void FindOrderThreaded()
{
try
{
int p = (int)Tab1nupFieldSize.Value;
if (!MathTools.IsPrime(p))
{
MessageBox.Show("Finite Field size must be a prime number!", this.Text, MessageBoxButtons.OK, MessageBoxIcon.Exclamation);
return;
}
FiniteField F = new FiniteField(p);
Polynomial P = Polynomial.Parse(F, Tab1txtPolyCoefs.Text.Trim(), true);
Tab1lblResult.Text = "";
Tab1lblResult.Text += "Recognized polynomial: " + P.ToString() + "\r\n\r\nComputing the order...\r\n\r\n";
Application.DoEvents();
int order = P.Order;
Tab1lblResult.Text += "Order of the polynomial is " + order.ToString();
}
catch (Exception exp)
{
MessageBox.Show(exp.Message);
}
}
private void btnFixField_Click(object sender, EventArgs e)
{
int t = 0;
bool dene = int.TryParse(txtSize.Text.Trim(), out t);
if (dene)
{
if (MathTools.IsPrime(t))
{
p = t;
F = new FiniteField(p);
lblInfo.Text = "Current Field: " + F.ToString();
}
else
{
MessageBox.Show("Please enter a prime number!", this.Text, MessageBoxButtons.OK, MessageBoxIcon.Exclamation);
txtSize.Focus();
}
}
else
{
MessageBox.Show("Please check the value you have written!", this.Text, MessageBoxButtons.OK, MessageBoxIcon.Exclamation);
txtSize.Focus();
}
btnFixField.Enabled = false;
btnFixValues.Enabled = true;
//lblInfo.Text = "Please enter the parameters";
}
public static Polynomial Random(FiniteField F, int degree, Random rnd)
{
int[] coefs = new int[degree + 1];
for (int i = 0; i < coefs.Length - 1; i++)
{
coefs[i] = rnd.Next(F.Elements[0].Value, F.Elements[F.Elements.Length - 1].Value + 1);
}
coefs[coefs.Length - 1] = rnd.Next(F.Elements[1].Value, F.Elements[F.Elements.Length - 1].Value + 1);
Polynomial p = new Polynomial(F, coefs);
return(p);
}
/// <summary>
/// If the characteristic of the finite field is less or equal then 7 you can't use seperators.
/// Example; For char=5 you should write string as "11232340134324320"
/// For char=11 you should write string as "1-10-0-8-2-1-3-10-9-2"
/// You can use . , ; _ - and space char as seperator.
/// </summary>
/// <param name="F"></param>
/// <param name="s"></param>
/// <returns></returns>
public static Polynomial Parse(FiniteField F, string s, bool trimZeros)
{
FiniteFieldElement[] list = new FiniteFieldElement[0];
if (F.Characteristic > 7)
{
string[] slist = s.Split('.', ',', ';', '_', '-', ' ');
for (int i = 0; i < slist.Length; i++)
{
FiniteFieldElement f = new FiniteFieldElement();
f.Field = F;
f.Value = int.Parse(slist[i].ToString()) % F.Characteristic;
Array.Resize(ref list, list.Length + 1);
list[list.Length - 1] = f;
}
}
else
{
for (int i = 0; i < s.Length; i++)
{
FiniteFieldElement f = new FiniteFieldElement();
f.Field = F;
f.Value = int.Parse(s[i].ToString()) % F.Characteristic;
Array.Resize(ref list, list.Length + 1);
list[list.Length - 1] = f;
}
}
// Trim 0s
if (trimZeros)
{
int listlen = list.Length;
for (int i = 0; i < listlen - 1; i++)
{
if (list[listlen - i - 1].Value == 0)
{
Array.Resize(ref list, list.Length - 1);
}
else
{
break;
}
}
}
return(new Polynomial(list));
}
public Polynomial(FiniteField F, params int[] coefficients)
{
_coefficients = new FiniteFieldElement[0];
for (int i = 0; i < coefficients.Length; i++)
{
FiniteFieldElement elt = new FiniteFieldElement();
elt.Field = F;
elt.Value = coefficients[i] % elt.Field.Characteristic;
Array.Resize(ref _coefficients, _coefficients.Length + 1);
_coefficients[_coefficients.Length - 1] = elt;
}
}
/// <summary>
/// Generates a polynomial which consists only 1 term over given field F. e.g. (F,alfa,4) returns the polynomial alfa*x^4 over F and alfa in F.
