/usr/include/crypto++/xtr.h is in libcrypto++-dev 5.6.1-6+deb8u3.
This file is owned by root:root, with mode 0o644.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 | #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 const 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
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