New Constructions of an Evolving 2-Threshold Scheme Based on Binary or D-ary Prefix Codes

Recently, Komargodski et al. proposed a nonconventional secret sharing scheme called an evolving k-threshold scheme. In the evolving k-threshold scheme, a dealer can generate infinitely many shares such that a secret is correctly decoded from arbitrary more than or equal to k shares while no information on the secret is revealed from any less than k shares. In this paper, we propose a new construction of an evolving 2-threshold scheme based on a binary prefix code for a secret with arbitrary length. In addition, we give a construction of an evolving 2-threshold scheme based on a D-ary prefix code, where D≥3 is an arbitrary integer. It is shown that the sizes of shares of this construction are more efficient than the binary case.