/// </summary>
public static Polynomial GenerateFromTerm(FiniteField F, FiniteFieldElement Coefficient, int Degree)
{
if (F.Characteristic != Coefficient.Field.Characteristic)
{
throw new Exception("Coefficient must be an element of given Finite Field F.");
}
FiniteFieldElement[] coefs = new FiniteFieldElement[0];
for (int i = 0; i < Degree; i++)
{
Array.Resize(ref coefs, coefs.Length + 1);
coefs[coefs.Length - 1] = F.Elements[0];
}
Array.Resize(ref coefs, coefs.Length + 1);
FiniteFieldElement f = Coefficient;
coefs[coefs.Length - 1] = f;
return(new Polynomial(coefs));
}
protected void btnRunBM_Click(object sender, EventArgs e)
{
FiniteField F = null;
int p = int.Parse(txtSize.Text.Trim());
if (MathTools.IsPrime(p))
{
F = new FiniteField(p);
}
else
{
Response.Clear();
Response.Write("Please write a prime number!");
Response.End();
}
// Clean The Mess
string seq = txtSeq.Text, newseq = "";
for (int i = 0; i < seq.Length; i++)
{
int t = 0;
bool dene = int.TryParse(seq[i].ToString(), out t);
if (dene)
{
if (t < F.Characteristic)
newseq += seq[i];
}
}
if (newseq.Length == 0)
{
Response.Clear();
Response.Write("Please enter the sequence.");
Response.End();
}
txtSeq.Text = newseq;
Polynomial poly = Polynomial.Parse(F, newseq, false);
Polynomial c;
int LC = LFSRTools.BerlekampMassey(poly, out c);
lblResult.Text = "Sequence Length = " + newseq.Length + "<br/>" +
"Linear Complexity = " + LC + "<br/>" +
"Connection Polynomial = " + c.ToString();
}
void GetTab2Ready()
{
// Finite Field
F3 = new FiniteField(3);
// LFSR 1 - 3
string strf1 = "201", stri1 = "001";
Polynomial feedback1 = Polynomial.Parse(F3, strf1, false);
Polynomial initial1 = Polynomial.Parse(F3, stri1, false);
L1 = new LFSR(feedback1, initial1.Coefficients);
Tab2lblLFSR1.Text += "\r\n" + "Feedback: " + Polynomial.Parse(F3, "1" + strf1, false).ToString() + "\r\nInitial: " + stri1 + "\r\nPeriod = " + L1.Period;
// LFSR 2 - 4
string strf2 = "2001", stri2 = "0001";
Polynomial feedback2 = Polynomial.Parse(F3, strf2, false);
Polynomial initial2 = Polynomial.Parse(F3, stri2, false);
L2 = new LFSR(feedback2, initial2.Coefficients);
Tab2lblLFSR2.Text += "\r\n" + "Feedback: " + Polynomial.Parse(F3, "2" + strf2, false).ToString() + "\r\nInitial: " + stri2 + "\r\nPeriod = " + L2.Period;
// LFSR 3 - 5
string strf3 = "20001", stri3 = "00001";
Polynomial feedback3 = Polynomial.Parse(F3, strf3, false);
Polynomial initial3 = Polynomial.Parse(F3, stri3, false);
L3 = new LFSR(feedback3, initial3.Coefficients);
Tab2lblLFSR3.Text += "\r\n" + "Feedback: " + Polynomial.Parse(F3, "1" + strf3, false).ToString() + "\r\nInitial: " + stri3 + "\r\nPeriod = " + L3.Period;
// LFSR 4 - 7
string strf4 = "0000201", stri4 = "1012220";
Polynomial feedback4 = Polynomial.Parse(F3, strf4, false);
Polynomial initial4 = Polynomial.Parse(F3, stri4, false);
L4 = new LFSR(feedback4, initial4.Coefficients);
Tab2lblLFSR4.Text += "\r\n" + "Feedback: " + Polynomial.Parse(F3, "1" + strf4, false).ToString() + "\r\nInitial: " + stri4 + "\r\nPeriod = 26 (precomputed)";// +L4.Period;
// Nonlinear Combiner
NonlinCombOutput = "";
Tab2lblNonLinComb.Text += "\r\n(X1+X3) * (X2+X4)";
}
private void Form1_Load(object sender, EventArgs e)
{
GF5 = new FiniteField(5);
GF56Primitive = new Polynomial(GF5, 2, 0, 1, 4, 1, 0, 1);
ExtF = new ExtensionField(GF56Primitive);
lblInfo.Text = "Current Field Info: " + ExtF.ToString();
}
private void txtSize_Leave(object sender, EventArgs e)
{
int t = 0;
bool dene = int.TryParse(txtSize.Text.Trim(), out t);
if (dene)
{
if (MathTools.IsPrime(t))
{
eskip = p;
p = t;
F = new FiniteField(p);
lblInfo.Text = "Current Field: " + F.ToString();
if (eskip > p)
{
txtSeq.Clear();
txtResult.Clear();
}
}
else
{
MessageBox.Show("Please enter a prime number!", this.Text, MessageBoxButtons.OK, MessageBoxIcon.Exclamation);
txtSize.Focus();
}
}
else
{
MessageBox.Show("Please check the value you have written!", this.Text, MessageBoxButtons.OK, MessageBoxIcon.Exclamation);
txtSize.Focus();
}
}
/// <summary>
/// Generates a polynomial which consists only 1 term over given field F. e.g. (F,alfa,4) returns the polynomial alfa*x^4 over F and alfa in F.
