ACCELERATED IMPLEMENTATION OF THE MODULAR EXHIBITION ON LOW-DISCHARGE MICROPROCESSORS AND INTEGRATED MICROCONTROLLERS - Samofalov, K. G.; Saliba Sunnah, Ramzi Anwar; Levchun , D. Yu. (Problems of Informatization and Control, 2021)
The article proposes new algorithms for modular squaring and multiplication by a fixed number, based on the Montgomery recursion. Due to the elimination of redundant operations and the use of precalculations, the computational complexity of the proposed algorithms is significantly lower compared to the Montgomery multiplication algorithm. It is shown that when the proposed algorithms are implemented on low-bit microprocessors, built-in microcontrollers or smart cards, the time for calculating the modular exponentiation is six times less compared to the Montgomery modular exponentiation algorithm.