In the paper, a method for accelerating computational implementation of the most massive open-key cryptography operation - modulo squaring of numbers whose length significantly exceeds the processor’s bit rate - is proposed and investigated. The acceleration of the calculations is achieved via the combined use of the Montgomery group reduction based on pre-calculations and dynamic reduction of the length of operands. Theoretically and experimentally, it is shown that the proposed approach reduces the modular multiplication time by 3-4 times and thereby speeds up the implementation of data protection in remote control systems based on IoT technologies.