Cryptographic algorithms (RSA, DSA, and ECC) use modular exponentiation as part of the principal operation. However, Non-profiled Side Channel Attacks such as Simple Power Analysis and Differential Power Analysis compromise cryptographic algorithms that use such operation. In this work, we present a modification of a modular exponentiation algorithm implemented in programmable devices, such as the Field Programmable Gate Array, for which we use Virtex-6 and Artix-7 evaluation boards. It is shown that this proposal is not vulnerable to the attacks mentioned previously. Further, a comparison was made with other related works, which use the same family of FPGAs. These comparisons show that this proposal not only defeats physical attack but also reduces the number of resources. For instance, the present work reduces the Look-Up Tables by 3550 and the number of Flip-Flops was decreased by 62,583 compared with other works. Besides, the number of memory blocks used is zero in the present work, in contrast with others that use a large number of blocks. Finally, the clock cycles (latency) are compared in different programmable devices to perform operations.
Keywords: BRIP; FPGA; Montgomery exponentiation; Montgomery multiplication; N − 1 Attack; RSA; SCA; SPA; SaMA.