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