_coefficients.size(); - while (count && ring.Equal(m_coefficients[count-1], ring.Identity())) - count--; - const_cast<std::vector<CoefficientType> &>(m_coefficients).resize(count); - return count; -} - -template <class T> -typename PolynomialOver<T>::CoefficientType PolynomialOver<T>::GetCoefficient(unsigned int i, const Ring &ring) const -{ - return (i < m_coefficients.size()) ? m_coefficients[i] : ring.Identity(); -} - -template <class T> -PolynomialOver<T>& PolynomialOver<T>::operator=(const PolynomialOver<T>& t) -{ - if (this != &t) - { - m_coefficients.resize(t.m_coefficients.size()); - for (unsigned int i=0; i<m_coefficients.size(); i++) - m_coefficients[i] = t.m_coefficients[i]; - } - return *this; -} - -template <class T> -PolynomialOver<T>& PolynomialOver<T>::Accumulate(const PolynomialOver<T>& t, const Ring &ring) -{ - unsigned int count = t.CoefficientCount(ring); - - if (count > CoefficientCount(ring)) - m_coefficients.resize(count, ring.Identity()); - - for (unsigned int i=0; i<count; i++) - ring.Accumulate(m_coefficients[i], t.GetCoefficient(i, ring)); - - return *this; -} - -template <class T> -PolynomialOver<T>& PolynomialOver<T>::Reduce(const PolynomialOver<T>& t, const Ring &ring) -{ - unsigned int count = t.CoefficientCount(ring); - - if (count > CoefficientCount(ring)) - m_coefficients.resize(count, ring.Identity()); - - for (unsigned int i=0; i<count; i++) - ring.Reduce(m_coefficients[i], t.GetCoefficient(i, ring)); - - return *this; -} - -template <class T> -typename PolynomialOver<T>::CoefficientType PolynomialOver<T>::EvaluateAt(const CoefficientType &x, const Ring &ring) const -{ - int degree = Degree(ring); - - if (degree < 0) - return ring.Identity(); - - CoefficientType result = m_coefficients[degree]; - for (int j=degree-1; j>=0; j--) - { - result = ring.Multiply(result, x); - ring.Accumulate(result, m_coefficients[j]); - } - return result; -} - -template <class T> -PolynomialOver<T>& PolynomialOver<T>::ShiftLeft(unsigned int n, const Ring &ring) -{ - unsigned int i = CoefficientCount(ring) + n; - m_coefficients.resize(i, ring.Identity()); - while (i > n) - { - i--; - m_coefficients[i] = m_coefficients[i-n]; - } - while (i) - { - i--; - m_coefficients[i] = ring.Identity(); - } - return *this; -} - -template <class T> -PolynomialOver<T>& PolynomialOver<T>::ShiftRight(unsigned int n, const Ring &ring) -{ - unsigned int count = CoefficientCount(ring); - if (count > n) - { - for (unsigned int i=0; i<count-n; i++) - m_coefficients[i] = m_coefficients[i+n]; - m_coefficients.resize(count-n, ring.Identity()); - } - else - m_coefficients.resize(0, ring.Identity()); - return *this; -} - -template <class T> -void PolynomialOver<T>::SetCoefficient(unsigned int i, const CoefficientType &value, const Ring &ring) -{ - if (i >= m_coefficients.size()) - m_coefficients.resize(i+1, ring.Identity()); - m_coefficients[i] = value; -} - -template <class T> -void PolynomialOver<T>::Negate(const Ring &ring) -{ - unsigned int count = CoefficientCount(ring); - for (unsigned int i=0; i<count; i++) - m_coefficients[i] = ring.Inverse(m_coefficients[i]); -} - -template <class T> -void PolynomialOver<T>::swap(PolynomialOver<T> &t) -{ - m_coefficients.swap(t.m_coefficients); -} - -template <class T> -bool PolynomialOver<T>::Equals(const PolynomialOver<T>& t, const Ring &ring) const -{ - unsigned int count = CoefficientCount(ring); - - if (count != t.CoefficientCount(ring)) - return false; - - for (unsigned int i=0; i<count; i++) - if (!ring.Equal(m_coefficients[i], t.m_coefficients[i])) - return false; - - return true; -} - -template <class T> -PolynomialOver<T> PolynomialOver<T>::Plus(const PolynomialOver<T>& t, const Ring &ring) const -{ - unsigned int i; - unsigned int count = CoefficientCount(ring); - unsigned int tCount = t.CoefficientCount(ring); - - if (count > tCount) - { - PolynomialOver<T> result(ring, count); - - for (i=0; i<tCount; i++) - result.m_coefficients[i] = ring.Add(m_coefficients[i], t.m_coefficients[i]); - for (; i<count; i++) - result.m_coefficients[i] = m_coefficients[i]; - - return result; - } - else - { - PolynomialOver<T> result(ring, tCount); - - for (i=0; i<count; i++) - result.m_coefficients[i] = ring.Add(m_coefficients[i], t.m_coefficients[i]); - for (; i<tCount; i++) - result.m_coefficients[i] = t.m_coefficients[i]; - - return result; - } -} - -template <class T> -PolynomialOver<T> PolynomialOver<T>::Minus(const PolynomialOver<T>& t, const Ring &ring) const -{ - unsigned int i; - unsigned int count = CoefficientCount(ring); - unsigned int tCount = t.CoefficientCount(ring); - - if (count > tCount) - { - PolynomialOver<T> result(ring, count); - - for (i=0; i<tCount; i++) - result.m_coefficients[i] = ring.Subtract(m_coefficients[i], t.m_coefficients[i]); - for (; i<count; i++) - result.m_coefficients[i] = m_coefficients[i]; - - return result; - } - else - { - PolynomialOver<T> result(ring, tCount); - - for (i=0; i<count; i++) - result.m_coefficients[i] = ring.Subtract(m_coefficients[i], t.m_coefficients[i]); - for (; i<tCount; i++) - result.m_coefficients[i] = ring.Inverse(t.m_coefficients[i]); - - return result; - } -} - -template <class T> -PolynomialOver<T> PolynomialOver<T>::Inverse(const Ring &ring) const -{ - unsigned int count = CoefficientCount(ring); - PolynomialOver<T> result(ring, count); - - for (unsigned int i=0; i<count; i++) - result.m_coefficients[i] = ring.Inverse(m_coefficients[i]); - - return result; -} - -template <class T> -PolynomialOver<T> PolynomialOver<T>::Times(const PolynomialOver<T>& t, const Ring &ring) const -{ - if (IsZero(ring) || t.IsZero(ring)) - return PolynomialOver<T>(); - - unsigned int count1 = CoefficientCount(ring), count2 = t.CoefficientCount(ring); - PolynomialOver<T> result(ring, count1 + count2 - 1); - - for (unsigned int i=0; i<count1; i++) - for (unsigned int j=0; j<count2; j++) - ring.Accumulate(result.m_coefficients[i+j], ring.Multiply(m_coefficients[i], t.m_coefficients[j])); - - return result; -} - -template <class T> -PolynomialOver<T> PolynomialOver<T>::DividedBy(const PolynomialOver<T>& t, const Ring &ring) const -{ - PolynomialOver<T> remainder, quotient; - Divide(remainder, quotient, *this, t, ring); - return quotient; -} - -template <class T> -PolynomialOver<T> PolynomialOver<T>::Modulo(const PolynomialOver<T>& t, const Ring &ring) const -{ - PolynomialOver<T> remainder, quotient; - Divide(remainder, quotient, *this, t, ring); - return remainder; -} - -template <class T> -PolynomialOver<T> PolynomialOver<T>::MultiplicativeInverse(const Ring &ring) const -{ - return Degree(ring)==0 ? ring.MultiplicativeInverse(m_coefficients[0]) : ring.Identity(); -} - -template <class T> -bool PolynomialOver<T>::IsUnit(const Ring &ring) const -{ - return Degree(ring)==0 && ring.IsUnit(m_coefficients[0]); -} - -template <class T> -std::istream& PolynomialOver<T>::Input(std::istream &in, const Ring &ring) -{ - char c; - unsigned int length = 0; - SecBlock<char> str(length + 16); - bool paren = false; - - std::ws(in); - - if (in.peek() == '(') - { - paren = true; - in.get(); - } - - do - { - in.read(&c, 1); - str[length++] = c; - if (length >= str.size()) - str.Grow(length + 16); - } - // if we started with a left paren, then read until we find a right paren, - // otherwise read until the end of the line - while (in && ((paren && c != ')') || (!paren && c != '\n'))); - - str[length-1] = '\0'; - *this = PolynomialOver<T>(str, ring); - - return in; -} - -template <class T> -std::ostream& PolynomialOver<T>::Output(std::ostream &out, const Ring &ring) const -{ - unsigned int i = CoefficientCount(ring); - if (i) - { - bool firstTerm = true; - - while (i--) - { - if (m_coefficients[i] != ring.Identity()) - { - if (firstTerm) - { - firstTerm = false; - if (!i || !ring.Equal(m_coefficients[i], ring.MultiplicativeIdentity())) - out << m_coefficients[i]; - } - else - { - CoefficientType inverse = ring.Inverse(m_coefficients[i]); - std::ostringstream pstr, nstr; - - pstr << m_coefficients[i]; - nstr << inverse; - - if (pstr.str().size() <= nstr.str().size()) - { - out << " + "; - if (!i || !ring.Equal(m_coefficients[i], ring.MultiplicativeIdentity())) - out << m_coefficients[i]; - } - else - { - out << " - "; - if (!i || !ring.Equal(inverse, ring.MultiplicativeIdentity())) - out << inverse; - } - } - - switch (i) - { - case 0: - break; - case 1: - out << "x"; - break; - default: - out << "x^" << i; - } - } - } - } - else - { - out << ring.Identity(); - } - return out; -} - -template <class T> -void PolynomialOver<T>::Divide(PolynomialOver<T> &r, PolynomialOver<T> &q, const