Polynomial Basis Multiplier over GF(2m) with Confusion and Error Detection Capabilities

Abstract

The communication system, coding theory, and modern cryptosystems employ the Galois field multiplier widely. Especially, Galois field multiplier is the most important part for computing elliptic curve cryptosystem. Recently, the new developed fault based cryptanalysis would attack both symmetrical and asymmetrical cryptosystems effectively. Therefore, this paper proposes two methods, termed RESO and parity prediction methods, for fighting against such new cryptanalysis. The concurrent error detection polynomial basis GF(2m) multiplier has advantage of low hardware cost. When the multiplier with error detection capability detects the fault, a random number would be added to its output for confusing hackers. Thus, the hacker will spend more huge time to decrypt the message and then the cryptosystems will become safe.