/// <param name="s">Output sequence as polynomial</param>
/// <param name="C">Fills the given polynomial with LFSR Connection Polynomial</param>
/// <returns>Returns the Linear Complexity of given sequence</returns>
public static int BerlekampMassey(Polynomial s, out Polynomial Conn)
{
Polynomial C = new Polynomial(s.Field, 1);
Polynomial B = new Polynomial(s.Field, 1);
int N = s.Degree + 1;
int L = 0;
int m = 1;
FiniteFieldElement b = s.Field.Elements[1];
int n;
for (n = 0; n < N; n++)
{
// calculate discrepency
FiniteFieldElement d = new FiniteFieldElement();
d = s.Coefficients[n];
for (int i = 1; i <= L; i++)
{
try
{
d += C.Coefficients[i] * s.Coefficients[n - i];
}
catch { }
}
if (d.Value == 0)
{
m++;
}
else if (2 * L <= n)
{
Polynomial T = new Polynomial();
T = C;
Polynomial c1 = Polynomial.GenerateFromTerm(s.Field, d * b.Inverse, m);
C = C - (c1 * B);
L = n + 1 - L;
B = T;
b = d;
m = 1;
}
else
{
Polynomial c1 = Polynomial.GenerateFromTerm(s.Field, d * b.Inverse, m);
C = C - (c1 * B);
m++;
}
}
Conn = C;
return(L);
}
/// <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 static FiniteFieldElement operator *(FiniteFieldElement element1, FiniteFieldElement element2)
{
if (element1.Field.Characteristic != element2.Field.Characteristic)
{
throw new Exception("Both elements should be in the same field.");
}
FiniteFieldElement result = new FiniteFieldElement();
result.Field = element1.Field;
result.Value = (element1.Value * element2.Value) % element1.Field.Characteristic;
return(result);
}
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 void Clock()
{
FiniteFieldElement r = new FiniteFieldElement();
r.Field = _feedbackPolynomial.Field;
r.Value = 0;
// 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;
}
/// <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 static Polynomial operator -(Polynomial poly1, Polynomial poly2)
{
if (poly1.Field.Characteristic != poly2.Field.Characteristic)
{
throw new Exception("Both polynomials should be defined in the same field.");
}
FiniteFieldElement[] elts = poly1.Degree > poly2.Degree ? (FiniteFieldElement[])poly1.Coefficients.Clone() : (FiniteFieldElement[])poly2.Coefficients.Clone();
Polynomial p = new Polynomial(elts);
int len = Math.Min(poly1.Degree, poly2.Degree);
for (int i = 0; i <= len; i++)
{
p._coefficients[i] = poly1._coefficients[i] - poly2._coefficients[i];
}
FiniteFieldElement sifir = new FiniteFieldElement();
sifir.Field = p.Field;
sifir.Value = 0;
for (int i = len + 1; i < p._coefficients.Length; i++)
{
p._coefficients[i] = sifir - p._coefficients[i];
}
int plen = p._coefficients.Length;
for (int i = 0; i < plen - 1; i++)
{
if (p._coefficients[plen - i - 1].Value == 0)
{
Array.Resize(ref p._coefficients, p._coefficients.Length - 1);
}
else
{
break;
}
}
return(p);
}
public FiniteField(int p)
{
if (!MathTools.IsPrime(p))
{
throw new Exception("p should be a prime number.");
}
_Elements = new FiniteFieldElement[0];
for (int i = 0; i < p; i++)
{
FiniteFieldElement elt = new FiniteFieldElement();
elt.Value = i;
elt.Field = this;
Array.Resize(ref _Elements, _Elements.Length + 1);
_Elements[_Elements.Length - 1] = elt;
}
this._Characteristic = p;
this._Order = p - 1;
}
public LFSR(Polynomial feedbackPolynomial, FiniteFieldElement[] 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;
periodOncedenHesaplandiysa = false;
}
public void Clock()
{
FiniteFieldElement r = new FiniteFieldElement();
r.Field = _feedbackPolynomial.Field;
r.Value = 0;
