101 lines
2.7 KiB
C++
101 lines
2.7 KiB
C++
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// cryptlib.cpp - written and placed in the public domain by Wei Dai
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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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NAMESPACE_BEGIN(CryptoPP)
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const GFP2Element & GFP2Element::Zero()
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{
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return Singleton<GFP2Element>().Ref();
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}
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void XTR_FindPrimesAndGenerator(RandomNumberGenerator &rng, Integer &p, Integer &q, GFP2Element &g, unsigned int pbits, unsigned int qbits)
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{
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assert(qbits > 9); // no primes exist for pbits = 10, qbits = 9
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assert(pbits > qbits);
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const Integer minQ = Integer::Power2(qbits - 1);
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const Integer maxQ = Integer::Power2(qbits) - 1;
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const Integer minP = Integer::Power2(pbits - 1);
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const Integer maxP = Integer::Power2(pbits) - 1;
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Integer r1, r2;
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do
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{
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bool qFound = q.Randomize(rng, minQ, maxQ, Integer::PRIME, 7, 12);
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assert(qFound);
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bool solutionsExist = SolveModularQuadraticEquation(r1, r2, 1, -1, 1, q);
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assert(solutionsExist);
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} while (!p.Randomize(rng, minP, maxP, Integer::PRIME, CRT(rng.GenerateBit()?r1:r2, q, 2, 3, EuclideanMultiplicativeInverse(p, 3)), 3*q));
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assert(((p.Squared() - p + 1) % q).IsZero());
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GFP2_ONB<ModularArithmetic> gfp2(p);
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GFP2Element three = gfp2.ConvertIn(3), t;
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while (true)
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{
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g.c1.Randomize(rng, Integer::Zero(), p-1);
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g.c2.Randomize(rng, Integer::Zero(), p-1);
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t = XTR_Exponentiate(g, p+1, p);
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if (t.c1 == t.c2)
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continue;
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g = XTR_Exponentiate(g, (p.Squared()-p+1)/q, p);
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if (g != three)
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break;
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}
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assert(XTR_Exponentiate(g, q, p) == three);
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}
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GFP2Element XTR_Exponentiate(const GFP2Element &b, const Integer &e, const Integer &p)
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{
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unsigned int bitCount = e.BitCount();
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if (bitCount == 0)
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return GFP2Element(-3, -3);
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// find the lowest bit of e that is 1
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unsigned int lowest1bit;
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for (lowest1bit=0; e.GetBit(lowest1bit) == 0; lowest1bit++) {}
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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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// do all exponents bits except the lowest zeros starting from the top
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unsigned int i;
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for (i = e.BitCount() - 1; i>lowest1bit; i--)
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{
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if (e.GetBit(i))
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{
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gfp2.RaiseToPthPower(S[0]);
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gfp2.Accumulate(S[0], gfp2.SpecialOperation2(S[2], c, S[1]));
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S[1] = gfp2.SpecialOperation1(S[1]);
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S[2] = gfp2.SpecialOperation1(S[2]);
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S[0].swap(S[1]);
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}
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else
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{
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gfp2.RaiseToPthPower(S[2]);
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gfp2.Accumulate(S[2], gfp2.SpecialOperation2(S[0], cp, S[1]));
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S[1] = gfp2.SpecialOperation1(S[1]);
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S[0] = gfp2.SpecialOperation1(S[0]);
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S[2].swap(S[1]);
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}
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}
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// now do the lowest zeros
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while (i--)
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S[1] = gfp2.SpecialOperation1(S[1]);
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return gfp2.ConvertOut(S[1]);
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}
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template class AbstractRing<GFP2Element>;
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template class AbstractGroup<GFP2Element>;
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NAMESPACE_END
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