PolyBoRi Master Reference
The core of PolyBoRi 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.
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 Gröbner base computation. PolyBoRi features a powerful reference
implementation for Gröbner basis computation.
The structure of the framework is illustrated as follows.
Documentation
The documentation of the PolyBoRi framework and incorporated works can be
accessed via the following documents.
PolyBoRi Tutorial
Release 0.8-3
PolyBoRi: Main Page
Python: package polybori
External documents
Dive into Python
ipython Documentation
Further Reading
See the following references for the mathematical background of the PolyBoRi
framework and related articles.
-
Brickenstein. Michael; Dreyer, Alexander.
Gröbner-free normal forms for Boolean polynomials,
Journal of Symbolic Computation, Volume 48, January 2013, pp. 37-53,
ISSN 0747-7171, doi: 10.1016/j.jsc.2011.04.002.
-
Brickenstein, Michael; Dreyer, Alexander.
PolyBoRi: A framework for Gröbner-basis computations with Boolean polynomials,
J. Symb. Comput. 44, No. 9, 1326-1345 (2009).
-
Albrecht, Martin; Cid, Carlos. Algebraic techniques in differential cryptanalysis,
In: Fast Software Encryption,
Lecture Notes in Computer Science Volume 5665, 2009, pp 193-208
-
Kreuzer, MartinAlgebraic attacks Galore!
Groups-Complexity-Cryptology,
Volume 1 (2009), No. 2, 231-259.
-
Eröcal, Burcin; Stein, William.
The Sage project: Unifying free mathematical software to create a
viable alternative to Magma, Maple, Mathematica and MATLAB,
http://www.sagemath.org
-
Brickenstein, Michael. Slimgb: Gröbner bases with slim polynomials,
Rev. Mat. Complut. 23, No. 2, 453-466 (2010).
-
Brickenstein, Michael.
Boolean Gröbner bases. Theory, algorithms and applications,
Berlin: Logos Verlag; Kaiserslautern: TU Kaiserslautern, Fachbereich Mathematik (Diss. 2010) (ISBN 978-3-8325-2597-2/pbk). x, 149 p. (2010).
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Chai, Fengjuan; Gao, Xiao-Shan; Yuan, Chunming.
A characteristic set method for solving Boolean equations and applications in cryptanalysis of stream ciphers,
J. Syst. Sci. Complex. 21, No. 2, 191-208 (2008).
-
Eibach, Tobias; Völkel, Gunnar; Pilz, Enrico.
Optimising Gröbner bases on Bivium,
Math. Comput. Sci. 3, No. 2, 159-172 (2010).
-
Bulygin, Stanislav; Brickenstein, MichaelObtaining and solving systems of equations in key variables only for the small variants of AES,
Math. Comput. Sci. 3, No. 2, 185-200 (2010).
-
Sato, Yosuke; Inoue, Shutaro; Suzuki, Akira; Nabeshima, Katsusuke;
Sakai, Ko.
Boolean Gröbner bases,
J. Symb. Comput. 46, No. 5, 622-632 (2011).
-
Albrecht, Martin; Cid, Carlos; Dullien, Thomas; Faugère, Jean-Charles; Perret, Ludovic.
Algebraic precomputations in differential and integral cryptanalysis. ,
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).
- Brickenstein, Michael; Dreyer, Alexander.
PolyBoRi: A Gröbner Basis Framework for Boolean
Polynomials,
Reports of Fraunhofer ITWM, No. 122,
Kaiserslautern, Germany, 2007.
- Brickenstein, Michael; Dreyer, Alexander.
PolyBoRi: A framework for Gröbner basis computations with
Boolean polynomials,
Electronic Proceedings of the MEGA 2007 - Effective Methods in
Algebraic Geometry,
Strobl, Austria, June 2007.
- Brickenstein, Michael.
Slimgb: Gröbner Bases with Slim Polynomials,
Reports On Computer Algebra, Centre for Computer Algebra, University of
Kaiserslautern, Volume 25, September 2005
- Somenzi, Fabio.
CUDD: CU Decision Diagram Package,
Department of Electrical and Computer Engineering,
University of Colorado at Boulder
-
Gregory V. Bard,
Accelerating Cryptanalysis with the Method of Four
Russians,
Preprint July 22, 2006.
Links
PolyBoRi's home at
SourceForge
PolyBoRi's project page at Fraunhofer ITWM

Copyright © 2007-2012 The PolyBoRi, Team