*******
Summary
*******

Table :ref:`Representations Table <Representation>` lists the member functions related to
methods of vector Boolean functions initialization. Table
:ref:`Characterizations Table <Characterization>` lists the member functions related to the characterizations of vector Boolean functions as described above. Most of the member
functions of *VBF* have an in-line definition, for instance: :code:`void TT(NTL::mat_GF2& X, VBF& F)` is also defined as :code:`inline NTL::mat_GF2 TT(VBF& F)`.

.. _Representation:

+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Representation of VBF													                                                                     |
+=============================================================+==============================================================================================================================+
| **SYNTAX**                                                  | **DESCRIPTION**                                                                                                              |
+-------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------+
| :code:`void puttt(const NTL::mat_GF2& X)`                   | :math:`\matr{TT}_F = \matr{T}`                                                                                               |
+-------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------+
| :code:`void putHexTT(istream& s)`                           | VBF which has an hexadecimal representation of its truth table defined by *s*                                                |
+-------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------+
| :code:`void putDecTT(const NTL::vec_long& d,const long& m)` | VBF with a decimal representation of its truth table defined by *d* and *m* is the number of component Boolean functions     |
+-------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------+
| :code:`void putltt(const NTL::mat_GF2& L)`                  | :math:`\matr{LTT}_F = \matr{L}`												     |
+-------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------+
| :code:`void putctt(const NTL::mat_ZZ& C)` 		      | :math:`\matr{CTT}_F = \matr{C}`												     |
+-------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------+
| :code:`void putirrpol(GF2X& g)`                             | Set *F* by its trace *f* and the irreducible polynomial *g*              						     |
| :code:`void puttrace(string& f)`                            |                                                                     							     |
+-------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------+
| :code:`void putpol(vec_pol& p)`                             | Set *F* with Polynomials in *ANF* equals to *p*                 							     |
+-------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------+
| :code:`void putanf(const NTL::mat_GF2& A)`                  | :math:`\matr{ANF}_F = \matr{A}`                                 							     |
+-------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------+
| :code:`void putchar(const NTL::mat_ZZ& C)`                  | :math:`\matr{Img}(F) = \matr{C}`                                 							     |
+-------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------+
| :code:`void putwalsh(const NTL::mat_ZZ& W)`                 | :math:`\matr{WS}(F) = \matr{W}`                                 							     |
+-------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------+
| :code:`void putper(const NTL::vec_ZZ& v)`                   | VBF which is a permutation defined by :math:`\vec{v}`	          							     |
+-------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------+
| :code:`void putexp_comp(const NTL::vec_ZZ& v)`              | VBF defined by Expansion and Compression DES vector :math:`\vec{v}`                      				     |
+-------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------+
| :code:`void putsbox(const NTL::mat_ZZ& S)`                  | VBF which is a DES S-Box defined by *S*                 	       							     |
+-------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------+

.. _Characterization:

+----------------------------------------------------------------------------------------------------------------------------------------------------------------+
| Characterization of VBF                                                                                                                                        |
+==============================================================+=================================================================================================+
| **SYNTAX**                                                   | **DESCRIPTION**                                                                                 |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+
| :code:`void TT(NTL::mat_GF2& X, VBF& F)`                     | :math:`\matr{X}=\matr{T}_F`                                                                     |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+
| :code:`void getHexTT(ostream& s)`                            | *s* is the hexadecimal representation of the truth table of *F*                                 |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+
| :code:`NTL::vec_long getDecTT() const`                       | Decimal representation of the truth table                                                       |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+
| :code:`long weight(VBF& F)`                                  | Weight of *F*           	         			                                 |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+
| :code:`void LTT(NTL::mat_GF2& X, VBF& F)`                    | :math:`\matr{X}=\matr{LTT}_F`				                                         |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+
| :code:`void CTT(NTL::mat_ZZ& X, VBF& F)`                     | :math:`\matr{X}=\matr{CTT}_F`				                                         |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+
| :code:`void Trace(GF2EX& f, VBF& F)`                         | *F* has a trace representation defined by *f*	                                                 |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+
| :code:`void Pol(NTL_SNS ostream& s, VBF& F)`                 | *s* contains the Polynomials in *ANF* of *F*                                                    |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+
| :code:`void ANF(NTL::mat_GF2& X, VBF& F)`                    | :math:`\matr{X}=\matr{ANF}_F`                                                                   |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+
| :code:`void Charact(NTL::mat_ZZ& X, VBF& F)`                 | :math:`\matr{X}=\matr{Img(F)}`                                                                  |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+
| :code:`void Walsh(NTL::mat_ZZ& X, VBF& F)`                   | :math:`\matr{X}=\matr{WS}(F)`                                                                   |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+
| :code:`void LAT(NTL::mat_ZZ& X, VBF& F)`                     | :math:`\matr{X}=\matr{LP}(F)`                                                                   |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+
| :code:`void lp(NTL::RR& x, VBF& F)`                          | :math:`\crit{lp}(F)=x`				                                                 |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+
| :code:`void linear(NTL_SNS ostream& s, VBF& F, ZZ& x)`       | Linear relations associated with the value *x* of the Linear Profile of *F*                     |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+
| :code:`void ProbLin(NTL::RR& x, VBF& F, NTL::ZZ& w)`         | Probability of Linear relations associated with the value *w* of the Linear Profile of *F*      |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+
| :code:`void DAT(NTL::mat_ZZ& X, VBF& F)`                     | :math:`\matr{X}=\matr{DP}(F)`                                                                   |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+
| :code:`void dp(NTL::RR& x, VBF& F)` 			       | :math:`\crit{dp}(F)=x`								                 |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+
| :code:`void differential(NTL_SNS ostream& s, VBF& F, ZZ& x)` | Differential relations associated with the value *x* of the Differential Profile of *F*         |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+
| :code:`void ProbDif(NTL::RR& x, VBF& F, NTL::ZZ& w)`         | Probability of characteristics associated with the value *w* of the Differential Profile of *F* |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+
| :code:`void AC(NTL::mat_ZZ& X, VBF& F)`                      | :math:`\matr{X}=\matr{R}(F)`                                                                    |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+
| :code:`NTL::mat_GF2 LS(VBF& F)`                              | Returns a matrix whose rows are the linear structures                                           |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+ 
| :code:`void printFWH(NTL_SNS ostream& s, VBF& F)`            | Frequency distribution of the absolute values of the Walsh Spectrum				 |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+
| :code:`void printFAC(NTL_SNS ostream& s, VBF& F)`            | Frequency distribution of the absolute values of the Autocorrelation Spectrum                   |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+
| :code:`void Cycle(NTL::vec_ZZ& v, VBF& F)`                   | :math:`\vec{v}` is the Cycle Structure							         |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+
| :code:`void printCycle(NTL_SNS ostream& s, VBF& F)` 	       | Print Cycle Structure									         |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+
| :code:`NTL::mat_GF2 fixedpoints(VBF& F)` 		       | Return fixed points										 |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+
| :code:`NTL::mat_GF2 negatedfixedpoints(VBF& F)` 	       | Return negated fixed points									 |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+ 
| :code:`void PER(NTL::vec_ZZ& v, VBF& F)`                     | :math:`\vec{v}` is the permutation vector defined by *F*                                        |
+--------------------------------------------------------------+-------------------------------------------------------------------------------------------------+