A Simple Publicly Verifiable Secret Sharing Scheme and Its Application to Electronic Voting

Abstract

Abstract.A publicly verifiable secret sharing (PVSS) scheme is a verifiable secret sharing scheme with the property that the validity of the shares distributed by the dealer can be verified by any party; hence verification is not limited to the respective participants receiving the shares. We present a new construction for PVSS schemes, which compared to previous solutions by Stadler and later by Fujisaki and Okamoto, achieves improvements both in efficiency and in the type of intractability assumptions. The running time is O(nk), where k is a security parameter, and n is the number of participants, hence essentially optimal. The intractability assumptions are the standard Diffie-Hellman assumption and its decisional variant. We present several applications of our PVSS scheme, among which is a new type of universally verifiable election scheme based on PVSS. The election scheme becomes quite practical and combines several advantages of related electronic voting schemes, which makes it of interest in its own right.

Privacy in Mobile Computing for Location-Sharing-Based Services

“…However, in the unlikely case of collusion between the LDS and the participants, the latter will be able to obtain other participants' preferences. In order to mitigate such a threat, the invited participants could agree on establishing a shared secret by using techniques from threshold cryptography [25]. The LDS should then collude with at least a given number of participants in order to obtain the shared secret and learn L i .…”

Optimistic Fair Exchange Based on Publicly Verifiable Secret Sharing

“…In the Shamir secret sharing scheme, there is a threshold k so that only subsets of at least k participants can reconstruct m. A drawback of the Shamir scheme is that participants cannot verify that the distributed shares effectively allow to recover the secret m. In other words, the basic secret sharing scheme assumes that the dealer is not malicious. Verifiable secret sharing [6,10,12,14] resists to a malicious dealer who sends wrong shares: each participant can indeed check his own share. In Publicly verifiable secret sharing [12,14], introduced by Stadler in 1996, anybody can perform this verification and not only the participants.…”

“…Verifiable secret sharing [6,10,12,14] resists to a malicious dealer who sends wrong shares: each participant can indeed check his own share. In Publicly verifiable secret sharing [12,14], introduced by Stadler in 1996, anybody can perform this verification and not only the participants. Below we describe a model for non-interactive publicly verifiable secret sharing (PVSS).…”

ID-Based Non-Interactive Universal Designated Verifier Signature for Privacy-Preserving Applications

“…electronic votings [8], [9], a signature should only be verified by some designated persons rather than anyone. In 1990, Chaum and Antwerpen [10] introduced the so-called undeniable signature scheme in which the signature must be verified with the assistance of signer.…”