Fast Modulus Algorithm for Internet of Things Key Exchange Based on Mersenne-like Numbers

In order to adapt to the limited computing performance and energy of numerous lightweight sensor nodes in the encrypted transmission of IoT (Internet of Things), this paper proposed a fast modulus algorithm (CZ-Mod algorithm) based on Mersenne-like numbers to slove the bottleneck problems of computing speed, power consumption and so on during the sensors run PKI (Public Key Infrastructure) encryption algorithms such as RSA (Rivest-Shamir-Adleman), DHM (Diffie-Hellman-Merkle), Elgamal, etc. , and to simplify the corresponding hardware encrypting circuit logic design. CZ-Mod algorithm uses the mathematic characteristics of Mersenne numbers, and lowers the time complexity of its essential operation mod (modulo) into O(n). Firstly, a fast modulus algorithm mod1 using Mersenne-like numbers as modulus was presented, changing complex mod operation into simple binary shift/add operation; secondly, a fast modulus algorithm mod2 using any positive integers near Mersenne-like numbers as modulus was presented, expanding the modulus value range while simplifying mod operation; and then logic circuits of mod1 and mod2 operations were designed, simplifying mod operation hardware circuit. Finally, the above work was applied to the key exchange of IoT nodes, so as to lower the computing complexity and improve the speed of PKI encryption algorithms. The experiment test results indicate that the speed of DHM key exchange with CZ-Mod algorithm can reach 2.5 to 4 times of that of the conventional algorithm; CZ-Mod algorithm is concise and fits the hardware circuit design for the IoT sensors.