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Polynomial multiplication stands out as a highly demanding arithmetic process in the development of post-quantum cryptosystems. The importance of the number-theoretic transform (NTT) extends beyond post-quantum cryptosystems, proving valuable in enhancing existing security protocols such as digital signature schemes and hash functions. CRYSTALS-KYBER stands out as the sole public key encryption (PKE) algorithm chosen by the National Institute of Standards and Technology (NIST) in its third round selection, making it highly regarded as a leading post-quantum cryptography (PQC) solution. Due to the potential for errors to significantly disrupt the operation of secure, cryptographically-protected systems, compromising data integrity, and safeguarding against side-channel attacks initiated through faults it is essential to incorporate mitigating error detection schemes. This paper introduces algorithm level fault detection schemes in the NTT multiplication using Negative Wrapped Convolution and the NTT tailored for Kyber Round 3, representing a significant enhancement compared to previous research. We evaluate this through the simulation of a fault model, ensuring that the conducted assessments accurately mirror the obtained results. Consequently, we attain a notably comprehensive coverage of errors. Furthermore, we assess the performance of our efficient error detection scheme for Negative Wrapped Convolution on FPGAs to showcase its implementation and resource requirements. Through implementation of our error detection approach on Xilinx/AMD Zynq Ultrascale+ and Artix-7, we achieve a comparable throughput with just a 9% increase in area and 13% increase in latency compared to the original hardware implementations. Finally, we attained an error detection ratio of nearly 100% for the NTT operation in Kyber Round 3, with a clock cycle overhead of 16% on the Cortex-A72 processor.

Whether stemming from malicious intent or natural occurrences, faults and errors can significantly undermine the reliability of any architecture. In response to this challenge, fault detection assumes a pivotal role in ensuring the secure deployment of cryptosystems. Even when a cryptosystem boasts mathematical security, its practical implementation may remain susceptible to exploitation through side-channel attacks. In this paper, we propose a lightweight fault detection architecture tailored for modular exponentiation, a building block of numerous cryptographic applications spanning from classical cryptography to post quantum cryptography. Based on our simulation and implementation results on ARM Cortex-A72 processor, and AMD/Xilinx Zynq Ultrascale+, and Artix-7 FPGAs, our approach achieves an error detection rate close to 100%, all while introducing a modest computational overhead of approximately 7% and area overhead of less than 1% compared to the unprotected architecture. To the best of our knowledge, such an approach benchmarked on ARM processor and FPGA has not been proposed and assessed to date., Comment: 5 pages, 2 figures