00001
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 const GFP2Element & GFP2Element::Zero()
00012 {
00013 return Singleton<GFP2Element>().Ref();
00014 }
00015
00016 void XTR_FindPrimesAndGenerator(RandomNumberGenerator &rng, Integer &p, Integer &q, GFP2Element &g, unsigned int pbits, unsigned int qbits)
00017 {
00018 assert(qbits > 9);
00019 assert(pbits > qbits);
00020
00021 const Integer minQ = Integer::Power2(qbits - 1);
00022 const Integer maxQ = Integer::Power2(qbits) - 1;
00023 const Integer minP = Integer::Power2(pbits - 1);
00024 const Integer maxP = Integer::Power2(pbits) - 1;
00025
00026 Integer r1, r2;
00027 do
00028 {
00029 bool qFound = q.Randomize(rng, minQ, maxQ, Integer::PRIME, 7, 12);
00030 assert(qFound);
00031 bool solutionsExist = SolveModularQuadraticEquation(r1, r2, 1, -1, 1, q);
00032 assert(solutionsExist);
00033 } while (!p.Randomize(rng, minP, maxP, Integer::PRIME, CRT(rng.GenerateBit()?r1:r2, q, 2, 3, EuclideanMultiplicativeInverse(p, 3)), 3*q));
00034 assert(((p.Squared() - p + 1) % q).IsZero());
00035
00036 GFP2_ONB<ModularArithmetic> gfp2(p);
00037 GFP2Element three = gfp2.ConvertIn(3), t;
00038
00039 while (true)
00040 {
00041 g.c1.Randomize(rng, Integer::Zero(), p-1);
00042 g.c2.Randomize(rng, Integer::Zero(), p-1);
00043 t = XTR_Exponentiate(g, p+1, p);
00044 if (t.c1 == t.c2)
00045 continue;
00046 g = XTR_Exponentiate(g, (p.Squared()-p+1)/q, p);
00047 if (g != three)
00048 break;
00049 }
00050 assert(XTR_Exponentiate(g, q, p) == three);
00051 }
00052
00053 GFP2Element XTR_Exponentiate(const GFP2Element &b, const Integer &e, const Integer &p)
00054 {
00055 unsigned int bitCount = e.BitCount();
00056 if (bitCount == 0)
00057 return GFP2Element(-3, -3);
00058
00059
00060 unsigned int lowest1bit;
00061 for (lowest1bit=0; e.GetBit(lowest1bit) == 0; lowest1bit++) {}
00062
00063 GFP2_ONB<MontgomeryRepresentation> gfp2(p);
00064 GFP2Element c = gfp2.ConvertIn(b);
00065 GFP2Element cp = gfp2.PthPower(c);
00066 GFP2Element S[5] = {gfp2.ConvertIn(3), c, gfp2.SpecialOperation1(c)};
00067
00068
00069 unsigned int i;
00070 for (i = e.BitCount() - 1; i>lowest1bit; i--)
00071 {
00072 if (e.GetBit(i))
00073 {
00074 gfp2.RaiseToPthPower(S[0]);
00075 gfp2.Accumulate(S[0], gfp2.SpecialOperation2(S[2], c, S[1]));
00076 S[1] = gfp2.SpecialOperation1(S[1]);
00077 S[2] = gfp2.SpecialOperation1(S[2]);
00078 S[0].swap(S[1]);
00079 }
00080 else
00081 {
00082 gfp2.RaiseToPthPower(S[2]);
00083 gfp2.Accumulate(S[2], gfp2.SpecialOperation2(S[0], cp, S[1]));
00084 S[1] = gfp2.SpecialOperation1(S[1]);
00085 S[0] = gfp2.SpecialOperation1(S[0]);
00086 S[2].swap(S[1]);
00087 }
00088 }
00089
00090
00091 while (i--)
00092 S[1] = gfp2.SpecialOperation1(S[1]);
00093
00094 return gfp2.ConvertOut(S[1]);
00095 }
00096
00097 template class AbstractRing<GFP2Element>;
00098 template class AbstractGroup<GFP2Element>;
00099
00100 NAMESPACE_END