Concurrent error detection architectures for Gaussian normal basis multiplication over GF(2m)

This paper presents a method of using a parity prediction scheme for detecting erroneous outputs in bit-parallel, sequential, and digit-serial Gaussian normal basis (GNB) multipliers over GF(2m). Although all-type NB multipliers have different time and space complexities, our analytical results indicate that all-type GNB multipliers have the same structure if they use parity prediction function. For example, in the field GF(2233), we have estimated that the error detection rate for a sequential multiplier is nearly 100% if a comparison is made as per clock cycle. Our analytical results also show that the area overhead of the proposed digit-serial multiplier with concurrent error detection does not exceed 5%. Several efficient parity prediction techniques will be shown in this work to provide a low overhead solution to concurrent error detection particularly when the cryptography implementations using GF(2m) multiplier require higher reliability and the protection against adversarial attacks.