public ExtensionLFSR(ExtensionPolynomial feedbackPolynomial, ExtensionFieldElement[] initialState)
{
if (feedbackPolynomial.Field.Characteristic != initialState[0].Field.Characteristic)
throw new Exception("Both values should be defined in the same field.");
if ((initialState.Length - 1) < feedbackPolynomial.Degree)
throw new ArgumentOutOfRangeException("Initial state size must be greater then feedback polynomial degree.");
this.currentState = initialState;
this._feedbackPolynomial = feedbackPolynomial;
}
public void Clock()
{
ExtensionFieldElement r = ExtensionFieldElement.Zero(_feedbackPolynomial.Field);
// Evaluate the current state on feedback polynomial
for (int i = 0; i < currentState.Length; i++)
r += _feedbackPolynomial.Coefficients[i] * currentState[i];
// Shift the currentState right.
_streamOutput = currentState[0];
Array.Copy(currentState, 1, currentState, 0, currentState.Length - 1);
currentState[currentState.Length - 1] = r;
}
public void Clock()
{
ExtensionFieldElement r = ExtensionFieldElement.Zero(_feedbackPolynomial.Field);
// Evaluate the current state on feedback polynomial
for (int i = 0; i < currentState.Length; i++)
{
r += _feedbackPolynomial.Coefficients[i] * currentState[i];
}
// Shift the currentState right.
_streamOutput = currentState[0];
Array.Copy(currentState, 1, currentState, 0, currentState.Length - 1);
currentState[currentState.Length - 1] = r;
}
public static ExtensionFieldElement operator *(ExtensionFieldElement element1, ExtensionFieldElement element2)
{
if (element1.Field != element2.Field)
{
throw new Exception("Both elements should be in the same field.");
}
ExtensionFieldElement result = new ExtensionFieldElement();
result.Field = element1.Field;
result.Value = (element1.Value * element2.Value) % element1.Field.DefiningPolynomial;
return(result);
}
public static ExtensionFieldElement operator %(ExtensionFieldElement element1, ExtensionFieldElement element2)
{
if (element1.Field != element2.Field)
{
throw new Exception("Both elements should be in the same field.");
}
ExtensionFieldElement result = new ExtensionFieldElement();
result.Field = element1.Field;
result.Value = (element1.Value % element2.Value) % element1.Field.DefiningPolynomial;
return(result);
//throw new NotImplementedException("There was a problem about element operation handling.");
}
public ExtensionFieldElement RandomPrimitiveElement(int degree)
{
if (degree > this._primitivePolynomial.Degree - 1)
{
throw new Exception("Element's degree can't be equal to or higher than Primitive polynomial's degree.");
}
Polynomial p = Polynomial.Random(this._baseField, degree, this.rnd);
while (!p.IsPrimitiveElement(this._primitivePolynomial))
{
p = Polynomial.Random(this._baseField, degree, this.rnd);
}
ExtensionFieldElement elt = new ExtensionFieldElement(this, p);
return(elt);
}
public static ExtensionPolynomial operator *(ExtensionPolynomial poly1, ExtensionPolynomial poly2)
{
if (poly1.Field.Characteristic != poly2.Field.Characteristic)
{
throw new Exception("Both polynomials should be defined in the same field.");
}
ExtensionFieldElement[] elts = new ExtensionFieldElement[poly1.Degree + poly2.Degree + 1];
for (int i = 0; i < elts.Length; i++)
{
ExtensionFieldElement e = ExtensionFieldElement.One(poly1.Field);
elts[i] = e;
}
ExtensionPolynomial p = new ExtensionPolynomial(elts);
for (int i = 0; i < poly1._coefficients.Length; i++)
{
for (int j = 0; j < poly2._coefficients.Length; j++)
{
p._coefficients[i + j] += poly1._coefficients[i] * poly2._coefficients[j];
}
}
int plen = p._coefficients.Length;
for (int i = 0; i < plen - 1; i++)
{
if (p._coefficients[plen - i - 1].Value.IsZero)
{
Array.Resize(ref p._coefficients, p._coefficients.Length - 1);
}
else
{
break;
}
}
return(p);
}
public static ExtensionFieldElement Zero(ExtensionField F)
{
ExtensionFieldElement zero = new ExtensionFieldElement(F, new Polynomial(F.DefiningPolynomial.Field, 0));
return(zero);
}
public static ExtensionFieldElement operator /(ExtensionFieldElement element1, ExtensionFieldElement element2)
{
if (element1.Field != element2.Field)
{
throw new Exception("Both elements should be in the same field.");
}
ExtensionFieldElement result = new ExtensionFieldElement();
result.Field = element1.Field;
result.Value = (element1.Value / element2.Value) % element1.Field.DefiningPolynomial;
return result;
//throw new NotImplementedException("There was a problem about element operation handling.");
}
public ExtensionFieldElement One()
{
ExtensionFieldElement one = new ExtensionFieldElement(this.Field, new Polynomial(this.Field.DefiningPolynomial.Field, 1));
return(one);
}
private void btnLFSR_Click(object sender, EventArgs e)
{
if (lfsr == null)
