Cryptographic Group Actions and Applications
Cryptographic Group Actions and Applications
复制标题
加密组操作和应用
DOI：
10.3929/ethz-b-000439880
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Sikhar Patranabis
中科院分区：
文献类型：
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作者：
Navid Alamati;L. D. Feo;H. Montgomery;Sikhar Patranabis
基于同源性的假设已成为量子安全密码学的可行选择。最近的工作已经展示了如何从基于同源的假设（例如 CSIDH 和 CSI-FiSh）构建有效的（公钥）原语。然而，就其目前的形式而言，同源景观似乎不太适合实现新的密码应用。基于同源的假设通常具有独特的效率和安全属性，这使得利用它们构建新的加密应用程序可能成为一项乏味且耗时的任务。在这项工作中，我们提出了一个基于群体行动的新框架，可以轻松使用各种基于同源的假设。我们的框架概括了 Brassard 和 Yung (Crypto’90) 以及 Couveignes (Eprint’06) 的作品。我们为群体行为提供了新的定义，赋予了自然硬度假设，模拟基于同源的结构，适合群体行为，例如 CSIDH 和 CSI-FiSh。我们通过利用新框架构建几个以前从基于同源的假设中未知的原语来展示新框架的实用性。其中包括平滑投影散列、双模式 PKE、两条消息统计发送者专用 OT 和 Naor-Reingold 风格的 PRF。这些原语是各种密码应用程序的有用构建块。我们引入了一种关于群体行为的新假设，称为线性隐移（LHS）假设。然后，我们对 LHS 假设的安全性进行了一些讨论，并表明它意味着对称 KDM 安全加密，这反过来又启用了许多其他原语，这些原语以前从基于同源的假设中未知。
Isogeny-based assumptions have emerged as a viable option for quantum-secure cryptography. Recent works have shown how to build efficient (public-key) primitives from isogeny-based assumptions such as CSIDH and CSI-FiSh. However, in its present form, the landscape of isogenies does not seem very amenable to realizing new cryptographic applications. Isogeny-based assumptions often have unique efficiency and security properties, which makes building new cryptographic applications from them a potentially tedious and time-consuming task. In this work, we propose a new framework based on group actions that enables the easy usage of a variety of isogeny-based assumptions. Our framework generalizes the works of Brassard and Yung (Crypto’90) and Couveignes (Eprint’06). We provide new definitions for group actions endowed with natural hardness assumptions that model isogeny-based constructions amenable to group actions such as CSIDH and CSI-FiSh. We demonstrate the utility of our new framework by leveraging it to construct several primitives that were not previously known from isogeny-based assumptions. These include smooth projective hashing, dual-mode PKE, two-message statistically sender-private OT, and Naor-Reingold style PRF. These primitives are useful building blocks for a wide range of cryptographic applications. We introduce a new assumption over group actions called Linear Hidden Shift (LHS) assumption. We then present some discussions on the security of the LHS assumption and we show that it implies symmetric KDM-secure encryption, which in turn enables many other primitives that were not previously known from isogeny-based assumptions.
DOI：
10.2140/obs.2020.4.39
发表时间：
2020-03
期刊：
ArXiv
影响因子：
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作者：
D. Bernstein;L. D. Feo;Antonin Leroux;Benjamin A. Smith
通讯作者：
D. Bernstein;L. D. Feo;Antonin Leroux;Benjamin A. Smith
张量上的一般线性群作用：后量子密码学的候选者
DOI：
10.1007/978-3-030-36030-6_11
发表时间：
2019
期刊：
17th Theory of Cryptography Conference
影响因子：
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作者：
Ji, Z.;Qiao, Y.;Song, F.;Yun, A.
通讯作者：
Yun, A.