Collaborative Research: SaTC: CORE: Medium: Theoretical Foundations of Block Ciphers

分组密码，如高级加密标准（AES），是基本的加密算法，在当今使用的大多数安全系统中充当基本的构建块。单独使用AES作为安全通信协议（如传输层安全协议（TLS））的一个组件来保护大部分Internet流量的机密性。因此，必须尽可能地评估现有和新的分组密码设计的安全性。根据密码学家在过去四十年中开发的成熟范例，安全性验证的黄金标准将是基于一些经过充分研究的计算问题的推测硬度来证明安全性。然而，由于极端的效率要求，实际的分组密码逃避了这种可证明安全性的经典范例。相反，信心依赖于数十年的密码分析和无法找到具体的攻击。该项目的主要目的是缩小可证明的安全性与密码分析之间的现有差距，特别是针对有限类别的攻击开发安全证明，并最终根据该项目的新发现设计新的算法和范式。最初的重点将是针对统计攻击的安全性证明，这些攻击试图揭示少量块密码输出中的非随机属性。第二个重点是开发技术来证明对代数攻击的安全性。最后，本课题将对分组密码中尚未被严格研究的重要组成部分进行研究，特别是引入一种新的密钥调度理论。处理将涵盖经典的设计，如替换置换网络，以及较少研究的，如添加-旋转-异或（ARX）密码。该项目的更广泛影响将包括一个旨在弥合理论密码学和密码分析之间差距的研讨会，以及一个本科生研究部分。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Block ciphers, such as the Advanced Encryption Standard (AES), are fundamental cryptographic algorithms which act as basic building blocks in most secure systems in use today. AES alone is used to protect the confidentiality of a large fraction of Internet traffic as a component of secure-communication protocols like Transport Layer Security (TLS). It is therefore imperative to assess the security of existing and new block cipher designs as far as possible. Following a well-established paradigm developed by cryptographers over the last four decades, the gold standard for security validation would be a proof of security based on the conjectured hardness of some well-studied computational problems. However, due to extreme efficiency demands, practical block ciphers evade this classical paradigm of provable security. Instead, confidence relies on decades of cryptanalysis and an inability to find concrete attacks.The main aim of this project is to narrow the existing gap between provable security and cryptanalysis, developing in particular security proofs against limited classes of attacks, and eventually designing new algorithms and paradigms based on the new findings of this project. The initial focus will be on proofs of security against classes of statistical attacks which attempt to uncover non-random properties in a small number of block-cipher outputs. A second thrust will then develop techniques to prove security against algebraic attacks. Finally, this project will initiate the study of important components of block ciphers which have not been studied rigorously so far, introducing in particular a new theory of key schedules. The treatment will cover both classical designs such as substitution-permutation networks, as well as less studied ones such as Add-Rotate-XOR (ARX) ciphers. The broader impacts of this project will include a workshop aimed at bridging the gap between theoretical cryptography and cryptanalysis, as well as an undergraduate research component.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.