{
ExtensionFieldElement[] eltlist1 = new ExtensionFieldElement[4];
for (int i = 0; i < 4; i++)
eltlist1[i] = ExtF.RandomElement;
ExtensionPolynomial extp1 = new ExtensionPolynomial(eltlist1);
ExtensionFieldElement[] eltlist2 = new ExtensionFieldElement[4];
for (int i = 0; i < 4; i++)
eltlist2[i] = ExtF.RandomElement;
lfsr = new ExtensionLFSR(extp1, eltlist2);
txtInfo.Clear();
txtInfo.AppendText("LFSR has been created.\r\n");
txtInfo.AppendText("Feedback Polynomial:\r\n" + lfsr.FeedbackPolynomial.ToString() + "\r\n");
txtInfo.AppendText("Initial State:\r\n");
for (int i = 0; i < lfsr.currentState.Length; i++)
txtInfo.AppendText("c_" + i + " = " + lfsr.currentState[i].ToString() + "\r\n");
btnLFSR.Text = "Clock the LFSR";
return;
}
// clock time
lfsr.Clock();
txtInfo.AppendText("\r\nOutput " + s++ + " : " + lfsr.StreamOutput + "\r\n");
txtInfo.AppendText("Current State:\r\n");
for (int i = 0; i < lfsr.currentState.Length; i++)
txtInfo.AppendText("c_" + i + " = " + lfsr.currentState[i].ToString() + "\r\n");
}
public static ExtensionFieldElement One(ExtensionField F)
{
ExtensionFieldElement one = new ExtensionFieldElement(F, new Polynomial(F.DefiningPolynomial.Field, 1));
return one;
}
public ExtensionFieldElement RandomPrimitiveElement(int degree)
{
if (degree > this._primitivePolynomial.Degree - 1)
{
throw new Exception("Element's degree can't be equal to or higher than Primitive polynomial's degree.");
}
Polynomial p = Polynomial.Random(this._baseField, degree, this.rnd);
while (!p.IsPrimitiveElement(this._primitivePolynomial))
{
p = Polynomial.Random(this._baseField, degree, this.rnd);
}
ExtensionFieldElement elt = new ExtensionFieldElement(this, p);
return elt;
}
public static ExtensionPolynomial operator *(ExtensionPolynomial poly1, ExtensionPolynomial poly2)
{
if (poly1.Field.Characteristic != poly2.Field.Characteristic)
{
throw new Exception("Both polynomials should be defined in the same field.");
}
ExtensionFieldElement[] elts = new ExtensionFieldElement[poly1.Degree + poly2.Degree + 1];
for (int i = 0; i < elts.Length; i++)
{
ExtensionFieldElement e = ExtensionFieldElement.One(poly1.Field);
elts[i] = e;
}
ExtensionPolynomial p = new ExtensionPolynomial(elts);
for (int i = 0; i < poly1._coefficients.Length; i++)
{
for (int j = 0; j < poly2._coefficients.Length; j++)
p._coefficients[i + j] += poly1._coefficients[i] * poly2._coefficients[j];
}
int plen = p._coefficients.Length;
for (int i = 0; i < plen - 1; i++)
{
if (p._coefficients[plen - i - 1].Value.IsZero)
Array.Resize(ref p._coefficients, p._coefficients.Length - 1);
else
break;
}
return p;
}
public ExtensionFieldElement Zero()
{
ExtensionFieldElement zero = new ExtensionFieldElement(this.Field, new Polynomial(this.Field.DefiningPolynomial.Field, 0));
return zero;
}
public ExtensionFieldElement One()
{
ExtensionFieldElement one = new ExtensionFieldElement(this.Field, new Polynomial(this.Field.DefiningPolynomial.Field, 1));
return one;
}
public static ExtensionFieldElement Zero(ExtensionField F)
{
ExtensionFieldElement zero = new ExtensionFieldElement(F, new Polynomial(F.DefiningPolynomial.Field, 0));
return zero;
}
private void btnExtPolyAdd_Click(object sender, EventArgs e)
{
ExtensionFieldElement[] eltlist1 = new ExtensionFieldElement[7];
for (int i = 0; i < 7; i++)
eltlist1[i] = ExtF.RandomElement;
ExtensionPolynomial extp1 = new ExtensionPolynomial(eltlist1);
ExtensionFieldElement[] eltlist2 = new ExtensionFieldElement[4];
for (int i = 0; i < 4; i++)
eltlist2[i] = ExtF.RandomElement;
ExtensionPolynomial extp2 = new ExtensionPolynomial(eltlist2);
ExtensionPolynomial result = extp1 + extp2;
txtInfo.Clear();
txtInfo.AppendText("Random Extension Polynomial 1\r\n" + extp1.ToString() + "\r\n");
txtInfo.AppendText("\r\nRandom Extension Polynomial 2\r\n" + extp2.ToString() + "\r\n");
txtInfo.AppendText("\r\nPolynomial 1 + Polynomial 2\r\n" + result.ToString() + "\r\n");
}
public ExtensionFieldElement Zero()
{
ExtensionFieldElement zero = new ExtensionFieldElement(this.Field, new Polynomial(this.Field.DefiningPolynomial.Field, 0));
return(zero);
}
public static ExtensionFieldElement One(ExtensionField F)
{
ExtensionFieldElement one = new ExtensionFieldElement(F, new Polynomial(F.DefiningPolynomial.Field, 1));
return(one);
}
public static ExtensionFieldElement operator -(ExtensionFieldElement element1, ExtensionFieldElement element2)
{
if (element1.Field != element2.Field)
{
throw new Exception("Both elements should be in the same field.");
}
ExtensionFieldElement result = new ExtensionFieldElement();
result.Field = element1.Field;
result.Value = (element1.Value - element2.Value) % element1.Field.DefiningPolynomial;
return result;
}
