diff options
Diffstat (limited to 'plugins/CryptoPP/crypto/xtr.cpp')
| -rw-r--r-- | plugins/CryptoPP/crypto/xtr.cpp | 100 |
1 files changed, 100 insertions, 0 deletions
diff --git a/plugins/CryptoPP/crypto/xtr.cpp b/plugins/CryptoPP/crypto/xtr.cpp new file mode 100644 index 0000000000..d2f3fb0708 --- /dev/null +++ b/plugins/CryptoPP/crypto/xtr.cpp @@ -0,0 +1,100 @@ +// cryptlib.cpp - written and placed in the public domain by Wei Dai
+
+#include "pch.h"
+#include "xtr.h"
+#include "nbtheory.h"
+
+#include "algebra.cpp"
+
+NAMESPACE_BEGIN(CryptoPP)
+
+const GFP2Element & GFP2Element::Zero()
+{
+ return Singleton<GFP2Element>().Ref();
+}
+
+void XTR_FindPrimesAndGenerator(RandomNumberGenerator &rng, Integer &p, Integer &q, GFP2Element &g, unsigned int pbits, unsigned int qbits)
+{
+ assert(qbits > 9); // no primes exist for pbits = 10, qbits = 9
+ assert(pbits > qbits);
+
+ const Integer minQ = Integer::Power2(qbits - 1);
+ const Integer maxQ = Integer::Power2(qbits) - 1;
+ const Integer minP = Integer::Power2(pbits - 1);
+ const Integer maxP = Integer::Power2(pbits) - 1;
+
+ Integer r1, r2;
+ do
+ {
+ bool qFound = q.Randomize(rng, minQ, maxQ, Integer::PRIME, 7, 12);
+ assert(qFound);
+ bool solutionsExist = SolveModularQuadraticEquation(r1, r2, 1, -1, 1, q);
+ assert(solutionsExist);
+ } while (!p.Randomize(rng, minP, maxP, Integer::PRIME, CRT(rng.GenerateBit()?r1:r2, q, 2, 3), 3*q));
+ assert(((p.Squared() - p + 1) % q).IsZero());
+
+ GFP2_ONB<ModularArithmetic> gfp2(p);
+ GFP2Element three = gfp2.ConvertIn(3), t;
+
+ while (true)
+ {
+ g.c1.Randomize(rng, Integer::Zero(), p-1);
+ g.c2.Randomize(rng, Integer::Zero(), p-1);
+ t = XTR_Exponentiate(g, p+1, p);
+ if (t.c1 == t.c2)
+ continue;
+ g = XTR_Exponentiate(g, (p.Squared()-p+1)/q, p);
+ if (g != three)
+ break;
+ }
+ assert(XTR_Exponentiate(g, q, p) == three);
+}
+
+GFP2Element XTR_Exponentiate(const GFP2Element &b, const Integer &e, const Integer &p)
+{
+ unsigned int bitCount = e.BitCount();
+ if (bitCount == 0)
+ return GFP2Element(-3, -3);
+
+ // find the lowest bit of e that is 1
+ unsigned int lowest1bit;
+ for (lowest1bit=0; e.GetBit(lowest1bit) == 0; lowest1bit++) {}
+
+ GFP2_ONB<MontgomeryRepresentation> gfp2(p);
+ GFP2Element c = gfp2.ConvertIn(b);
+ GFP2Element cp = gfp2.PthPower(c);
+ GFP2Element S[5] = {gfp2.ConvertIn(3), c, gfp2.SpecialOperation1(c)};
+
+ // do all exponents bits except the lowest zeros starting from the top
+ unsigned int i;
+ for (i = e.BitCount() - 1; i>lowest1bit; i--)
+ {
+ if (e.GetBit(i))
+ {
+ gfp2.RaiseToPthPower(S[0]);
+ gfp2.Accumulate(S[0], gfp2.SpecialOperation2(S[2], c, S[1]));
+ S[1] = gfp2.SpecialOperation1(S[1]);
+ S[2] = gfp2.SpecialOperation1(S[2]);
+ S[0].swap(S[1]);
+ }
+ else
+ {
+ gfp2.RaiseToPthPower(S[2]);
+ gfp2.Accumulate(S[2], gfp2.SpecialOperation2(S[0], cp, S[1]));
+ S[1] = gfp2.SpecialOperation1(S[1]);
+ S[0] = gfp2.SpecialOperation1(S[0]);
+ S[2].swap(S[1]);
+ }
+ }
+
+ // now do the lowest zeros
+ while (i--)
+ S[1] = gfp2.SpecialOperation1(S[1]);
+
+ return gfp2.ConvertOut(S[1]);
+}
+
+template class AbstractRing<GFP2Element>;
+template class AbstractGroup<GFP2Element>;
+
+NAMESPACE_END
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