A method for secure implementation in the cloud of the basic public key cryptography operation modular exponentiation - is proposed. The method is intended for the rapid implementation of information security functions in remote control systems based on IoT technology. It is theoretically and experimentally proven that by using the results of intermediate calculations from the cloud on an IoT microcontroller terminal, the proposed method allows to increase the security level by several orders of magnitude compared to known methods with the same performance characteristics.