A Message Transmission Scheme for IoT Inspired by The Shamir Scheme and Based on The Hidden Number Problem (HNP)

Abstract

The Internet of Things (IoT) requires cryptographic mechanisms that are both lightweight and resistant to emerging attacks. Classical public-key protocols such as RSA or ElGamal, as well as many post-quantum lattice-based schemes, consume too many resources for devices with limited memory, processing power, and energy. In this study, we propose a three-pass message transmission protocol that avoids any prior key exchange. Inspired by Shamir’s keyless scheme and relying on the hardness of the Hidden Number Problem (HNP) and the Decisional Diffie–Hellman (DDH) assumption, the protocol operates in a finite field with safe primes and refreshes random masks at each execution, providing strong resistance to brute-force and small-subgroup attacks. We formally prove IND-CPA security and implement the HNP 3-pass scheme, showing that each pass executes in 1.4--1.8 ms on a workstation, with 132-byte public keys and 192--256-byte secret keys. Estimated energy consumption per iteration is 101.562 mJ. Comparative simulations on a workstation and embedded platforms (Arduino Uno and Raspberry Pi) against RSA-512, ECC (secp256r1/secp521r1), and post-quantum Kyber-512 show that our scheme achieves execution times comparable to ECC and Shamir’s 3-pass protocol, is significantly faster than RSA, and consumes less energy than Kyber-512. This combination of low latency, moderate key sizes, and energy efficiency highlights the practicality of the HNP 3-pass protocol for resource-constrained IoT environments