A novel verifiable secret sharing mechanism using theory of numbers and a method for sharing secrets

Verifiable secret sharing (VSS) has been extensively used as a cryptographic tool in many applications of information security in recent years. A VSS enables a dealer to divide a secret s into n shares and allows shareholders to verify whether their shares are generated by the dealer consistently without revealing the secrecy of both shares and the secret. More specifically, shareholders can verify that (i) the secret can be recovered by any t or more than t shares and (ii) the secret cannot be obtained by fewer than t shares. Many VSSs are based on polynomial, and only a few of them are based on the Chinese Remainder Theorem (CRT). Recently, Harn et al. proposed a CRT‐based VSS in which multiple verification secrets are used during the phase of verification. In this paper, we propose a VSS based on Asmuth‐Bloom's (t, n) SS scheme, which depends on the CRT. Our proposed VSS is simpler and more efficient than the scheme of Harn et al. Our proposed VSS is unconditionally secure. Copyright © 2014 John Wiley & Sons, Ltd.