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

在互联网无处不在的时代，隐私和保密问题扮演着非常重要的角色。因此，评估提供上述属性的加密原语对于在线银行、电子商务、电子邮件通信等应用程序一直至关重要。分组密码是用于构建加密协议的完善的构建块。在这个项目中，我们处理分组密码的密码分析。近年来，分组密码的代数密码分析成为一个迅速发展的研究领域。另一方面，随着时间的推移，这种方法的一些局限性变得明显起来。因此，我们的目标是追求结合新的代数攻击和传统统计攻击的最新趋势。我们将特别关注使用模算法来提供非线性的密码：这种分析的代数方面是新颖的。在这个项目中，我们将开发组合攻击的密码分析方法以及计算机代数的工具，这些工具对于提供有效的攻击是绝对必要的。在代数统计密码分析的特定背景下，快速发现矛盾和系统求解是我们在本项目中解决的一个挑战。我们相信，两个申请团队的联合能力和经验将为成功实现项目目标提供良好的机会。

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.