// GHS Attack test file
// written by Florian Hess, version 20050829


k := GF(2);
K := GF(2^3);
n := 3;

a := K!0;
c := K!1;
b := K.1;

E := ArtinSchreierExtension(c, a, b);
WeilDescentGenus(E, k);
WeilDescentGenus(E, K);
WeilDescentComposita(E, k);
WeilDescentDeltas(E, k);

WeilDescentRationalParametrization(E, k);
WeilDescentFrobeniusExtensions(E, k);

E := ArtinSchreierExtension(c, a, b);
WeilDescent(E, k);

a := K!0;
c := NormalElement(K, k);
b := c^2 + c;
E := ArtinSchreierExtension(c, a, b);
WeilDescent(E, k);


a := K!0;
c := K.1;
b := K!0;
E := ArtinSchreierExtension(c, a, b);
WeilDescent(E, k);


k := GF(2);
K := GF(2^3);
n := 3;
a := K!0;
c := K.1;
b := K.1;
E := ArtinSchreierExtension(c, a, b);
WeilDescent(E, k);

k := GF(2);
K := GF(2^4);
n := 4;
a := NormalElement(K, k);
c := a + 1;
b := a^2 + a;
b := b^2 + b;
E := ArtinSchreierExtension(c, a, b);
WeilDescent(E, k);
  
k := GF(2);
K := GF(2, 2);
a := K!0;
c := NormalElement(K, k);
b := c^3 + c;
E := ArtinSchreierExtension(c, a, b);
WeilDescent(E, k);


k := GF(3);
K := GF(3, 2);
a := K!0;
c := NormalElement(K, k);
b := c^3 + c;
E := ArtinSchreierExtension(c, a, b);
WeilDescent(E, k);



k := GF(3);
K := GF(3, 4);
a := NormalElement(K, k) + 1;
c := NormalElement(K, k);
b := c^3 + c;
E := ArtinSchreierExtension(c, a, b);
WeilDescent(E, k);




k := GF(2);
K := GF(2, 7);
a := K!0;
c := K!1;
b := K.1;
E := ArtinSchreierExtension(c, a, b);
WeilDescent(E, k);

k := GF(2);
K := GF(2, 31);
a := K!0;
c := K!1;
b := K.1;
E := ArtinSchreierExtension(c, a, b);
WeilDescent(E, k);


k := GF(2);
K := GF(2, 127);
a := K!0;
c := K!1;
b := K.1;
E := ArtinSchreierExtension(c, a, b);
WeilDescent(E, k);


  

a := K!0;
c := K.1;
b := K.1;


k := GF(2);
K := GF(2^7);
n := 7;

a := K!0;
c := Random(K);
b := Random(K);

C, g, y, Kxf, Frob := ASfromDelta(c, a, b, k);
RationalEquation(C, y, Kxf, Frob, k);






/////////////////////////////////////////////////////////////////////////////


k := GF(2,5);
K := GF(2,155);
n := 31;

gf2t<t> := PolynomialRing(GF(2));
h := Factorisation(t^n - 1)[2][1];
hh := (t^n - 1) div h;

a := K!0;
c := Mult(hh, Random(K), k);
b := Mult(hh, Random(K), k);

data := WeilDescent(c, a, b, k);
  
//  Beispiel:
  
kxf<x> := RationalFunctionField(k);
kxfy<y> := PolynomialRing(kxf);

f := y^32 + k.1^28*y^16 + y^8 + k.1^13*y^4 + k.1^16*y^2 + k.1^18*y + 
  (k.1^19*x^32 + k.1^16*x^24 + k.1^15*x^20 + k.1^3*x^18 +
   k.1^25*x^17 + k.1^21*x^16
   + k.1^22*x^15 + k.1^24*x^14 + k.1^19*x^12 + k.1^3*x^8 +
   k.1^6)/x^16;