A Multiple User Cryptography Approach Using a One-Time User Key Model and a (1, n) Threshold Polynomial Secret Sharing

Classical approaches to cryptography exhibit several limitations when applied to scenarios involving more than two users. The One-Time User Key (OTUK) meta-cryptographic model addresses these limitations by enabling multi-user encryption that is flexible, applicable to any cryptographic algorithm, and designed for systematic deployment without compromising system security. Each user possesses an individual key from which One-Time keys are derived; these keys feed a secret-sharing function ((Formula presented.)) that establishes the multi-user encrypted channel. In this paper, we present a polynomial-based implementation of the (Formula presented.) function under a (Formula presented.) threshold model. The generated polynomial has roots at points corresponding to valid user keys and is mapped to the real encryption key. We provide a formal threat model, pseudocode for the complete protocol, and a detailed computational analysis across the numerical domains (Formula presented.), (Formula presented.), and (Formula presented.). Furthermore, we present experimental benchmarks measuring encryption/decryption speed, scalability up to 30 users, parameter sensitivity, and a comparative evaluation against Shamir’s Secret Sharing scheme. A systematic security analysis examines partial-information attacks, derivative-root distance margins, and brute-force resistance, demonstrating that the effective security margin remains above 245 bits for configurations of up to 30 users with 256-bit keys. The proposed method offers a concrete, efficient, and secure foundation for multi-user encrypted communication in domains such as IoT, public administration, and e-health.