Simplest (3,2) Threshold Secret Sharing Schemes Based on EXCLUSIVE-OR Function

This paper presents a new XOR-based secret sharing scheme designed for simplicity, efficiency, and strong security guarantees. Unlike traditional threshold schemes that rely on matrix operations and work on large data blocks, the proposed method operates on a per-byte basis, applying lightweight bytewise XOR calculations. The goal of this research is to create a minimalistic yet robust (3,2) threshold secret sharing algorithm that is practical for real-world systems with constrained computational resources. The proposed scheme divides a secret file into three independent shadow shares using a simple transformation: each share is generated as the XOR of the secret with a random byte string and a shifted version of that string. Specifically, the algorithm uses one random string and constructs the second and third shares by XOR-ing the secret with the random string and with the string shifted by one byte in opposite directions. This process is applied independently to each byte of the secret file. The resulting scheme is both perfect and ideal: each share is the same size as the original file, and no information about the secret can be obtained from a single share. Any two out of three shares are sufficient to reconstruct the original data, while fewer reveal nothing. The encoding and decoding procedures are transparent, computationally efficient, and well-suited for implementation in hardware or constrained environments. The algorithm was implemented in Fortran and can be easily integrated into secure cloud storage systems, distributed communication protocols, or embedded devices. This work contributes a lightweight alternative to existing XOR-based sharing methods, providing a novel balance between cryptographic strength and algorithmic simplicity.