A real time S-box construction using arithmetic modulo prime numbers

This paper proposes an implementation of the inverse function of the Advanced Encryption Standard using the field of prime numbers instead of the Galois Field originally proposed by Rijndael. The paper will show that the former approach is simpler and requires less execution time and implementation circuitry compared to the latter. The authors analyzed several implementations of the inverse function for the S-Box using various approaches in search for an optimal one. In particular, simulation was used to analyze performances of algorithms for computing the inverse function based on: the arithmetic modulo a power-of-two; arithmetic modulo a power-of-two plus one; and arithmetic modulo a prime number. The simulation revealed that the modulo a prime number approach has the best performance. Furthermore, the analysis revealed that using this approach may enhance security relative to the original approach. The proposed implementation will provide a better alternative that can be embedded in many systems.