Error Detection Architectures for Ring Polynomial Multiplication and Modular Reduction of Ring-LWE in $\boldsymbol{\frac{\mathbb{Z}/p\mathbb{Z}[x]}{x^{n}+1}}$ Benchmarked on ASIC

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Ring learning with error (ring-LWE) within lattice-based cryptography is a promising cryptographic scheme for the post-quantum era. In this article, we explore efficient error detection approaches for implementing ring-LWE encryption. For achieving accurate operation of the ring-LWE problem and thwarting active side-channel attacks, error detection schemes need to be devised so that the induced overhead is not a burden to deeply embedded and constrained applications. This article, for the first time, investigates error detection schemes for both stages of the ring-LWE encryption operation, i.e., ring polynomial multiplication and modular reduction. Our schemes exploit recomputing with encoded operands, which successfully counter both natural faults (for the stuck-at model). We implement our schemes on an application-specific integrated circuit. As performance metrics show hardware overhead, our schemes prove to be low complexity with high error coverage. The proposed efficient architectures can be tailored and utilized for post-quantum cryptographic schemes in different usage models with diverse constraints.