Publicly verifiable secret sharing (PVSS) allows not only shareholders themselves but also everyone verify the shares of a secret distributed by a dealer. It has a lot of electronic applications. In this paper, we propose a publicly verifiable member-join protocol for threshold signatures. In our proposal, a new member can join a PVSS scheme to share the secret only with the help of old shareho...

In the paper we propose general framework for Automatic Secret Generation and Sharing (ASGS) that should be independent of underlying secret sharing scheme. ASGS allows to prevent the dealer from knowing the secret or even to eliminate him at all. Two situations are discussed. First concerns simultaneous generation and sharing of the random, prior nonexistent secret. Such a secret remains unkno...

The private key of electronic elections is a very critical piece of information that, with an incorrect or improper use, may disrupt the elections results. To enforce the privacy and security of the private key, secret sharing schemes (or threshold schemes) are used to generate a distributed key into several entities. In this fashion, a threshold of at least t out of the n entities will be nece...

We show that if a set of players hold shares of a value a ∈ Zp for some prime p (where the set of shares is written [a]p), it is possible to compute, in constant round and with unconditional security, sharings of the bits of a, i.e. compute sharings [a0]p, . . . , [a`−1]p such that ` = dlog 2 (p)e, a0, . . . , a`−1 ∈ {0, 1} and a = ∑`−1 i=0 ai2 . Our protocol is secure against active adversarie...

In the paper we propose general framework for Automatic Secret Generation and Sharing (ASGS) that should be independent of underlying secret sharing scheme. ASGS allows to prevent the dealer from knowing the secret or even to eliminate him at all. Two situations are discussed. First concerns simultaneous generation and sharing of the random, prior nonexistent secret. Such a secret remains unkno...

In Chen-Cramer Crypto 2006 paper \cite{cc} algebraic geometric secret sharing schemes were proposed such that the Fundamental Theorem in Information-Theoretically Secure Multiparty Computation by Ben-Or, Goldwasser and Wigderson \cite{BGW88} Chaum, Crepeau Damgard \cite{CCD88} can be established over constant-size base finite fields. These defined a curve of genus $g$ constant size field ${\bf ...

Secret sharing in user hierarchy represents a challenging area for research. Although a lot of work has already been done in this direction, this paper presents a novel approach to share a secret among a hierarchy of users while overcoming the limitations of the already existing mechanisms. Our work is based on traditional (k+ 1, n)-threshold secret sharing, which is secure as long as an advers...

2-level shared secret schemes are defined by Simmons in 1989. In this paper, we describe a survey of 2-level secret sharing schemes using finite geometry.