In this paper, we present a very important primitive called Information Checking Protocol (ICP) which plays an important role in constructing statistical Verifiable Secret Sharing (VSS) and Weak Secret Sharing (WSS) protocols. Informally, ICP is a tool for authenticating messages in the presence of computationally unbounded corrupted parties. Here we extend the basic bare-bone definition of ICP...

We introduce and formally define polynomial commitment schemes, and provide two efficient constructions. A polynomial commitment scheme allows a committer to commit to a polynomial with a short string that can be used by a verifier to confirm claimed evaluations of the committed polynomial. Although the homomorphic commitment schemes in the literature can be used to achieve this goal, the sizes...

Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, School of Computer Science and Technology, Anhui University, Hefei, 230039, China Department of Computer Science and Information Engineering, Asia University, Taichung, 413, Taiwan Department of Computer Science and Electrical Engineering, University of Missouri—Kansas City, Kansas City, Missouri 64110-2499,...

In the standard general-adversary model for multi-party protocols, a global adversary structure is given, and every party must trust in this particular structure. We introduce a more general model, the asymmetric-trust model, wherein every party is allowed to trust in a different, personally customized adversary structure. We have two main contributions. First, we present non-trivial lower and ...

The round complexity of interactive protocols is one of their most important complexity measures. In this work we prove that existing lower bounds for the round complexity of VSS can be circumvented by introducing a negligible probability of error in the reconstruction phase. Previous results show matching lower and upper bounds of three rounds for VSS, with n = 3t + 1, where the reconstruction...

Verifiable secret sharing schemes (VSS) are secret sharing schemes (SSS) dealing with possible cheating by participants. In this paper we use the VSS proposed by Cramer, Damgard and Maurer [6, 7, 5]. They introduced a purely linear algebraic method to transform monotone span program (MSP) based secret sharing schemes into VSS. In fact, the monotone span program model of Karchmer and Wigderson [...

Threshold secret sharing schemes are used to divide a given secret by a dealer in parts such that no less than the threshold number of shareholders can reconstruct the secret. However, these schemes are susceptible to the malicious behavior of a shareholder or a dealer. To prevent such attacks, it is necessary to make a provision for verification of the integrity of the shares distributed by th...

This paper investigates the security of Proactive Secret Sharing Schemes. We first consider the approach of using commitment to 0 in the renewal phase in order to refresh the player’s shares and we present two types of attacks in the information theoretic case. Then we prove the conditions for the security of such a proactive scheme. Proactivity can be added also using re-sharing instead of com...

We propose a tracing scheme of e-cash which has not only fair tracing ability but also lower computational complexity for comparisons. Many other protocols allow optimistic fair tracing which means that illegal tracing can be found after tracing and depositing in bank. But in this scheme, illegal tracing done by bank alone is impossible. We propose a marking mechanism based on a variant of an O...

Voice communication carried out using the Internet Protocol (IP) for the transaction is known as Voice over Internet Protocol (VoIP). Voice over Internet Protocol is a technology for communicating using “Internet protocol” instead of traditional analog systems. Some VoIP services need only a regular phone connection, while others allows making telephone calls using an Internet connection instea...