Has MIMO decoding been proved hard from lattice problems?

Abstract

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.