*****************
Design Philosophy
*****************

The core of VBF library is the VBF class which represents Vector Boolean Functions whose data members and member functions make use of the NTL modules listed in Table :ref:`NTL Modules <NTLModules>`. However, some new cryptography-related member functions were added to the previous modules. Besides, new modules which are not present in NTL, are defined and they are listed in Table :ref:`New Modules <NewModules>`.

.. _NTLModules:

+---------------------------------------------------------------------------------+
| NTL modules used in VBF                                                         |
+=================+===============================================================+
| **CLASS NAME**  | **DESCRIPTION**                                               |
+-----------------+---------------------------------------------------------------+
| :code:`GF2`     | Galois Field of order :math:`2` denoted by :math:`\gf{GF(2)}` |
+-----------------+---------------------------------------------------------------+
| :code:`vec_GF2` | Vectors over :math:`\gf{GF(2)}`                               |
+-----------------+---------------------------------------------------------------+
| :code:`mat_GF2` | Matrices over :math:`\gf{GF(2)}`                              |
+-----------------+---------------------------------------------------------------+
| :code:`RR`      | Arbitrary-precision floating point numbers                    |
+-----------------+---------------------------------------------------------------+
| :code:`vec_RR`  | Vectors over reals                                            |
+-----------------+---------------------------------------------------------------+
| :code:`mat_RR`  | Matrices over reals                                           |
+-----------------+---------------------------------------------------------------+
| :code:`ZZ`      | Signed, arbitrary length integers                             |
+-----------------+---------------------------------------------------------------+
| :code:`vec_ZZ`  | Vectors over integers                                         |
+-----------------+---------------------------------------------------------------+
| :code:`mat_ZZ`  | Matrices over integers                                        |
+-----------------+---------------------------------------------------------------+
| :code:`GF2X`    | Implements polynomial arithmetic modulo 2                     |
+-----------------+---------------------------------------------------------------+
| :code:`GF2E`    | Polynomials in :math:`F_2[X]` modulo a polynomial :math:`P`   |
+-----------------+---------------------------------------------------------------+
| :code:`GF2EX`   | Polynomials over :math:`\gf{GF2E}`                            |
+-----------------+---------------------------------------------------------------+
| :code:`vec_GF2E`| Vectors over :math:`\gf{GF2E}`                                |
+-----------------+---------------------------------------------------------------+

Note that the modulus *P* in :math:`\gf{GF2E}` may be any polynomial with degree greater than 0, not necessarily irreducible. Objects of the class :math:`\gf{GF2E}` are represented as a :math:`\gf{GF2X}` of degree less than the degree of *P*. :math:`\gf{GF2EX}` can be used, for example, for arithmetic in :math:`\gf{GF(2^n)[X]}`.

.. _NewModules:

+-------------------------------------------------------------------+
| New modules created for VBF                                       |
+=================+=================================================+
| **CLASS NAME**  | **DESCRIPTION**                                 |
+-----------------+-------------------------------------------------+
| :code:`pol`     | Polynomial in ANF of a Boolean Function         |
+-----------------+-------------------------------------------------+
| :code:`vec_pol` | Polynomials in ANF of a Vector Boolean Function |
+-----------------+-------------------------------------------------+

The main file in the library, called *VBF.h* has the definitions of the objects described in the next chapters.