Isogeny-based cryptography: from theory to practice

基于同源的密码学：从理论到实践

• 批准号: EP/S01361X/1
• 负责人: Christophe Petit
• 金额: $ 41.76万
• 依托单位: University of Birmingham
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FS01361X%2F1
• 关键词: Isogeny; based; cryptography; theory; practice

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 have recommended a move towards post-quantum protocols, and the new generation of cryptographic standards will aim at post-quantum security.This project will consider cryptography based on isogeny problems, a particular family of protocols that are considered for post-quantum security. Isogeny-based protocols are particularly appealing for three reasons 1) they require very small keys compared to other post-quantum cryptography candidates, saving on bandwidth and storage 2) there exists an isogeny-based version of the widely used Diffie-Hellman protocol, which can be used as a direct replacement of current instantiations 3) their mathematical grounding has a lot in common with currently used elliptic curve protocols, which will accelerate implementations in a wide range of devices.Isogeny-based cryptography protocols have only been invented recently, and like many other protocols currently investigated for post-quantum security they yet have to survive the "test of time". As they have not been investigated as thoroughly as currently deployed solutions, they may be more vulnerable to unanticipated weaknesses. Moreover, the protocols are still at the stage of theoretical papers and remain to be evaluated against the specific constraints of real-life applications. This project will advance the field of isogeny-based cryptography, from its mathematical grounding right up to the application of protocols in the real world. We will develop new protocols, new analysis techniques, and determine the suitability of isogeny-based cryptography for selected applications.

当今使用的许多加密协议的安全性依赖于整数分解等数学问题的计算难度。这些问题可以通过量子计算机来解决，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。后量子密码学旨在开发即使在量子计算机建成后也能保持安全的安全协议。包括 GCHQ 和 NSA 在内的世界上最大的安全机构已建议转向后量子协议，新一代密码标准将瞄准后量子安全。该项目将考虑基于同源问题的密码学，这是一个被考虑用于后量子安全的特殊协议族。基于同源的协议特别有吸引力，原因有三个：1) 与其他后量子加密候选方案相比，它们需要非常小的密钥，从而节省带宽和存储空间 2) 存在广泛使用的 Diffie-Hellman 协议的基于同源的版本，可以用作当前实例的直接替代 3) 它们的数学基础与当前使用的椭圆曲线协议有很多共同点，这将加速广泛的实现 基于同源的加密协议最近才被发明，与目前研究后量子安全的许多其他协议一样，它们还必须经受住“时间的考验”。由于它们没有像当前部署的解决方案那样得到彻底的调查，因此它们可能更容易受到意想不到的弱点的影响。此外，这些协议仍处于理论论文阶段，有待根据现实应用的具体限制进行评估。该项目将推动基于同源密码学领域的发展，从数学基础到协议在现实世界中的应用。我们将开发新协议、新分析技术，并确定基于同源密码学对选定应用的适用性。

项目成果

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

Advances in Cryptology - ASIACRYPT 2021 - 27th International Conference on the Theory and Application of Cryptology and Information Security, Singapore, December 6-10, 2021, Proceedings, Part I

密码学进展 - ASIACRYPT 2021 - 第 27 届密码学理论与应用与信息安全国际会议，新加坡，2021 年 12 月 6-10 日，会议记录，第一部分

• DOI: 10.1007/978-3-030-92062-3_6
• 发表时间: 2021
• 作者: Basso A

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.

Predicting inflation component drivers in Nigeria: a stacked ensemble approach.

预测尼日利亚的通货膨胀因素驱动因素：堆叠集成方法。

• DOI: 10.1007/978-3-319-40715-9_9
• 发表时间: 2023
• 期刊: SN business & economics
• 作者: Akande EO

Failing to hash into supersingular isogeny graphs

未能哈希成超奇异同源图

• DOI: 10.48550/arxiv.2205.00135
• 发表时间: 2022
• 作者: Booher J