Fault-tolerant Gaussian normal basis multiplier over GF(2m)

Abstract

Fault-tolerant design of a finite field multiplier is an efficient method for resisting fault-based cryptanalysis in Elliptic curve cryptosystems. A novel fault-tolerant bit-parallel Gaussian normal basis (GNB) multiplier with type-t over GF(2m), which can tolerate multiple module failures at one time, is presented. No hardware modification in the proposed GNB multiplier is required to achieve the fault-tolerant function. Hence, the proposed fault-tolerant GNB multiplier has low hardware cost. The reliability of the proposed fault-tolerant GNB multiplier with type-t increases as t increases. However, the behaviour of existing GNB multipliers with concurrent error correction (CEC) resembles triple modular redundancy (TRM) when t>3. In practice, most of suggested m's by NIST use GNB with type-t>3. The proposed fault-tolerant GNB multiplier is an N-modular redundancy (NMR) system with N=t. Thus, the proposed fault-tolerant GNB multiplier with type-t can tolerate at most t/2-1 failed modules simultaneously, while existing GNB multipliers with CEC only can tolerate one failed module. The proposed GNB multiplier requires less extra space and time complexities than similar multipliers. System reliability of the proposed fault-tolerant GNB multiplier is better than that of similar GNB multipliers.