/// <summary> /// Creates a new GF2nField of degree <c>i</c> and uses the given <c>G</c> as field polynomial. /// <para>The <c>G</c> is checked whether it is irreducible. This can take some time if <c>Degree</c> is huge!</para> /// </summary> /// /// <param name="Degree">The degree of the GF2nField</param> /// <param name="G">The field polynomial to use</param> public GF2nPolynomialField(int Degree, GF2Polynomial G) { if (Degree < 3) throw new ArgumentException("degree must be at least 3"); if (G.Length != Degree + 1) throw new Exception(); if (!G.IsIrreducible()) throw new Exception(); DegreeN = Degree; // fieldPolynomial = new Bitstring(polynomial); FieldPoly = G; ComputeSquaringMatrix(); int k = 2; // check if the polynomial is a trinomial or pentanomial for (int j = 1; j < FieldPoly.Length - 1; j++) { if (FieldPoly.TestBit(j)) { k++; if (k == 3) _tc = j; if (k <= 5) _pc[k - 3] = j; } } if (k == 3) _isTrinomial = true; if (k == 5) _isPentanomial = true; Fields = new ArrayList(); Matrices = new ArrayList(); }
/// <summary> /// Tests random polynomials of degree (n+1) until an irreducible is found and stores the result in <c>field polynomial</c>. /// This can take very long for huge degrees. /// </summary> /// /// <returns>Returns true</returns> private bool TestRandom() { int l; bool done = false; FieldPoly = new GF2Polynomial(DegreeN + 1); l = 0; while (!done) { l++; FieldPoly.Randomize(); FieldPoly.SetBit(DegreeN); FieldPoly.SetBit(0); if (FieldPoly.IsIrreducible()) { done = true; return done; } } return done; }
/// <summary> /// Tests all trinomials of degree (n+1) until a irreducible is found and stores the result in <c>field polynomial</c>. /// Returns false if no irreducible trinomial exists in GF(2^n). This can take very long for huge degrees. /// </summary> /// /// <returns>Returns true if an irreducible trinomial is found</returns> private bool TestTrinomials() { int i, l; bool done = false; l = 0; FieldPoly = new GF2Polynomial(DegreeN + 1); FieldPoly.SetBit(0); FieldPoly.SetBit(DegreeN); for (i = 1; (i < DegreeN) && !done; i++) { FieldPoly.SetBit(i); done = FieldPoly.IsIrreducible(); l++; if (done) { _isTrinomial = true; _tc = i; return done; } FieldPoly.ResetBit(i); done = FieldPoly.IsIrreducible(); } return done; }
/// <summary> /// Tests all pentanomials of degree (n+1) until a irreducible is found and stores the result in <c>field polynomial</c>. /// Returns false if no irreducible pentanomial exists in GF(2^n). /// This can take very long for huge degrees. /// </summary> /// /// <returns>Returns true if an irreducible pentanomial is found</returns> private bool TestPentanomials() { int i, j, k, l; bool done = false; l = 0; FieldPoly = new GF2Polynomial(DegreeN + 1); FieldPoly.SetBit(0); FieldPoly.SetBit(DegreeN); for (i = 1; (i <= (DegreeN - 3)) && !done; i++) { FieldPoly.SetBit(i); for (j = i + 1; (j <= (DegreeN - 2)) && !done; j++) { FieldPoly.SetBit(j); for (k = j + 1; (k <= (DegreeN - 1)) && !done; k++) { FieldPoly.SetBit(k); if (((DegreeN & 1) != 0) | ((i & 1) != 0) | ((j & 1) != 0) | ((k & 1) != 0)) { done = FieldPoly.IsIrreducible(); l++; if (done) { _isPentanomial = true; _pc[0] = i; _pc[1] = j; _pc[2] = k; return done; } } FieldPoly.ResetBit(k); } FieldPoly.ResetBit(j); } FieldPoly.ResetBit(i); } return done; }