Improving and Combining Gröbner bases and SAT solving techniques for algebraic cryptanalysis

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In the era of ubiquitous use of the Internet the questions of privacy and confidentiality play a very important role. Therefore, evaluating cryptographic primitives that provide the above properties has always been crucial for applications like online banking, eCommerce, e-mail communications etc. Block ciphers are well-established building blocks for constructing cryptographic protocols. In this project we address the cryptanalysis of block ciphers. In recent years algebraic cryptanalysis of block ciphers became a rapidly developing area of research. On the other side, some limitations of the method became apparent over the time. Our goal is, therefore, to pursue a quite recent trend of combining new algebraic and conventional statistical attacks. We will pay a special attention to ciphers that employ modular arithmetic to provide non-linearity: algebraic aspects of such an analysis are novel. Within this project we will develop cryptanalytic methods of combined attacks as well as tools from computer algebra that are absolutely necessary to provide efficient attacks. Fast contradiction finding and system solving in the specific context of algebraic-statistic cryptanalysis is a challenge we address in this project. We believe that united competence and experience of the two applying groups will give a good chance to successfully fulfill the goals of the project.