Reliable CRC-Based Error Detection Constructions for Finite Field Multipliers With Applications in Cryptography

Abstract

Finite-field multiplication has received prominent attention in the literature with applications in cryptography and error-detecting codes. For many cryptographic algorithms, this arithmetic operation is a complex, costly, and time-consuming task that may require millions of gates. In this work, we propose efficient hardware architectures based on cyclic redundancy check (CRC) as error-detection schemes for postquantum cryptography (PQC) with case studies for the Luov cryptographic algorithm. Luov was submitted for the National Institute of Standards and Technology (NIST) PQC standardization competition and was advanced to the second round. The CRC polynomials selected are in-line with the required error-detection capabilities and with the field sizes as well. We have developed verification codes through which software implementations of the proposed schemes are performed to verify the derivations of the formulations. Additionally, hardware implementations of the original multipliers with the proposed error-detection schemes are performed over a Xilinx field-programmable gate array (FPGA), verifying that the proposed schemes achieve high error coverage with acceptable overhead.