Post-Quantum Cryptography: a Cryptanalysis Approach

后量子密码学：一种密码分析方法

• 批准号: EP/V011324/1
• 负责人: Christophe Petit
• 金额: $ 212.02万
• 依托单位: University of Birmingham
• 依托单位国家: 英国
• 项目类别: Fellowship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FV011324%2F1
• 关键词: Post; Quantum; Cryptography; Cryptanalysis; Approach

The security of many cryptographic protocols in use today relies on the computational hardness of mathematical problems such as integer factorization. These problems can be solved using quantum computers, and therefore most of our security infrastructures will become completely insecure once quantum computers are built. Post-quantum cryptography aims at developing security protocols that will remain secure even after quantum computers are built. The biggest security agencies in the world including GCHQ and the NSA (the American National Security Agency) have recommended a move towards post-quantum protocols, and the new generation of cryptographic standards will aim at post-quantum security.Driven by the need to upgrade our cybersecurity infrastructures, many cryptographic algorithms have recently been developed which are claimed to offer post-quantum security. These proposals are based on a few distinct mathematical problems which are hoped to remain difficult for quantum computers, including lattice problems, multivariate polynomial system solving, coding theory problems, isogeny problems, and the security of cryptographic hash functions. Unfortunately, many of these problems, and more importantly the cryptographic algorithms that are built on top of them, have not been subject to a thorough security analysis yet, therefore leaving us with a risk to oversee major weaknesses in algorithms to be deployed in security applications. In this fellowship, we will develop breakthrough cryptanalysis techniques to analyse the security of post-quantum cryptography candidate algorithms, and determine which algorithms may or may not be further considered for digital security applications. Using the insight gained through cryptanalysis, we will then develop new post-quantum cryptographic algorithms offering better security, efficiency and functionality properties in applications.

当今使用的许多密码协议的安全性依赖于诸如整数因子分解之类的数学问题的计算难度。这些问题可以使用量子计算机来解决，因此，一旦量子计算机建成，我们的大多数安全基础设施将变得完全不安全。后量子密码学的目标是开发安全协议，即使在量子计算机建成后也能保持安全。GCHQ和NSA（美国国家安全局）等世界上最大的安全机构已经建议向后量子协议迈进，新一代的密码标准将以后量子安全为目标。在网络安全基础设施升级的需求驱动下，最近开发了许多声称提供后量子安全的密码算法。这些建议是基于几个不同的数学问题，希望量子计算机仍然很难，包括格问题，多元多项式系统求解，编码理论问题，issumption问题，以及加密哈希函数的安全性。不幸的是，这些问题中的许多问题，更重要的是建立在它们之上的加密算法，还没有经过彻底的安全分析，因此我们有风险监督要部署在安全应用程序中的算法的主要弱点。在这项研究中，我们将开发突破性的密码分析技术来分析后量子密码学候选算法的安全性，并确定哪些算法可能会或可能不会被进一步考虑用于数字安全应用。利用通过密码分析获得的洞察力，我们将开发新的后量子密码算法，在应用程序中提供更好的安全性，效率和功能特性。

项目成果

On Fp-roots of the Hilbert class polynomial modulo p

关于 Hilbert 类多项式模 p 的 Fp 根

• 发表时间: 2022
• 期刊: Journal of Mathematics (PRC)
• 作者: Chen M

Proving knowledge of isogenies: a survey

证明同基因知识：一项调查

• DOI: 10.1007/s10623-023-01243-3
• 发表时间: 2023
• 期刊: Designs, Codes and Cryptography
• 作者: Beullens W

Improved Torsion-Point Attacks on SIDH Variants

改进对 SIDH 变体的扭转点攻击

• DOI: 10.1007/978-3-030-84252-9_15
• 发表时间: 2021
• 期刊: Advances in Cryptology -- CRYPTO 2021
• 作者: de Quehen, Victoria;Kutas, Péter;Leonardi, Chris;Martindale, Chloe;Panny, Lorenz;Petit, Christophe;Stange, Katherine E.
• 通讯作者: Stange, Katherine E.

Explicit isomorphisms of quaternion algebras over quadratic global fields

二次全局域上四元数代数的显式同构

• DOI: 10.1007/s40993-022-00380-3
• 发表时间: 2022
• 期刊: Research in Number Theory
• 影响因子: 0.8
• 作者: Csahók, Tímea;Kutas, Péter;Montessinos, Mickaël;Zábrádi, Gergely
• 通讯作者: Zábrádi, Gergely

Finding Orientations of Supersingular Elliptic Curves and Quaternion Orders

寻找超奇异椭圆曲线和四元数阶的方向

• DOI: 10.48550/arxiv.2308.11539
• 发表时间: 2023
• 作者: Arpin S