A Versatile Multi-Input Multiplier over Finite Fields

Multiplication of three elements over finite fields is used extensively in multivariate public key cryptography and solving system of linear equations over finite fields. This contribution shows the enhancements of multiplication of three elements over finite fields by using specific architecture. We firstly propose a versatile multi-input multiplier over finite fields. The parameters of this multiplier can be changed according to the requirement of the users which makes it reusable in different applications. Our evaluation of this multiplier gives optimum choices for multiplication of three elements over finite fields. Implemented results show that we takes 22.062 ns and 16.354 ns to execute each multiplication of three elements over GF ((24)2) based on table look-up and polynomial basis on a FPGA respectively. Experimental results and mathematical proofs clearly demonstrate the improvement of the proposed versatile multiplier over finite fields.