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

改进并结合 Gröbner 基和 SAT 求解技术进行代数密码分析

• 批准号: 171743725
• 负责人: Professor Dr. Johannes Buchmann
• 金额: --
• 依托单位: Fachbereich Mathematik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2010
• 资助国家: 德国
• 起止时间: 2009-12-31 至 2016-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/171743725?language=en
• 关键词: Improving; Combining; Gr; bner; bases

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.

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密码原语对于在线银行，电子商务，电子邮件通信等应用程序一直是至关重要的。块密码是构建密码协议的成熟构建块。在这个项目中，我们解决了分组密码的密码分析。分组密码的代数密码分析是近年来发展迅速的一个研究领域。另一方面，随着时间的推移，该方法的一些局限性变得明显。因此，我们的目标是追求一个新的代数和传统的统计攻击相结合的最近的趋势。我们将特别关注采用模运算提供非线性的密码：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，以及提供有效攻击所必需的计算机代数工具。在代数统计密码分析的特定背景下，快速发现矛盾和解决系统是我们在这个项目中面临的一个挑战。我们相信，两个申请小组的能力和经验将为成功实现项目目标提供一个很好的机会。