Reliable Architectures for Finite Field Multipliers Using Cyclic Codes on FPGA Utilized in Classic and Post-Quantum Cryptography

Abstract

Fault detection is becoming greatly important in protecting cryptographic designs that can suffer from both natural or malicious faults. Finite fields over <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text {GF}(2^{m})$ </tex-math></inline-formula> are widely used in such designs, since their data are coded in binary form for practical reasons. Among the different finite field arithmetic, multiplication is the bottleneck operation for many cryptosystems due to its complexity. Therefore, in this work, fault detection schemes based on cyclic codes for finite field multipliers using different fields found in traditional and post-quantum cryptography are derived. Moreover, we implement such schemes by embedding them into the original architectures to perform an exhaustive study, benchmark the different overheads obtained, and prove their suitability for deeply constrained embedded systems. These implementations are performed on advanced micro devices (AMD)/Xilinx field-programmable gate array (FPGA) and provide a very high error coverage with acceptable overhead.