New Compact Finite-Field Arithmetic Circuits over GF(p) Based on Spiking Neural P Systems with Communication on Request Implemented in a Low Cost FPGA

Finite-field arithmetic operations are vital for the computation of complex cryptography algorithms used in several cutting-edge applications, such as side-channel attacks, authentication, and digital signatures, among others. Currently, the simulation of these algorithms exceeds the computational capabilities of conventional computing systems. This aspect becomes critical, especially when these algorithms are implemented in resource-constrained electronic appliances. In particular, the improvement of execution time in these devices generally require more area. To overcome this issue, a large number of works have been focused on the development of compact conventional binary finite-field arithmetic circuits over GF(p) since these demand a large area consumption. Inspired by neural phenomena, a new emerging branch of computer science has made intensive efforts to improve area consumption of conventional arithmetic circuits. However, the development of compact finite-field arithmetic circuits over GF(p) is a still a challenging task. In this letter, we present for the first time, the design of four new finite-field arithmetic circuits over GF(p) based on spiking neural P (SN P) systems with communication on request. In addition, we propose a neural processor to perform four new finite-field arithmetic operations over GF(p) by using the same processing core, which is not feasible with the use of conventional binary circuits since each finite-field arithmetic-binary circuit over GF(p) is implemented separately, to significantly improve the area consumption. This has mainly been achieved since the neural processor dynamically change its configuration, which is defined in terms of the connectivity and firing rules of each neuron.