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1 files changed, 215 insertions, 0 deletions

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+#ifndef CRYPTOPP_XTR_H
+#define CRYPTOPP_XTR_H
+
+/** \file
+	"The XTR public key system" by Arjen K. Lenstra and Eric R. Verheul
+*/
+
+#include "modarith.h"
+
+NAMESPACE_BEGIN(CryptoPP)
+
+//! an element of GF(p^2)
+class GFP2Element
+{
+public:
+	GFP2Element() {}
+	GFP2Element(const Integer &c1, const Integer &c2) : c1(c1), c2(c2) {}
+	GFP2Element(const byte *encodedElement, unsigned int size)
+		: c1(encodedElement, size/2), c2(encodedElement+size/2, size/2) {}
+
+	void Encode(byte *encodedElement, unsigned int size)
+	{
+		c1.Encode(encodedElement, size/2);
+		c2.Encode(encodedElement+size/2, size/2);
+	}
+
+	bool operator==(const GFP2Element &rhs)	const {return c1 == rhs.c1 && c2 == rhs.c2;}
+	bool operator!=(const GFP2Element &rhs) const {return !operator==(rhs);}
+
+	void swap(GFP2Element &a)
+	{
+		c1.swap(a.c1);
+		c2.swap(a.c2);
+	}
+
+	static GFP2Element & Zero();
+
+	Integer c1, c2;
+};
+
+//! GF(p^2), optimal normal basis
+template <class F>
+class GFP2_ONB : public AbstractRing<GFP2Element>
+{
+public:
+	typedef F BaseField;
+
+	GFP2_ONB(const Integer &p) : modp(p)
+	{
+		if (p%3 != 2)
+			throw InvalidArgument("GFP2_ONB: modulus must be equivalent to 2 mod 3");
+	}
+
+	const Integer& GetModulus() const {return modp.GetModulus();}
+
+	GFP2Element ConvertIn(const Integer &a) const
+	{
+		t = modp.Inverse(modp.ConvertIn(a));
+		return GFP2Element(t, t);
+	}
+
+	GFP2Element ConvertIn(const GFP2Element &a) const
+		{return GFP2Element(modp.ConvertIn(a.c1), modp.ConvertIn(a.c2));}
+
+	GFP2Element ConvertOut(const GFP2Element &a) const
+		{return GFP2Element(modp.ConvertOut(a.c1), modp.ConvertOut(a.c2));}
+
+	bool Equal(const GFP2Element &a, const GFP2Element &b) const
+	{
+		return modp.Equal(a.c1, b.c1) && modp.Equal(a.c2, b.c2);
+	}
+
+	const Element& Identity() const
+	{
+		return GFP2Element::Zero();
+	}
+
+	const Element& Add(const Element &a, const Element &b) const
+	{
+		result.c1 = modp.Add(a.c1, b.c1);
+		result.c2 = modp.Add(a.c2, b.c2);
+		return result;
+	}
+
+	const Element& Inverse(const Element &a) const
+	{
+		result.c1 = modp.Inverse(a.c1);
+		result.c2 = modp.Inverse(a.c2);
+		return result;
+	}
+
+	const Element& Double(const Element &a) const
+	{
+		result.c1 = modp.Double(a.c1);
+		result.c2 = modp.Double(a.c2);
+		return result;
+	}
+
+	const Element& Subtract(const Element &a, const Element &b) const
+	{
+		result.c1 = modp.Subtract(a.c1, b.c1);
+		result.c2 = modp.Subtract(a.c2, b.c2);
+		return result;
+	}
+
+	Element& Accumulate(Element &a, const Element &b) const
+	{
+		modp.Accumulate(a.c1, b.c1);
+		modp.Accumulate(a.c2, b.c2);
+		return a;
+	}
+
+	Element& Reduce(Element &a, const Element &b) const
+	{
+		modp.Reduce(a.c1, b.c1);
+		modp.Reduce(a.c2, b.c2);
+		return a;
+	}
+
+	bool IsUnit(const Element &a) const
+	{
+		return a.c1.NotZero() || a.c2.NotZero();
+	}
+
+	const Element& MultiplicativeIdentity() const
+	{
+		result.c1 = result.c2 = modp.Inverse(modp.MultiplicativeIdentity());
+		return result;
+	}
+
+	const Element& Multiply(const Element &a, const Element &b) const
+	{
+		t = modp.Add(a.c1, a.c2);
+		t = modp.Multiply(t, modp.Add(b.c1, b.c2));
+		result.c1 = modp.Multiply(a.c1, b.c1);
+		result.c2 = modp.Multiply(a.c2, b.c2);
+		result.c1.swap(result.c2);
+		modp.Reduce(t, result.c1);
+		modp.Reduce(t, result.c2);
+		modp.Reduce(result.c1, t);
+		modp.Reduce(result.c2, t);
+		return result;
+	}
+
+	const Element& MultiplicativeInverse(const Element &a) const
+	{
+		return result = Exponentiate(a, modp.GetModulus()-2);
+	}
+
+	const Element& Square(const Element &a) const
+	{
+		const Integer &ac1 = (&a == &result) ? (t = a.c1) : a.c1;
+		result.c1 = modp.Multiply(modp.Subtract(modp.Subtract(a.c2, a.c1), a.c1), a.c2);
+		result.c2 = modp.Multiply(modp.Subtract(modp.Subtract(ac1, a.c2), a.c2), ac1);
+		return result;
+	}
+
+	Element Exponentiate(const Element &a, const Integer &e) const
+	{
+		Integer edivp, emodp;
+		Integer::Divide(emodp, edivp, e, modp.GetModulus());
+		Element b = PthPower(a);
+		return AbstractRing<GFP2Element>::CascadeExponentiate(a, emodp, b, edivp);
+	}
+
+	const Element & PthPower(const Element &a) const
+	{
+		result = a;
+		result.c1.swap(result.c2);
+		return result;
+	}
+
+	void RaiseToPthPower(Element &a) const
+	{
+		a.c1.swap(a.c2);
+	}
+
+	// a^2 - 2a^p
+	const Element & SpecialOperation1(const Element &a) const
+	{
+		assert(&a != &result);
+		result = Square(a);
+		modp.Reduce(result.c1, a.c2);
+		modp.Reduce(result.c1, a.c2);
+		modp.Reduce(result.c2, a.c1);
+		modp.Reduce(result.c2, a.c1);
+		return result;
+	}
+
+	// x * z - y * z^p
+	const Element & SpecialOperation2(const Element &x, const Element &y, const Element &z) const
+	{
+		assert(&x != &result && &y != &result && &z != &result);
+		t = modp.Add(x.c2, y.c2);
+		result.c1 = modp.Multiply(z.c1, modp.Subtract(y.c1, t));
+		modp.Accumulate(result.c1, modp.Multiply(z.c2, modp.Subtract(t, x.c1)));
+		t = modp.Add(x.c1, y.c1);
+		result.c2 = modp.Multiply(z.c2, modp.Subtract(y.c2, t));
+		modp.Accumulate(result.c2, modp.Multiply(z.c1, modp.Subtract(t, x.c2)));
+		return result;
+	}
+
+protected:
+	BaseField modp;
+	mutable GFP2Element result;
+	mutable Integer t;
+};
+
+void XTR_FindPrimesAndGenerator(RandomNumberGenerator &rng, Integer &p, Integer &q, GFP2Element &g, unsigned int pbits, unsigned int qbits);
+
+GFP2Element XTR_Exponentiate(const GFP2Element &b, const Integer &e, const Integer &p);
+
+NAMESPACE_END
+
+#endif