<HTML>
<HEAD>
<TITLE>PolyBoRi Master Reference</TITLE>
</HEAD>
<BODY>
<h1>PolyBoRi Master Reference</h1>

<p> The core of <i>PolyBoRi</i> is a C++ library, which provides high-level data types
for Boolean polynomials and monomials, exponent vectors, as well as for the
underlying polynomial rings and subsets of the powerset of the Boolean
variables. As a unique approach, binary decision diagrams are 
used as internal storage type for polynomial structures.</p>	

<p> On top of this C++-library we provide a Python interface. This allows
parsing of complex polynomial systems, as well as sophisticated and extendable
strategies for Gr&ouml;bner base computation. <i>PolyBoRi</i> features a powerful reference
implementation for Gr&ouml;bner basis computation.</p>			

The structure of the framework is illustrated as follows.
<p><img src="images/overview.png" alt="Overview" align="middle" border="0">

<H2>Documentation</H2>
The documentation of the <i>PolyBoRi</i> framework and incorporated works can be
accessed via the following documents.

$PBDOCLINKS

<h3>External documents</h3>
<p><a href="http://www.diveintopython.org/">
Dive into Python</a></p>
<p><a href="http://ipython.scipy.org/moin/Documentation/">
ipython Documentation</a></p>

<h2>Further Reading</h2>
See the following references for the mathematical background of the <i>PolyBoRi</i>
framework and related articles. 
 <ul>
      <li>
        Brickenstein. Michael; Dreyer, Alexander.
        <i>Gr&ouml;bner-free normal forms for Boolean polynomials</i>,
        Journal of Symbolic Computation, Volume 48, January 2013, pp. 37-53,
        ISSN 0747-7171, doi: 10.1016/j.jsc.2011.04.002.
      </li>
      <li>
        Brickenstein, Michael; Dreyer, Alexander.
        <i>PolyBoRi: A framework for Gr&ouml;bner-basis computations with Boolean polynomials</i>,
        J. Symb. Comput. 44, No. 9, 1326-1345 (2009).
      </li>
      <li>
        Albrecht, Martin; Cid, Carlos. <i>Algebraic techniques in differential cryptanalysis</i>,
        In: <i>Fast Software Encryption</i>,
        Lecture Notes in Computer Science Volume 5665, 2009, pp 193-208 
      </li>
      <li>
        Kreuzer, Martin<i>Algebraic attacks Galore!</i>
        Groups-Complexity-Cryptology,
        Volume 1 (2009), No. 2, 231-259.
      </li>
      <li>
        Er&ouml;cal, Burcin; Stein, William.
        <i>The Sage project: Unifying free mathematical software to create a
          viable alternative to Magma, Maple, Mathematica and MATLAB</i>, 
             <a href="http://www.sagemath.org">http://www.sagemath.org</a>
      </li>
      <li>
        Brickenstein, Michael. <i>Slimgb: Gr&ouml;bner bases with slim polynomials</i>,
        Rev. Mat. Complut. 23, No. 2, 453-466 (2010).
      </li>
      <li>
        Brickenstein, Michael.
        <i>Boolean Gr&ouml;bner bases. Theory, algorithms and applications</i>,
        Berlin: Logos Verlag; Kaiserslautern: TU Kaiserslautern, Fachbereich Mathematik (Diss. 2010) (ISBN 978-3-8325-2597-2/pbk). x, 149&nbsp;p. (2010).
      </li>
      <li>
        Chai, Fengjuan; Gao, Xiao-Shan; Yuan, Chunming.
        <i>A characteristic set method for solving Boolean equations and applications in cryptanalysis of stream ciphers</i>,
        J. Syst. Sci. Complex. 21, No. 2, 191-208 (2008).
        
      </li>
      <li>
        Eibach, Tobias; V&ouml;lkel, Gunnar; Pilz, Enrico.
        <i>Optimising Gr&ouml;bner bases on Bivium</i>,
        Math. Comput. Sci. 3, No. 2, 159-172 (2010).
      </li>
      <li>
        Bulygin, Stanislav; Brickenstein, Michael<i>Obtaining and solving systems of equations in key variables only for the small variants of AES</i>,
        
        Math. Comput. Sci. 3, No. 2, 185-200 (2010).
      </li>
      <li>
        Sato, Yosuke; Inoue, Shutaro; Suzuki, Akira; Nabeshima, Katsusuke;
        Sakai, Ko.
        <i>Boolean Gr&ouml;bner bases</i>,
        J. Symb. Comput. 46, No. 5, 622-632 (2011).
      </li>
      <li>
        
        Albrecht, Martin; Cid, Carlos; Dullien, Thomas; Faug&egrave;re, Jean-Charles; Perret, Ludovic.
        <i>Algebraic precomputations in differential and integral cryptanalysis. </i>,
        Lai, Xuejia (ed.) et al., Information security and cryptology. 6th
        international conference, Inscrypt 2010, Shanghai, China, October 20-24, 2010. Revised selected papers. Berlin: Springer (ISBN 978-3-642-21517-9/pbk). Lecture Notes in Computer Science 6584, 387-403 (2011).
      </li>
      <li>Brickenstein, Michael; Dreyer, Alexander.
        <i>PolyBoRi: A Gr&ouml;bner Basis Framework for Boolean
          Polynomials</i>,
        <a 
          href="http://www.itwm.fhg.de/zentral/download/berichte/bericht122.pdf">
          Reports of Fraunhofer ITWM, No. 122,
        </a>
        Kaiserslautern, Germany, 2007.
      </li>
      
       <li>Brickenstein, Michael; Dreyer, Alexander.
       <i>PolyBoRi: A framework for Gr&ouml;bner basis computations with
	Boolean polynomials</i>,
     
        <a href="http://www.ricam.oeaw.ac.at/mega2007/openconf/electronic/electronic.html">   Electronic Proceedings of the MEGA 2007&nbsp;- Effective Methods in
 	Algebraic Geometry,
                      </a>
       Strobl, Austria, June 2007.
       </li>
       <li>Brickenstein, Michael.
     
        <a href="http://www.mathematik.uni-kl.de/~zca/Reports_on_ca/35/paper_35_full.ps.gz">  
          <i>Slimgb: Gr&ouml;bner Bases with Slim Polynomials</i></a>, 
        Reports On Computer Algebra, Centre for Computer Algebra, University of         
        Kaiserslautern, Volume 25, September 2005
       </li>
       <li>Somenzi, Fabio.
     
        <a href="http://vlsi.colorado.edu/~fabio/CUDD/">  
          <i> CUDD: CU Decision Diagram Package</i></a>, 
        Department of Electrical and Computer Engineering,
        University of Colorado at Boulder     
       </li>
       <li>
        Gregory V. Bard,
        <a href="http://eprint.iacr.org/2006/251.pdf">  
          <i>Accelerating Cryptanalysis with the Method of Four
            Russians</i></a>, 
        Preprint July 22, 2006.
       </li>
</ul>

<h2>Links</h2>
<p><a href="http://polybori.sourceforge.net"> <i>PolyBoRi</i>'s home at
SourceForge</a></p>
<p> <a href="http://www.itwm.fraunhofer.de/polybori.html"></p>	
<i>PolyBoRi</i>'s project page at Fraunhofer ITWM</a>

<P><img src="images/logo.png" alt="<i>PolyBoRi</i>," align="middle" border="0"></p>	
<P> Copyright &copy; 2007-2012 The <i>PolyBoRi</i>, Team</p>	
</BODY>
</HTML>