/// </summary>
public static Polynomial GenerateFromTerm(FiniteField F, FiniteFieldElement Coefficient, int Degree)
{
if (F.Characteristic != Coefficient.Field.Characteristic)
{
throw new Exception("Coefficient must be an element of given Finite Field F.");
}
FiniteFieldElement[] coefs = new FiniteFieldElement[0];
for (int i = 0; i < Degree; i++)
{
Array.Resize(ref coefs, coefs.Length + 1);
coefs[coefs.Length - 1] = F.Elements[0];
}
Array.Resize(ref coefs, coefs.Length + 1);
FiniteFieldElement f = Coefficient;
coefs[coefs.Length - 1] = f;
return new Polynomial(coefs);
}
public Polynomial(FiniteField F, params int[] coefficients)
{
_coefficients = new FiniteFieldElement[0];
for (int i = 0; i < coefficients.Length; i++)
{
FiniteFieldElement elt = new FiniteFieldElement();
elt.Field = F;
elt.Value = coefficients[i] % elt.Field.Characteristic;
Array.Resize(ref _coefficients, _coefficients.Length + 1);
_coefficients[_coefficients.Length - 1] = elt;
}
}
public ExtensionField(Polynomial primitivePolynomial)
{
this._baseField = primitivePolynomial.Field;
this._primitivePolynomial = primitivePolynomial;
this.rnd = new Random();
}
/// <summary>
/// Generates a monic polynomial of given degree over given field F.
/// </summary>
public static Polynomial RandomMonic(FiniteField F, int degree)
{
Random rnd = new Random();
int[] coefs = new int[degree + 1];
for (int i = 0; i < coefs.Length - 1; i++)
coefs[i] = rnd.Next(F.Elements[0].Value, F.Elements[F.Elements.Length - 1].Value + 1);
coefs[coefs.Length - 1] = 1;
Polynomial p = new Polynomial(F, coefs);
return p;
}
/// <summary>
/// If the characteristic of the finite field is less or equal then 7 you can't use seperators.
/// Example; For char=5 you should write string as "11232340134324320"
/// For char=11 you should write string as "1-10-0-8-2-1-3-10-9-2"
/// You can use . , ; _ - and space char as seperator.
/// </summary>
/// <param name="F"></param>
/// <param name="s"></param>
/// <returns></returns>
public static Polynomial Parse(FiniteField F, string s, bool trimZeros)
{
FiniteFieldElement[] list = new FiniteFieldElement[0];
if (F.Characteristic > 7)
{
string[] slist = s.Split('.', ',', ';', '_', '-', ' ');
for (int i = 0; i < slist.Length; i++)
{
FiniteFieldElement f = new FiniteFieldElement();
f.Field = F;
f.Value = int.Parse(slist[i].ToString()) % F.Characteristic;
Array.Resize(ref list, list.Length + 1);
list[list.Length - 1] = f;
}
}
else
{
for (int i = 0; i < s.Length; i++)
{
FiniteFieldElement f = new FiniteFieldElement();
f.Field = F;
f.Value = int.Parse(s[i].ToString()) % F.Characteristic;
Array.Resize(ref list, list.Length + 1);
list[list.Length - 1] = f;
}
}
// Trim 0s
if (trimZeros)
{
int listlen = list.Length;
for (int i = 0; i < listlen - 1; i++)
{
if (list[listlen - i - 1].Value == 0)
Array.Resize(ref list, list.Length - 1);
else
break;
}
}
return new Polynomial(list);
}
