A publicly verifiable secret sharing (PVSS) scheme, proposed by Stadler in [Sta96], is a VSS scheme in which anyone, not only the shareholders, can verify that the secret shares are correctly distributed. PVSS can play essential roles in the systems using VSS. Achieving simultaneously the following two features for PVSS is a challenging job: – Efficient non-interactive public verification. – Pr...

In 2004, C.-C. Yang, T.-Y. Chang and M.-S. Hwang proposed an efficient multi-secret sharing scheme based on two-variable one-way function and Shamir's secret sharing. In order to add the verifiable property into previous scheme, J. Shao and Z. Cao proposed an efficient (t,n) verifiable multi-secret sharing based on YCH [C.-C. Yang, T.-Y. Chang, M.-S. Hwang, A (t,n) multi-secret sharing scheme, ...

Secret sharing schemes as basic building blocks for many applications in distributed systems should be efficient and robust to any possible attacks. Based on bilinear pairing, this paper will propose a new (t, n) threshold verifiable multi-secret sharing scheme and a GGOC verifiable multi-secret sharing scheme that improve the security and minimizes the number of published values.

Cheater detection and identification are important issues in the process of secret reconstruction. To detect and identify cheaters most of the algorithms need the dealer to generate and distribute additional information to shareholders. Recently, algorithms have been proposed to detect and identify cheaters. If more than t (i.e. the threshold) shares, for example j (i.e. t < j) shares in the se...

The round complexity of verifiable secret sharing (VSS) schemes has been studied extensively for threshold adversaries. In particular, Fitzi et al. showed an efficient 3-round VSS for n ≥ 3t+1 [4], where an infinitely powerful adversary can corrupt t (or less) parties out of n parties. This paper shows that for non-threshold adversaries, 1. Two round VSS is possible iff the underlying adversary...

In this work we provide efficient distributed protocols for generating shares of random noise, secure against malicious participants. The purpose of the noise generation is to create a distributed implementation of the privacy-preserving statistical databases described in recent papers [14, 4, 13]. In these databases, privacy is obtained by perturbing the true answer to a database query by the ...

In a threshold scheme, the sensitivity of the secret as well as the number of players may fluctuate due to various reasons, e.g., mutual trust may vary or the structure of the players’ organization might be changed. A possible solution to this problem is to modify the threshold and/or change the secret. Moreover, a common problem with almost all secret sharing schemes is that they are “one-time...

In this paper, we investigate how to achieve verifiable secret sharing (VSS) schemes by using the Chinese Remainder Theorem (CRT). We first show that two schemes proposed earlier are not secure by an attack where the dealer is able to distribute inconsistent shares to the users. Then we propose a new VSS scheme based on the CRT and prove its security. Using the proposed VSS scheme, we develop a...

In a (t,n) secret sharing scheme, a mutually trusted dealer divides a secret into n shares in such a way that any t or more than t shares can reconstruct the secret, but fewer than t shares cannot reconstruct the secret. When there is no mutually trusted dealer, a (n,t,n) secret sharing scheme can be used to set up a (t,n) secret sharing because each shareholder also acts as a dealer to decide ...

Verifiable secret sharing is a cryptographic primitive used in many distributed applications. To engineer realistic applications, it is beneficial to have dynamically changing shares and shareholder groups. Proactive secret sharing schemes deal with dynamically changing shares. Secret redistribution schemes solve issues of both dynamically changing shares and shareholder groups. In this dissert...