PKC-Sec: Security Analysis of Classical and Post-Quantum Public Key Cryptography Assumptions

PKC-Sec：经典和后量子公钥密码学假设的安全性分析

• 批准号: EP/W021633/1
• 负责人: Robert Granger
• 金额: $ 37.96万
• 依托单位: University of Surrey
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2023
• 资助国家: 英国
• 起止时间: 2023 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FW021633%2F1
• 关键词: PKC; Sec; Security; Analysis; Classical

Public key cryptography (PKC) depends on the existence of computational problems that are incredibly hard - but not impossible - to solve. Classical examples that were fundamental to the origins of PKC in the 1970s (and indeed were prominent centuries earlier) are the integer factorisation problem and the discrete logarithm problem (DLP). While there are no known efficient, i.e., polynomial-time algorithms for solving these problems that run on classical computers, thanks to Shor's astounding breakthrough ideas in 1994, both can be solved efficiently on a quantum computer of sufficient size. Intense research in the areas of quantum computation, quantum information theory and quantum algorithms ensued, and replacement post-quantum (PQ) cryptosystems have been studied in earnest for the past 15 years or so, with standardisation efforts in process by both NIST and ETSI. PQ cryptosystems must be secure against both classical and quantum computers and therefore their underlying hardness assumptions must be studied intensely before they can be fully trusted to replace our existing PKC hardness assumptions. Until these standards have been established and cryptographic practice migrates entirely to PQ cryptography, it is also essential that the study of classical hardness assumptions persists, particularly as sporadic and sometimes spectacular progress can occur: for instance, for a special but large family of finite fields the DLP can be solved on a classical computer in quasi-polynomial time, i.e., `very nearly' efficiently, thanks to a series of results due to Dr. Granger and his collaborators, and Joux and his collaborators.In this project we will research and develop algorithms for solving computational problems that are foundational to the security of PKC, both now and in the future. In particular, we will study: the DLP in the aforementioned special family of finite fields, for which an efficient classical algorithm is potentially on the horizon; the security of the Legendre pseudo-random function, which is extremely well suited for multi-party computation and has been proposed for use in the next iteration of Ethereum - the de facto standard blockchain platform - but is not so well-studied; and finally the security of supersingular isogeny-based PQ cryptography, which although a relatively young field offers many very promising applications. Due to their nature, any cryptographic assumptions based on mathematical constructions are potentially weaker than currently believed, and we will deepen our understanding and assess the hardness of these natural and fundamental problems, thus providing security assurances to the cryptography community and more generally all users of cryptography.

公钥密码学（PKC）依赖于计算问题的存在，这些问题非常难以解决，但并非不可能解决。在20世纪70年代，对PKC起源至关重要的经典例子是整数因子分解问题和离散对数问题（DLP）。虽然没有已知的有效的，即，由于Shor在1994年的惊人突破性想法，解决这些问题的多项式时间算法在经典计算机上运行，两者都可以在足够大的量子计算机上有效地解决。在量子计算、量子信息理论和量子算法领域的深入研究随之而来，在过去的15年左右时间里，人们一直在认真研究替代后量子（PQ）密码系统，NIST和ETSI正在进行标准化工作。PQ密码系统必须对经典计算机和量子计算机都是安全的，因此在完全信任它们来取代我们现有的PKC硬度假设之前，必须对其潜在的硬度假设进行深入研究。直到这些标准已经建立并且密码学实践完全迁移到PQ密码学之前，对经典硬度假设的研究仍然是至关重要的，特别是当零星的并且有时是壮观的进展可能发生时：例如，对于一个特殊但很大的有限域族，DLP可以在经典计算机上以准多项式时间求解，即，由于格兰杰博士和他的合作者以及Joux和他的合作者的一系列结果，“非常接近”有效。在这个项目中，我们将研究和开发用于解决计算问题的算法，这些问题是现在和将来PKC安全性的基础。特别是，我们将研究：上述特殊的有限域族中的DLP，一种有效的经典算法可能即将出现; Legendre伪随机函数的安全性，它非常适合多方计算，并已被提议用于以太坊的下一次迭代-事实上的标准区块链平台-但没有得到很好的研究;最后是基于超奇异同构的PQ密码的安全性，尽管这是一个相对年轻的领域，但它提供了许多非常有前途的应用。由于其性质，任何基于数学构造的密码学假设都可能比目前认为的要弱，我们将加深对这些自然和基本问题的理解并评估其难度，从而为密码学社区和更广泛的密码学用户提供安全保证。

项目成果

Three proofs of an observation on irreducible polynomials over GF(2)

GF(2) 上不可约多项式观测值的三个证明

• DOI: 10.1016/j.ffa.2023.102192
• 发表时间: 2023
• 期刊: Finite Fields and Their Applications
• 影响因子: 1
• 作者: Granger R