// 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 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 static FiniteFieldElement operator -(FiniteFieldElement element1, FiniteFieldElement element2)
{
if (element1.Field.Characteristic != element2.Field.Characteristic)
{
throw new Exception("Both elements should be in the same field.");
}
FiniteFieldElement result = new FiniteFieldElement();
result.Field = element1.Field;
result.Value = (element1.Value - element2.Value) % element1.Field.Characteristic;
if (result.Value < 0)
result.Value += result.Field.Characteristic;
return result;
}
public static Polynomial operator -(Polynomial poly1, Polynomial poly2)
{
if (poly1.Field.Characteristic != poly2.Field.Characteristic)
{
throw new Exception("Both polynomials should be defined in the same field.");
}
FiniteFieldElement[] elts = poly1.Degree > poly2.Degree ? (FiniteFieldElement[])poly1.Coefficients.Clone() : (FiniteFieldElement[])poly2.Coefficients.Clone();
Polynomial p = new Polynomial(elts);
int len = Math.Min(poly1.Degree, poly2.Degree);
for (int i = 0; i <= len; i++)
p._coefficients[i] = poly1._coefficients[i] - poly2._coefficients[i];
FiniteFieldElement sifir = new FiniteFieldElement();
sifir.Field = p.Field;
sifir.Value = 0;
for (int i = len + 1; i < p._coefficients.Length; i++)
p._coefficients[i] = sifir - p._coefficients[i];
int plen = p._coefficients.Length;
for (int i = 0; i < plen - 1; i++)
{
if (p._coefficients[plen - i - 1].Value == 0)
Array.Resize(ref p._coefficients, p._coefficients.Length - 1);
else
break;
}
return p;
}
/// <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);
}
FiniteFieldElement NonLinearCombiner(FiniteFieldElement X1, FiniteFieldElement X2, FiniteFieldElement X3, FiniteFieldElement X4)
{
return (X1 * X3) + (X2 * X4);
}
public FiniteField(int p)
{
if (!MathTools.IsPrime(p))
throw new Exception("p should be a prime number.");
_Elements = new FiniteFieldElement[0];
for (int i = 0; i < p; i++)
{
FiniteFieldElement elt = new FiniteFieldElement();
elt.Value = i;
elt.Field = this;
Array.Resize(ref _Elements, _Elements.Length + 1);
_Elements[_Elements.Length - 1] = elt;
}
this._Characteristic = p;
this._Order = p - 1;
}
private bool IsEqualStates(FiniteFieldElement[] s1, FiniteFieldElement[] s2)
{
bool kontrol = true;
for (int i = 0; i < s1.Length; i++)
{
if (s1[i].Value != s2[i].Value)
{
kontrol = false;
break;
}
}
return kontrol;
}
/// <param name="s">Output sequence as polynomial</param>
/// <param name="C">Fills the given polynomial with LFSR Connection Polynomial</param>
/// <returns>Returns the Linear Complexity of given sequence</returns>
public static int BerlekampMassey(Polynomial s, out Polynomial Conn)
{
Polynomial C = new Polynomial(s.Field, 1);
Polynomial B = new Polynomial(s.Field, 1);
int N = s.Degree + 1;
int L = 0;
int m = 1;
FiniteFieldElement b = s.Field.Elements[1];
int n;
for (n = 0; n < N; n++)
{
// calculate discrepency
FiniteFieldElement d = new FiniteFieldElement();
d = s.Coefficients[n];
for (int i = 1; i <= L; i++)
{
try
{
d += C.Coefficients[i] * s.Coefficients[n - i];
}
catch { }
}
if (d.Value == 0)
{
m++;
}
else if (2 * L <= n)
{
Polynomial T = new Polynomial();
T = C;
Polynomial c1 = Polynomial.GenerateFromTerm(s.Field, d * b.Inverse, m);
C = C - (c1 * B);
L = n + 1 - L;
B = T;
b = d;
m = 1;
}
else
{
Polynomial c1 = Polynomial.GenerateFromTerm(s.Field, d * b.Inverse, m);
C = C - (c1 * B);
m++;
}
}
Conn = C;
return L;
}
/// <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);
}
