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# xtr.cpp

    00001 // cryptlib.cpp - written and placed in the public domain by Wei Dai
    00002
    00003 #include "pch.h"
    00004 #include "xtr.h"
    00005 #include "nbtheory.h"
    00006
    00007 #include "algebra.cpp"
    00008
    00009 NAMESPACE_BEGIN(CryptoPP)
    00010
    00011 GFP2Element & GFP2Element::Zero()
    00012 {
    00013         static GFP2Element zero;
    00014         return zero;
    00015 }
    00016
    00017 void XTR_FindPrimesAndGenerator(RandomNumberGenerator &rng, Integer &p, Integer &q, GFP2Element &g, unsigned int pbits, unsigned int qbits)
    00018 {
    00019         assert(qbits > 9);      // no primes exist for pbits = 10, qbits = 9
    00020         assert(pbits > qbits);
    00021
    00022         const Integer minQ = Integer::Power2(qbits - 1);
    00023         const Integer maxQ = Integer::Power2(qbits) - 1;
    00024         const Integer minP = Integer::Power2(pbits - 1);
    00025         const Integer maxP = Integer::Power2(pbits) - 1;
    00026
    00027         Integer r1, r2;
    00028         do
    00029         {
    00030                 bool qFound = q.Randomize(rng, minQ, maxQ, Integer::PRIME, 7, 12);
    00031                 assert(qFound);
    00032                 bool solutionsExist = SolveModularQuadraticEquation(r1, r2, 1, -1, 1, q);
    00033                 assert(solutionsExist);
    00034         } while (!p.Randomize(rng, minP, maxP, Integer::PRIME, CRT(rng.GenerateBit()?r1:r2, q, 2, 3), 3*q));
    00035         assert(((p.Squared() - p + 1) % q).IsZero());
    00036
    00037         GFP2_ONB<ModularArithmetic> gfp2(p);
    00038         GFP2Element three = gfp2.ConvertIn(3), t;
    00039
    00040         while (true)
    00041         {
    00042                 g.c1.Randomize(rng, Integer::Zero(), p-1);
    00043                 g.c2.Randomize(rng, Integer::Zero(), p-1);
    00044                 t = XTR_Exponentiate(g, p+1, p);
    00045                 if (t.c1 == t.c2)
    00046                         continue;
    00047                 g = XTR_Exponentiate(g, (p.Squared()-p+1)/q, p);
    00048                 if (g != three)
    00049                         break;
    00050         }
    00051         assert(XTR_Exponentiate(g, q, p) == three);
    00052 }
    00053
    00054 GFP2Element XTR_Exponentiate(const GFP2Element &b, const Integer &e, const Integer &p)
    00055 {
    00056         unsigned int bitCount = e.BitCount();
    00057         if (bitCount == 0)
    00058                 return GFP2Element(-3, -3);
    00059
    00060         // find the lowest bit of e that is 1
    00061         unsigned int lowest1bit;
    00062         for (lowest1bit=0; e.GetBit(lowest1bit) == 0; lowest1bit++) {}
    00063
    00064         GFP2_ONB<MontgomeryRepresentation> gfp2(p);
    00065         GFP2Element c = gfp2.ConvertIn(b);
    00066         GFP2Element cp = gfp2.PthPower(c);
    00067         GFP2Element S[5] = {gfp2.ConvertIn(3), c, gfp2.SpecialOperation1(c)};
    00068
    00069         // do all exponents bits except the lowest zeros starting from the top
    00070         unsigned int i;
    00071         for (i = e.BitCount() - 1; i>lowest1bit; i--)
    00072         {
    00073                 if (e.GetBit(i))
    00074                 {
    00075                         gfp2.RaiseToPthPower(S[0]);
    00076                         gfp2.Accumulate(S[0], gfp2.SpecialOperation2(S[2], c, S[1]));
    00077                         S[1] = gfp2.SpecialOperation1(S[1]);
    00078                         S[2] = gfp2.SpecialOperation1(S[2]);
    00079                         S[0].swap(S[1]);
    00080                 }
    00081                 else
    00082                 {
    00083                         gfp2.RaiseToPthPower(S[2]);
    00084                         gfp2.Accumulate(S[2], gfp2.SpecialOperation2(S[0], cp, S[1]));
    00085                         S[1] = gfp2.SpecialOperation1(S[1]);
    00086                         S[0] = gfp2.SpecialOperation1(S[0]);
    00087                         S[2].swap(S[1]);
    00088                 }
    00089         }
    00090
    00091         // now do the lowest zeros
    00092         while (i--)
    00093                 S[1] = gfp2.SpecialOperation1(S[1]);
    00094
    00095         return gfp2.ConvertOut(S[1]);
    00096 }
    00097
    00098 template class AbstractRing<GFP2Element>;
    00099 template class AbstractGroup<GFP2Element>;
    00100
    00101 NAMESPACE_END