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xtr.h
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    00001 #ifndef CRYPTOPP_XTR_H
    00002 #define CRYPTOPP_XTR_H
    00003
    00004 /** \file
    00005     "The XTR public key system" by Arjen K. Lenstra and Eric R. Verheul
    00006 */
    00007
    00008 #include "modarith.h"
    00009
    00010 NAMESPACE_BEGIN(CryptoPP)
    00011
    00012 //! an element of GF(p^2)
    00013 class GFP2Element
    00014 {
    00015 public:
    00016     GFP2Element() {}
    00017     GFP2Element(const Integer &c1, const Integer &c2) : c1(c1), c2(c2) {}
    00018     GFP2Element(const byte *encodedElement, unsigned int size)
    00019         : c1(encodedElement, size/2), c2(encodedElement+size/2, size/2) {}
    00020
    00021     void Encode(byte *encodedElement, unsigned int size)
    00022     {
    00023         c1.Encode(encodedElement, size/2);
    00024         c2.Encode(encodedElement+size/2, size/2);
    00025     }
    00026
    00027     bool operator==(const GFP2Element &rhs) const {return c1 == rhs.c1 && c2 == rhs.c2;}
    00028     bool operator!=(const GFP2Element &rhs) const {return !operator==(rhs);}
    00029
    00030     void swap(GFP2Element &a)
    00031     {
    00032         c1.swap(a.c1);
    00033         c2.swap(a.c2);
    00034     }
    00035
    00036     static const GFP2Element & Zero();
    00037
    00038     Integer c1, c2;
    00039 };
    00040
    00041 //! GF(p^2), optimal normal basis
    00042 template <class F>
    00043 class GFP2_ONB : public AbstractRing<GFP2Element>
    00044 {
    00045 public:
    00046     typedef F BaseField;
    00047
    00048     GFP2_ONB(const Integer &p) : modp(p)
    00049     {
    00050         if (p%3 != 2)
    00051             throw InvalidArgument("GFP2_ONB: modulus must be equivalent to 2 mod 3");
    00052     }
    00053
    00054     const Integer& GetModulus() const {return modp.GetModulus();}
    00055
    00056     GFP2Element ConvertIn(const Integer &a) const
    00057     {
    00058         t = modp.Inverse(modp.ConvertIn(a));
    00059         return GFP2Element(t, t);
    00060     }
    00061
    00062     GFP2Element ConvertIn(const GFP2Element &a) const
    00063         {return GFP2Element(modp.ConvertIn(a.c1), modp.ConvertIn(a.c2));}
    00064
    00065     GFP2Element ConvertOut(const GFP2Element &a) const
    00066         {return GFP2Element(modp.ConvertOut(a.c1), modp.ConvertOut(a.c2));}
    00067
    00068     bool Equal(const GFP2Element &a, const GFP2Element &b) const
    00069     {
    00070         return modp.Equal(a.c1, b.c1) && modp.Equal(a.c2, b.c2);
    00071     }
    00072
    00073     const Element& Identity() const
    00074     {
    00075         return GFP2Element::Zero();
    00076     }
    00077
    00078     const Element& Add(const Element &a, const Element &b) const
    00079     {
    00080         result.c1 = modp.Add(a.c1, b.c1);
    00081         result.c2 = modp.Add(a.c2, b.c2);
    00082         return result;
    00083     }
    00084
    00085     const Element& Inverse(const Element &a) const
    00086     {
    00087         result.c1 = modp.Inverse(a.c1);
    00088         result.c2 = modp.Inverse(a.c2);
    00089         return result;
    00090     }
    00091
    00092     const Element& Double(const Element &a) const
    00093     {
    00094         result.c1 = modp.Double(a.c1);
    00095         result.c2 = modp.Double(a.c2);
    00096         return result;
    00097     }
    00098
    00099     const Element& Subtract(const Element &a, const Element &b) const
    00100     {
    00101         result.c1 = modp.Subtract(a.c1, b.c1);
    00102         result.c2 = modp.Subtract(a.c2, b.c2);
    00103         return result;
    00104     }
    00105
    00106     Element& Accumulate(Element &a, const Element &b) const
    00107     {
    00108         modp.Accumulate(a.c1, b.c1);
    00109         modp.Accumulate(a.c2, b.c2);
    00110         return a;
    00111     }
    00112
    00113     Element& Reduce(Element &a, const Element &b) const
