Fault Detection Structures for the Montgomery Multiplication over Binary Extension Fields

Abstract

Finite field arithmetic is used in applications like cryptography, where it is crucial to detect the errors. Therefore, concurrent error detection is very beneficial to increase the reliability in such applications. Multiplication is one of the most important operations and is widely used in different applications. In this paper, we target concurrent error detection in the Montgomery multiplication over binary extension fields. We propose error detection schemes for two Montgomery multiplication architectures. First, we present a new concurrent error detection scheme using the time redundancy and apply it on semi-systolic array Montgomery multipliers. Then, we propose a parity based error detection scheme for the bit-serial Montgomery multiplier over binary extension Fields.