/// <summary>
/// Compute a random root of the given GF2Polynomial
/// </summary>
///
/// <param name="G">The polynomial</param>
///
/// <returns>Returns a random root of <c>G</c></returns>
public override GF2nElement RandomRoot(GF2Polynomial G)
{
// We are in B1!!!
GF2nPolynomial c;
GF2nPolynomial ut;
GF2nElement u;
GF2nPolynomial h;
int hDegree;
// 1. Set g(t) <- f(t)
GF2nPolynomial g = new GF2nPolynomial(G, this);
int gDegree = g.Degree;
int i;
// 2. while deg(g) > 1
while (gDegree > 1)
{
do
{
// 2.1 choose random u (element of) GF(2^m)
u = new GF2nPolynomialElement(this, new Random());
ut = new GF2nPolynomial(2, GF2nPolynomialElement.Zero(this));
// 2.2 Set c(t) <- ut
ut.Set(1, u);
c = new GF2nPolynomial(ut);
// 2.3 For i from 1 to m-1 do
for (i = 1; i <= DegreeN - 1; i++)
{
// 2.3.1 c(t) <- (c(t)^2 + ut) mod g(t)
c = c.MultiplyAndReduce(c, g);
c = c.Add(ut);
}
// 2.4 set h(t) <- GCD(c(t), g(t))
h = c.Gcd(g);
// 2.5 if h(t) is constant or deg(g) = deg(h) then go to
// step 2.1
hDegree = h.Degree;
gDegree = g.Degree;
}while ((hDegree == 0) || (hDegree == gDegree));
// 2.6 If 2deg(h) > deg(g) then set g(t) <- g(t)/h(t) ...
if ((hDegree << 1) > gDegree)
{
g = g.Quotient(h);
}
else
{
g = new GF2nPolynomial(h); // ... else g(t) <- h(t)
}
gDegree = g.Degree;
}
// 3. Output g(0)
return(g.At(0));
}
/// <summary>
/// Compute a random root of the given GF2Polynomial
/// </summary>
///
/// <param name="G">The polynomial</param>
///
/// <returns>Returns a random root of <c>G</c></returns>
public override GF2nElement RandomRoot(GF2Polynomial G)
{
// We are in B1!!!
GF2nPolynomial c;
GF2nPolynomial ut;
GF2nElement u;
GF2nPolynomial h;
int hDegree;
// 1. Set g(t) <- f(t)
GF2nPolynomial g = new GF2nPolynomial(G, this);
int gDegree = g.Degree;
int i;
// 2. while deg(g) > 1
while (gDegree > 1)
{
do
{
// 2.1 choose random u (element of) GF(2^m)
u = new GF2nPolynomialElement(this, new Random());
ut = new GF2nPolynomial(2, GF2nPolynomialElement.Zero(this));
// 2.2 Set c(t) <- ut
ut.Set(1, u);
c = new GF2nPolynomial(ut);
// 2.3 For i from 1 to m-1 do
for (i = 1; i <= DegreeN - 1; i++)
{
// 2.3.1 c(t) <- (c(t)^2 + ut) mod g(t)
c = c.MultiplyAndReduce(c, g);
c = c.Add(ut);
}
// 2.4 set h(t) <- GCD(c(t), g(t))
h = c.Gcd(g);
// 2.5 if h(t) is constant or deg(g) = deg(h) then go to
// step 2.1
hDegree = h.Degree;
gDegree = g.Degree;
}
while ((hDegree == 0) || (hDegree == gDegree));
// 2.6 If 2deg(h) > deg(g) then set g(t) <- g(t)/h(t) ...
if ((hDegree << 1) > gDegree)
g = g.Quotient(h);
else
g = new GF2nPolynomial(h); // ... else g(t) <- h(t)
gDegree = g.Degree;
}
// 3. Output g(0)
return g.At(0);
}
