A new look-up table-based multiplier/squarer design for cryptosystems over GF(2m)

This paper presents a high-speed multiplier/squarer design over finite field GF(2^m) for large m. We extended the look-up table (LUT) based multiplication algorithm introduced by Hasan to reduce the LUT generation time and then showed how to effectively add the squaring operation to the developed multiplier. The unified multiplication/squaring module is very suitable for applications like Elliptic Curve Cryptography (ECC) in which these two types of operations are operated alternately. Experimental results exhibit that using the proposed sub-group, multiple look-up tables (SG-MLUT) based scheme, up to 29% improvement in the total computation time of multiplication can be achieved in comparison with that using Hasan´s algorithm. When employing the unified multiplier/squarer module instead of Hasan´s design in ECC applications, we can gain further improvement in the scalar multiplication time because no LUT generation is needed using our design, and obtain about 24.5% reduction on the resulting area-time (AT) complexity.