用于基于编码的密码分析及其对ISD局限性的量子筛法
Quantum Sieving for Code-Based Cryptanalysis and Its Limitations for ISD
AI总结：
本文提出了首批基于量子游走技术的编码筛法量子算法，实现了对经典算法的加速，并指出基于筛法的ISD框架的量子类比无法直接超越现有量子ISD算法。
摘要：
使用近邻搜索技术的筛法是基于格的密码分析中一种众所周知的方法，在经典[BDGL16]和量子[BCSS23]环境下均产生了最短向量问题当前的最佳运行时间。最近，筛法也成为基于编码的密码分析中的重要工具。具体而言，通过使用筛法子程序，[GJN23, DEEK24]提出了信息集解码（ISD）框架的一种变体，该框架通常用于攻击解码问题的密码学相关实例。由此产生的基于筛法的ISD框架产生的复杂度接近于解码问题性能最佳的经典算法，例如[BJMM12, BM18]。因此，很自然地要探究量子版本的性能如何。在这项工作中，我们通过设计上述筛法子程序的量子变体，引入了首批用于编码筛法的量子算法。特别是，使用量子游走技术，我们提供了比[DEEK24]中已知最佳经典算法以及使用Grover算法[Gro96]的变体更快的速度。我们的量子游走算法利用了底层搜索问题的结构，通过添加一层局部敏感过滤，其灵感来源于[CL21]中用于格筛法的量子游走算法。我们用量子算法的渐近分析补充了数值结果，并观察到我们为编码筛法提供的量子加速与在格筛法中观察到的加速表现相似。此外，我们表明，基于筛法的ISD框架的自然量子类比并未比首个提出的量子ISD算法[Ber10]提供任何加速。我们的分析强调，为了超越最先进的量子ISD算法[KT17, Kir18]，必须对该框架进行适配。
英文摘要：
Sieving using near-neighbor search techniques is a well-known method in lattice-based cryptanalysis, yielding the current best runtime for the shortest vector problem in both the classical [BDGL16] and quantum [BCSS23] setting. Recently, sieving has also become an important tool in code-based cryptanalysis. Specifically, using a sieving subroutine, [GJN23, DEEK24] presented a variant of the information-set decoding (ISD) framework, which is commonly used for attacking cryptographically relevant instances of the decoding problem. The resulting sieving-based ISD framework yields complexities close to the best-performing classical algorithms for the decoding problem such as [BJMM12, BM18]. It is therefore natural to ask how well quantum versions perform. In this work, we introduce the first quantum algorithms for code sieving by designing quantum variants of the aforementioned sieving subroutine. In particular, using quantum-walk techniques, we provide a speed-up over the best known classical algorithm from [DEEK24] and over a variant using Grover's algorithm [Gro96]. Our quantum-walk algorithm exploits the structure of the underlying search problem by adding a layer of locality-sensitive filtering, inspired by the quantum-walk algorithm for lattice sieving from [CL21]. We complement our asymptotic analysis of the quantum algorithms with numerical results, and observe that our quantum speed-ups for code sieving behave similarly as those observed in lattice sieving. In addition, we show that a natural quantum analog of the sieving-based ISD framework does not provide any speed-up over the first presented quantum ISD algorithm [Ber10]. Our analysis highlights that the framework should be adapted in order to outperform the state-of-the-art of quantum ISD algorithms [KT17, Kir18].
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