Information-theoretically secure timed-release secret sharing schemes

Abstract

In modern cryptography, the secret sharing scheme is an important cryptographic primitive, and it is used in various situations. In this paper, timed-release secret sharing (TR-SS) schemes with information-theoretic security is first studied. TR-SS is a secret sharing scheme with the property that more than a threshold number of participants can reconstruct a secret by using their shares only when the time specified by a dealer has come. Specifically, in this paper we first introduce models and formalization of security for two kinds of TR-SS based on the traditional secret sharing scheme and information-theoretic timed-release security. We also derive tight lower bounds on the sizes of shares, time-signals, and entities’ secret-keys required for each TR-SS scheme. In addition, we propose direct constructions for the TR-SS schemes. Each direct construction is optimal in the sense that the construction meets equality in each of our bounds, respectively. As a result, it is shown that timed-release security can be realized without any additional redundancy on the share size.