Protocols are given for allowing a “prover” to convince a “verifier” that the prover knows some verifiable secret information, without allowing the verifier to learn anything about the secret. The secret can be probabilistically or deterministically verifiable, and only one of the prover or the verifier need have constrained resources. This paper unifies and extends models and techniques previo...

We present a new protocol to perform non-interactive verifiable secret redistribution (VSR) for secrets distributed with Shamir’s secret sharing scheme. We base our VSR protocol on Desmedt and Jajodia’s redistribution protocol for linear secret sharing schemes, which we specialize for Shamir’s scheme. We extend their redistribution protocol with Feldman’s non-interactive verifiable secret shari...

Secret sharing schemes are methods for distributing a secret among n participants in such a way that any qualified subsets of participants can recover the secret, and unqualified participants can not. In 1979, secret sharing schemes were first independently introduced by Blakley and Shamir. In 1987, Feldman proposed a verifiable secret sharing scheme based on Shamir’s Scheme, that every partici...

‎In a (t,n)-threshold secret sharing scheme‎, ‎a secret s is distributed among n participants such that any group of t or more participants can reconstruct the secret together‎, ‎but no group of fewer than t participants can do‎. In this paper, we propose a verifiable (t,n)-threshold multi-secret sharing scheme based on Shao and Cao‎, ‎and the intractability of the elliptic curve discrete logar...

Threshold secret sharing schemes do not prevent any malicious behavior of the dealer or shareholders and so we need verifiable secret sharing, to detect and identify the cheaters, to achieve fair reconstruction of a secret. The problem of verifiable secret sharing is to verify the shares distributed by the dealer. A novel approach for verifiable secret sharing is presented in this paper where b...

This paper describes an efficient (k, n) threshold digital signature scheme. In the scheme, k out of n signers cooperate to issue a signature without using trusted center. No secret communication is required among signers across the network. As a base scheme, Pedersen's verifiable secret sharing (VSS) is applied to generate shared secret keys in such a way that no secret communication is requir...

This paper addresses the problem of designing practical protocols for proving properties about encrypted data. To this end, it presents a variant of the new public key encryption of Cramer and Shoup based on Paillier’s decision composite residuosity assumption, along with efficient protocols for verifiable encryption and decryption of discrete logarithms (and more generally, of representations ...

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...