基于拟阿贝尔译码困难性的相关伪随机性
Correlated Pseudorandomness from the Hardness of Quasi-Abelian Decoding
AI总结：
本文提出拟阿贝尔校正子译码问题QA-SD，并据此构造任意q>2域上支持OLE的可编程PCG，突破大域与可分裂Ring-LPN限制，得到首个高效N方静默通用算术电路安全计算协议。
摘要：
安全计算通常受益于使用相关随机性，以实现快速的、非密码学的在线协议。Boyle等人（CCS 2018，Crypto 2019）提出的一种新范式展示了如何利用伪随机相关生成器（PCG），通过极少交互并随后仅进行本地计算，生成大量有用形式的相关（伪）随机性，从而得到静默的安全双方计算协议（即预处理阶段几乎不需要通信的协议）。一种称为可编程性的附加属性允许将其扩展以构建N方协议。然而，已知的可编程PCG构造只能在大域上生成OLE，并且使用相当新的可分裂Ring-LPN假设。在本工作中，我们克服了这两个限制。为此，我们引入拟阿贝尔校正子译码问题（QA-SD），这是一个假设族，推广了已得到充分确立的拟循环校正子译码假设。在QA-SD的基础上，我们为任意q>2的域F_q上的OLE构造了新的可编程PCG。我们的分析还阐明了Boyle等人（Crypto 2020）中使用的ring-LPN假设的安全性。利用我们的新PCG，我们首次获得了高效的N方静默安全计算协议，用于在任意q>2的F_q上计算通用算术电路。
英文摘要：
Secure computation often benefits from the use of correlated randomness to achieve fast, non-cryptographic online protocols. A recent paradigm put forth by Boyle $\textit{et al.}$ (CCS 2018, Crypto 2019) showed how pseudorandom correlation generators (PCG) can be used to generate large amounts of useful forms of correlated (pseudo)randomness, using minimal interactions followed solely by local computations, yielding silent secure two-party computation protocols (protocols where the preprocessing phase requires almost no communication). An additional property called programmability allows to extend this to build N-party protocols. However, known constructions for programmable PCG's can only produce OLE's over large fields, and use rather new splittable Ring-LPN assumption. In this work, we overcome both limitations. To this end, we introduce the quasi-abelian syndrome decoding problem (QA-SD), a family of assumptions which generalises the well-established quasi-cyclic syndrome decoding assumption. Building upon QA-SD, we construct new programmable PCG's for OLE's over any field $\mathbb{F}_q$ with $q>2$. Our analysis also sheds light on the security of the ring-LPN assumption used in Boyle $\textit{et al.}$ (Crypto 2020). Using our new PCG's, we obtain the first efficient N-party silent secure computation protocols for computing general arithmetic circuit over $\mathbb{F}_q$ for any $q>2$.
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