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#include "pch.h"
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#include "xtr.h"
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#include "nbtheory.h"
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#include "algebra.cpp"
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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;
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const Integer minP =
Integer::Power2(pbits - 1);
00024
const Integer maxP =
Integer::Power2(pbits) - 1;
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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), 3*q));
00034 assert(((p.
Squared() - p + 1) % q).IsZero());
00035
00036
GFP2_ONB<ModularArithmetic> gfp2(p);
00037
GFP2Element three = gfp2.ConvertIn(3), t;
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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);
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if (t.c1 == t.c2)
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continue;
00046 g = XTR_Exponentiate(g, (p.
Squared()-p+1)/q, p);
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if (g != three)
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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)
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return GFP2Element(-3, -3);
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00059
00060
unsigned int lowest1bit;
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for (lowest1bit=0; e.GetBit(lowest1bit) == 0; lowest1bit++) {}
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00063
GFP2_ONB<MontgomeryRepresentation> gfp2(p);
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GFP2Element c = gfp2.ConvertIn(b);
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GFP2Element cp = gfp2.PthPower(c);
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GFP2Element S[5] = {gfp2.ConvertIn(3), c, gfp2.SpecialOperation1(c)};
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00068
00069
unsigned int i;
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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
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while (i--)
00092 S[1] = gfp2.SpecialOperation1(S[1]);
00093
00094
return gfp2.ConvertOut(S[1]);
00095 }
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00097
template class AbstractRing<GFP2Element>;
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template class AbstractGroup<GFP2Element>;
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00100 NAMESPACE_END