“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.”
I expect great things from PolyBori for the field of algebraic cryptanalysis. If you are interested in polynomial system solving, please also make sure to read the paper by the authors on the techniques used in PolyBori in the electronic proceedings of MEGA 2007.