diff options
Diffstat (limited to 'plugins/CryptoPP/crypto/polynomi.cpp')
| -rw-r--r-- | plugins/CryptoPP/crypto/polynomi.cpp | 577 |
1 files changed, 577 insertions, 0 deletions
diff --git a/plugins/CryptoPP/crypto/polynomi.cpp b/plugins/CryptoPP/crypto/polynomi.cpp new file mode 100644 index 0000000000..40258ad94a --- /dev/null +++ b/plugins/CryptoPP/crypto/polynomi.cpp @@ -0,0 +1,577 @@ +// 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
|