MIMO 译码是否已被证明是格问题困难的？

中文摘要 AI 辅助

多输入多输出（MIMO）技术是现代无线通信的基础。物理层安全旨在利用噪声通信信道的特性保护传输信息。Dean 和 Goldsmith 通过调整 Regev 针对带错误学习（LWE）的归约，提出了从格问题到 MIMO 译码的多项式时间归约。若该归约有效，将为物理层安全提供基于已确立格问题困难性的强计算基础。后续研究针对该构造提出了攻击和反例，使其安全性受到质疑，但归约的精确有效性和局限性仍未被完全理解。我们对修订后的归约进行理论检验，确定 LWE 归约的结构特征无法推广到非模块化 MIMO 场景，从而证明其已发表的证明未确立 MIMO 译码的声称困难性。我们的结果区分了困难性证明中的缺陷与对特定参数选择的直接攻击，并阐明了任何尝试修复所需的条件。我们并未否定 MIMO 系统的一般物理层安全，而是表明已有的归约无法推导出声称的格困难性保证。

英文摘要

Multiple-input multiple-output (MIMO) technology is fundamental to modern wireless communication. Physical layer security seeks to protect transmitted information by exploiting properties of the noisy communication channel. Dean and Goldsmith proposed a polynomial time reduction from lattice problems to MIMO decoding by adapting Regev's reduction for learning with errors (LWE). If valid, this reduction would give physical layer security a strong computational foundation based on the hardness of established lattice problems. Subsequent works presented attacks and counterexamples against the resulting construction, casting doubt on its security but leaving the precise validity and limitations of the underlying reduction incompletely understood. We provide a theoretical examination of the revised reduction and identify the structural features of the LWE reduction that fail to carry over to the non-modular MIMO setting, hence showing that its published proof does not establish the claimed hardness of MIMO decoding. Our results distinguish flaws in the hardness proof from direct attacks on particular parameter choices and clarify what would be required of any attempted repair. We do not rule out physical layer security for MIMO systems in general, but show that the claimed lattice hardness guarantee does not follow from the existing reduction.

发表机构

• Deakin University（迪肯大学）

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