    00114     {
    00115         modp.Reduce(a.c1, b.c1);
    00116         modp.Reduce(a.c2, b.c2);
    00117         return a;
    00118     }
    00119
    00120     bool IsUnit(const Element &a) const
    00121     {
    00122         return a.c1.NotZero() || a.c2.NotZero();
    00123     }
    00124
    00125     const Element& MultiplicativeIdentity() const
    00126     {
    00127         result.c1 = result.c2 = modp.Inverse(modp.MultiplicativeIdentity());
    00128         return result;
    00129     }
    00130
    00131     const Element& Multiply(const Element &a, const Element &b) const
    00132     {
    00133         t = modp.Add(a.c1, a.c2);
    00134         t = modp.Multiply(t, modp.Add(b.c1, b.c2));
    00135         result.c1 = modp.Multiply(a.c1, b.c1);
    00136         result.c2 = modp.Multiply(a.c2, b.c2);
    00137         result.c1.swap(result.c2);
    00138         modp.Reduce(t, result.c1);
    00139         modp.Reduce(t, result.c2);
    00140         modp.Reduce(result.c1, t);
    00141         modp.Reduce(result.c2, t);
    00142         return result;
    00143     }
    00144
    00145     const Element& MultiplicativeInverse(const Element &a) const
    00146     {
    00147         return result = Exponentiate(a, modp.GetModulus()-2);
    00148     }
    00149
    00150     const Element& Square(const Element &a) const
    00151     {
    00152         const Integer &ac1 = (&a == &result) ? (t = a.c1) : a.c1;
    00153         result.c1 = modp.Multiply(modp.Subtract(modp.Subtract(a.c2, a.c1), a.c1), a.c2);
    00154         result.c2 = modp.Multiply(modp.Subtract(modp.Subtract(ac1, a.c2), a.c2), ac1);
    00155         return result;
    00156     }
    00157
    00158     Element Exponentiate(const Element &a, const Integer &e) const
    00159     {
    00160         Integer edivp, emodp;
    00161         Integer::Divide(emodp, edivp, e, modp.GetModulus());
    00162         Element b = PthPower(a);
    00163         return AbstractRing<GFP2Element>::CascadeExponentiate(a, emodp, b, edivp);
    00164     }
    00165
    00166     const Element & PthPower(const Element &a) const
    00167     {
    00168         result = a;
    00169         result.c1.swap(result.c2);
    00170         return result;
    00171     }
    00172
    00173     void RaiseToPthPower(Element &a) const
    00174     {
    00175         a.c1.swap(a.c2);
    00176     }
    00177
    00178     // a^2 - 2a^p
    00179     const Element & SpecialOperation1(const Element &a) const
    00180     {
    00181         assert(&a != &result);
    00182         result = Square(a);
    00183         modp.Reduce(result.c1, a.c2);
    00184         modp.Reduce(result.c1, a.c2);
    00185         modp.Reduce(result.c2, a.c1);
    00186         modp.Reduce(result.c2, a.c1);
    00187         return result;
    00188     }
    00189
    00190     // x * z - y * z^p
    00191     const Element & SpecialOperation2(const Element &x, const Element &y, const Element &z) const
    00192     {
    00193         assert(&x != &result && &y != &result && &z != &result);
    00194         t = modp.Add(x.c2, y.c2);
    00195         result.c1 = modp.Multiply(z.c1, modp.Subtract(y.c1, t));
    00196         modp.Accumulate(result.c1, modp.Multiply(z.c2, modp.Subtract(t, x.c1)));
    00197         t = modp.Add(x.c1, y.c1);
    00198         result.c2 = modp.Multiply(z.c2, modp.Subtract(y.c2, t));
    00199         modp.Accumulate(result.c2, modp.Multiply(z.c1, modp.Subtract(t, x.c2)));
    00200         return result;
    00201     }
    00202
    00203 protected:
    00204     BaseField modp;
    00205     mutable GFP2Element result;
    00206     mutable Integer t;
    00207 };
    00208
    00209 void XTR_FindPrimesAndGenerator(RandomNumberGenerator &rng, Integer &p, Integer &q, GFP2Element &g, unsigned int pbits, unsigned int qbits);
    00210
    00211 GFP2Element XTR_Exponentiate(const GFP2Element &b, const Integer &e, const Integer &p);
    00212
    00213 NAMESPACE_END
    00214
    00215 #endif