Initial revision

1 files changed, 101 insertions, 0 deletions

diff --git a/xtr.cpp b/xtr.cpp
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index 00000000..c0777319
--- /dev/null
+++ b/xtr.cpp
@@ -0,0 +1,101 @@
+// 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)
+
+GFP2Element & GFP2Element::Zero()
+{
+	static GFP2Element zero;
+	return zero;
+}
+
+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