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This work presents a new framework for Gröbner basis computations with Boolean polynomials. Boolean polynomials can be modelled in a rather simple way, with both coefficients and degree per variable lying in {0, 1}. The ring of Boolean polynomials is, however, not a polynomial ring, but rather the quotient ring of the polynomial ring over the field with two… (More)

We present foundational work on standard bases over rings and on Boolean Gröbner bases in the framework of Boolean functions. The research was motivated by our collaboration with electrical engineers and computer scientists on problems arising from formal verification of digital circuits. In fact, algebraic modelling of formal verification problems is… (More)

This work presents a new framework for Gröbner basis computations with Bool-ean polynomials. Boolean polynomials can be modeled in a rather simple way, with both coefficients and degree per variable lying in {0, 1}. The ring of Bool-ean polynomials is, however, not a polynomial ring, but rather the quotient ring of the polynomial ring over the field with… (More)

This work is devoted to attacking the small scale variants of the Advanced Encryption Standard (AES) via systems that contain only the initial key variables. To this end, we introduce a system of equations that naturally arises in the AES, and then eliminate all the intermediate variables via normal form reductions. The resulting system in key variables… (More)

An information service for mathematical software is presented. Publications and software are two closely connected facets of mathematical knowledge. This relation can be used to identify mathematical software and find relevant information about it. The approach and the state of the art of the information service are described here.

We apply the PolyBoRi framework for Gröbner bases computations with Boolean polynomials to bit-valued problems from algebraic cryptanalysis and formal verification. First, we proposed zero-suppressed binary decision diagrams (ZDDs) as a suitable data structure for Boolean poly-nomials. Utilizing the advantages of ZDDs we develop new reduced normal form… (More)

This paper introduces a new method for interpolation of Boolean functions using Boolean polynomials. It was motivated by some problems arising from computational biology, for reverse engineering the structure of mechanisms in gene regulatory networks. For this purpose polynomial expressions have to be generated, which match known state combinations observed… (More)

We overview numerous algorithms in computational D-module theory together with the theoretical background as well as the implementation in the computer algebra system Singular. We discuss new approaches to the computation of Bern-stein operators, of logarithmic annihilator of a polynomial, of annihilators of rational functions as well as complex powers of… (More)

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