秩支持学习问题的代数方法
An algebraic approach to the Rank Support Learning problem
摘要：
基于秩度量码的密码学依赖于在秩度量中解码随机线性码的难度。秩支持学习问题（RSL）是一个变体，其中攻击者可以访问N个解码实例，这些解码实例的错误具有相同的支持，并希望解决其中一个。这个问题例如在Durandal签名方案中使用。在本文中，我们提出了一个代数攻击RSL明显优于以前的攻击来解决这个问题。我们以Bardet等人为基础，Asiacrypt 2020，其中使用类似的技术来解决MinRank和RD。然而，我们的分析是简单的，总的来说，我们的攻击依赖于非常基本的假设相比，标准的Gr{<$}bner基地的攻击。特别是，我们的研究结果表明，对Durandal的密钥恢复攻击比以前认为的更有效。
英文摘要：
Rank-metric code-based cryptography relies on the hardness of decoding a random linear code in the rank metric. The Rank Support Learning problem (RSL) is a variant where an attacker has access to N decoding instances whose errors have the same support and wants to solve one of them. This problem is for instance used in the Durandal signature scheme. In this paper, we propose an algebraic attack on RSL which clearly outperforms the previous attacks to solve this problem. We build upon Bardet et al., Asiacrypt 2020, where similar techniques are used to solve MinRank and RD. However, our analysis is simpler and overall our attack relies on very elementary assumptions compared to standard Gr{ö}bner bases attacks. In particular, our results show that key recovery attacks on Durandal are more efficient than was previously thought.
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