Accelerating exp-log based finite field multiplication

Overview & Synopsis

Finite field multiplication is widely used for masking countermeasures against side-channel attacks. The execution time of finite field multipli- cation implementation is critical as it greatly impacts the overhead of the countermeasure. In this context, the use of exp-log tables is popular for the implementation of finite field multiplication. Yet, its performance is affected by the need for particular code to handle the case where one of the operands equals zero, as log is undefined for zero. As noticed by two recent papers, the zero case can be managed without any extra code by extending the exp table and setting log[0] to a large-enough value. The multiplication of a and b then becomes as simple as: exp[log[a] + log[b]]. In this paper, we compare this approach with other implementations of finite field multiplication and show that it provides a good trade-off be- tween memory use and execution time.