TC: Small: The Design of Secure Hash Functions and Block Ciphers

虽然密码学的数学研究已经产生了丰富的理论，虽然密码学的使用已经变得相当广泛，但不幸的是，密码学的理论和实践之间仍然存在着巨大的差距。 这个项目的目标就是弥合这一差距。 重点将放在基本的密码原语的设计和分析上，如哈希函数和块密码，以及从它们派生的其他原语，这些原语既实用又理论上合理。实际上，散列函数和块密码几乎用于任何密码应用中。然而，许多这样的实际应用往往没有足够的理论基础。因此，研究哈希函数的基本设计原则以及如何在应用中恰当地使用哈希函数，已成为一种新的兴趣和紧迫性。本项目将重新审视构建安全哈希函数、分组密码以及由它们构建的各种重要密码原语的基本设计原则。特别是，本项目将研究基于更坚实的理论基础，但仍然足够有效的实际使用的新型结构。 PI将特别关注分析和改进散列函数和分组密码作为消息代理、密钥导出函数、消息认证码、承诺方案和随机预言机的使用。 此外，该项目将研究新的操作模式，以从更简单的固定长度组件（如分组密码和固定长度压缩函数）构建复杂的可变长度原语。 最后，本计划将为在理想安全模型（如随机预言机模型和理想密码模型）下分析密码方案建立更坚实的基础，从而有可能产生更安全的哈希函数和分组密码，以及哈希函数和分组密码在重要密码应用中更安全和/或更有效的使用。 该项目将对技术以及教育和合作产生影响。例如，除了推进密码学理论之外，该项目还将影响安全系统的实际设计。 在适当的情况下，PI将努力将新的原语和协议转化为标准，以便它们可以在实践中使用。 此外，PI定期教授密码学和网络安全课程，并将能够将新成果纳入他所教授的课程。 最后，该项目有一个重要的研究生和博士后培训组成部分。

While the mathematical study of cryptography has yielded a rich theory, and while the use of cryptography has become quite widespread, there is unfortunately still a significant gap between the theory and practice of cryptography. The goal of this project is to bridge this gap. The emphasis will be on the design and analysis of fundamental cryptographic primitives, such as hash functions and block ciphers, as well as other primitives derived from them, that are practical and yet theoretically sound. Indeed, hash functions and block ciphers are used in almost any cryptographic application. Yet, many such practical applications often do not have sufficient theoretical foundations behind them. Therefore, there is renewed interest and urgency to study the basic design principles of hash functions, as well as how such hash functions should be appropriately used in applications.This project will revisit the basic design principle for constructing secure hash functions, block ciphers, and various important cryptographic primitives which are built from them. In particular, this project will investigate new types of constructions that are based on firmer theoretical foundations, and yet are still efficient enough for practical use. The PI will devote special attention to analyzing and improving the use of hash functions and block ciphers as message digests, key derivation functions, message authentication codes, commitment schemes and random oracles. Additionally, this project will study novel modes of operation to build complex variable-length primitives from simpler, fixed length components, such as block ciphers and fixed-length compression functions. Finally, the project will build firmer foundations for analyzing cryptographic schemes in the idealized security models, such as the random oracle and the ideal cipher models.As a result, this project will potentially yield more secure hash functions and block ciphers, and more secure and/or efficient usage of hash functions and block ciphers in important cryptographic applications. The project will have impact both on technology, as well as on education and collaboration. For example, besides advancing the theory of cryptography, this project will also impact the real-world design of secure systems. Where appropriate, the PI will strive to turn the new primitives and protocols into standards, so that they can be used in practice. Additionally, the PI regularly teaches courses in cryptography and network security, and will be able incorporate the new results into the courses he teaches. Finally, the project has a significant graduate student and postdoc training component.