A Latin square autotopism secret sharing scheme

Abstract

We present a novel secret sharing scheme where the secret is an autotopism (a symmetry) of a Latin square. Previously proposed secret sharing schemes involving Latin squares have many drawbacks: (a) Latin squares contain n2 entries, which may be too large, (b) partial information about the secret may be directly revealed, (c) a subsequently discovered subtle “flaw”, (d) difficulty in initialization and reconstruction, (e) difficulty in verification, and (f) difficulty in generalizing to a multi-level scheme. We carefully analyze the security of the proposed scheme, and identify how it overcomes all of these problems.