PolynomialOver<T> &a, const PolynomialOver<T> &d, const Ring &ring) -{ - unsigned int i = a.CoefficientCount(ring); - const int dDegree = d.Degree(ring); - - if (dDegree < 0) - throw DivideByZero(); - - r = a; - q.m_coefficients.resize(STDMAX(0, int(i - dDegree))); - - while (i > (unsigned int)dDegree) - { - --i; - q.m_coefficients[i-dDegree] = ring.Divide(r.m_coefficients[i], d.m_coefficients[dDegree]); - for (int j=0; j<=dDegree; j++) - ring.Reduce(r.m_coefficients[i-dDegree+j], ring.Multiply(q.m_coefficients[i-dDegree], d.m_coefficients[j])); - } - - r.CoefficientCount(ring); // resize r.m_coefficients -} - -// ******************************************************** - -// helper function for Interpolate() and InterpolateAt() -template <class T> -void RingOfPolynomialsOver<T>::CalculateAlpha(std::vector<CoefficientType> &alpha, const CoefficientType x[], const CoefficientType y[], unsigned int n) const -{ - for (unsigned int j=0; j<n; ++j) - alpha[j] = y[j]; - - for (unsigned int k=1; k<n; ++k) - { - for (unsigned int j=n-1; j>=k; --j) - { - m_ring.Reduce(alpha[j], alpha[j-1]); - - CoefficientType d = m_ring.Subtract(x[j], x[j-k]); - if (!m_ring.IsUnit(d)) - throw InterpolationFailed(); - alpha[j] = m_ring.Divide(alpha[j], d); - } - } -} - -template <class T> -typename RingOfPolynomialsOver<T>::Element RingOfPolynomialsOver<T>::Interpolate(const CoefficientType x[], const CoefficientType y[], unsigned int n) const -{ - assert(n > 0); - - std::vector<CoefficientType> alpha(n); - CalculateAlpha(alpha, x, y, n); - - std::vector<CoefficientType> coefficients((size_t)n, m_ring.Identity()); - coefficients[0] = alpha[n-1]; - - for (int j=n-2; j>=0; --j) - { - for (unsigned int i=n-j-1; i>0; i--) - coefficients[i] = m_ring.Subtract(coefficients[i-1], m_ring.Multiply(coefficients[i], x[j])); - - coefficients[0] = m_ring.Subtract(alpha[j], m_ring.Multiply(coefficients[0], x[j])); - } - - return PolynomialOver<T>(coefficients.begin(), coefficients.end()); -} - -template <class T> -typename RingOfPolynomialsOver<T>::CoefficientType RingOfPolynomialsOver<T>::InterpolateAt(const CoefficientType &position, const CoefficientType x[], const CoefficientType y[], unsigned int n) const -{ - assert(n > 0); - - std::vector<CoefficientType> alpha(n); - CalculateAlpha(alpha, x, y, n); - - CoefficientType result = alpha[n-1]; - for (int j=n-2; j>=0; --j) - { - result = m_ring.Multiply(result, m_ring.Subtract(position, x[j])); - m_ring.Accumulate(result, alpha[j]); - } - return result; -} - -template <class Ring, class Element> -void PrepareBulkPolynomialInterpolation(const Ring &ring, Element *w, const Element x[], unsigned int n) -{ - for (unsigned int i=0; i<n; i++) - { - Element t = ring.MultiplicativeIdentity(); - for (unsigned int j=0; j<n; j++) - if (i != j) - t = ring.Multiply(t, ring.Subtract(x[i], x[j])); - w[i] = ring.MultiplicativeInverse(t); - } -} - -template <class Ring, class Element> -void PrepareBulkPolynomialInterpolationAt(const Ring &ring, Element *v, const Element &position, const Element x[], const Element w[], unsigned int n) -{ - assert(n > 0); - - std::vector<Element> a(2*n-1); - unsigned int i; - - for (i=0; i<n; i++) - a[n-1+i] = ring.Subtract(position, x[i]); - - for (i=n-1; i>1; i--) - a[i-1] = ring.Multiply(a[2*i], a[2*i-1]); - - a[0] = ring.MultiplicativeIdentity(); - - for (i=0; i<n-1; i++) - { - std::swap(a[2*i+1], a[2*i+2]); - a[2*i+1] = ring.Multiply(a[i], a[2*i+1]); - a[2*i+2] = ring.Multiply(a[i], a[2*i+2]); - } - - for (i=0; i<n; i++) - v[i] = ring.Multiply(a[n-1+i], w[i]); -} - -template <class Ring, class Element> -Element BulkPolynomialInterpolateAt(const Ring &ring, const Element y[], const Element v[], unsigned int n) -{ - Element result = ring.Identity(); - for (unsigned int i=0; i<n; i++) - ring.Accumulate(result, ring.Multiply(y[i], v[i])); - return result; -} - -// ******************************************************** - -template <class T, int instance> -const PolynomialOverFixedRing<T, instance> &PolynomialOverFixedRing<T, instance>::Zero() -{ - return Singleton<ThisType>().Ref(); -} - -template <class T, int instance> -const PolynomialOverFixedRing<T, instance> &PolynomialOverFixedRing<T, instance>::One() -{ - return Singleton<ThisType, NewOnePolynomial>().Ref(); -} - -NAMESPACE_END |