Efficient (<i>k</i>, <i>n</i>) Secret Sharing on Media Data for Small <i>k</i>

A threshold k out of n, or (k, n), secret sharing with perfect security encodes a secret into n shadows for the n participants such that any k participants are capable of reconstructing the secret using their shadows, while any less than k ones cannot obtain any information about the secret. The shared data is not only safeguarded by the n participants in the threshold access structure, but also tolerant to any loss of up to n̶k shadows. Exploiting the properties of orthogonal Latin k-cubes, we propose a novel threshold secret sharing scheme with perfect security. The correctness and security of our scheme are formally proved. It is the first threshold scheme with perfect security based on Latin cubes. The computational results demonstrate the applicability and efficiency for sharing media data. The fast encoding/decoding efficiency for small k enables practical applications where timely retrieval of large shared data is required, particularly in scenarios involving consumer electronic devices and cloud services of distributed databases.