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The Implementation and Complexity Analysis of the Branch Gröbner Bases Algorithm Over Boolean Polynomial Rings

In: Computer Mathematics

Author

Listed:
  • Yao Sun

    (SKLOIS, Institute of Information Engineering, CAS)

  • Dingkang Wang

    (KLMM, Academy of Mathematics and Systems Science, CAS)

Abstract

A new branch of Gröbner basis algorithm over boolean ring has been presented in an earlier paper. In this paper, the detailed implementation and a rough complexity analysis is given. The branch Gröbner basis algorithm implements a variation of the F5 algorithm and bases on the ZDD data structure, which is also the data structure of the framework PolyBoRi. This branch Gröbner basis algorithm is mainly used to solve algebraic systems and attack multivariable cryptosystems, and its goal is to lower the complexity in each branch and expect better total complexity. An important proposition ensures the two original criteria of the non-branch F5 algorithm could still reject almost all unnecessary computations in this new branch algorithm. The timings show this branch algorithm performs very well for randomly generated systems as well as a class of stream ciphers which is generated by the linear feedback shift register (LFSR).

Suggested Citation

  • Yao Sun & Dingkang Wang, 2014. "The Implementation and Complexity Analysis of the Branch Gröbner Bases Algorithm Over Boolean Polynomial Rings," Springer Books, in: Ruyong Feng & Wen-shin Lee & Yosuke Sato (ed.), Computer Mathematics, edition 127, pages 157-169, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-43799-5_14
    DOI: 10.1007/978-3-662-43799-5_14
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