36,862 research outputs found
Ideal hierarchical secret sharing schemes
Hierarchical secret sharing is among the most natural generalizations of threshold secret sharing, and it has attracted a lot of attention from the invention of secret sharing until nowadays. Several constructions of ideal hierarchical secret sharing schemes have been proposed, but it was not known what access structures admit such a scheme. We solve this problem by providing a natural definition for the family of the hierarchical access structures and, more importantly, by presenting a complete characterization of the ideal hierarchical access structures, that is, the ones admitting an ideal secret sharing scheme. Our characterization deals with the properties of the hierarchically minimal sets of the access structure, which are the minimal qualified sets whose participants are in the lowest possible levels in the hierarchy. By using our characterization, it can be efficiently checked whether any given hierarchical access structure that is defined by its hierarchically minimal sets is ideal. We use the well known connection between ideal secret sharing and matroids and, in particular, the fact that every ideal access structure is a matroid port. In addition, we use recent results on ideal multipartite access structures and the connection between multipartite matroids and integer polymatroids. We prove that every ideal hierarchical access structure is the port of a representable matroid and, more specifically, we prove that every ideal structure in this family admits ideal linear secret sharing schemes over fields of all characteristics. In addition, methods to construct such ideal schemes can be derived from the results in this paper and the aforementioned ones on ideal multipartite secret sharing. Finally, we use our results to find a new proof for the characterization of the ideal weighted threshold access structures that is simpler than the existing one.Peer ReviewedPostprint (author's final draft
Making Code Voting Secure against Insider Threats using Unconditionally Secure MIX Schemes and Human PSMT Protocols
Code voting was introduced by Chaum as a solution for using a possibly
infected-by-malware device to cast a vote in an electronic voting application.
Chaum's work on code voting assumed voting codes are physically delivered to
voters using the mail system, implicitly requiring to trust the mail system.
This is not necessarily a valid assumption to make - especially if the mail
system cannot be trusted. When conspiring with the recipient of the cast
ballots, privacy is broken.
It is clear to the public that when it comes to privacy, computers and
"secure" communication over the Internet cannot fully be trusted. This
emphasizes the importance of using: (1) Unconditional security for secure
network communication. (2) Reduce reliance on untrusted computers.
In this paper we explore how to remove the mail system trust assumption in
code voting. We use PSMT protocols (SCN 2012) where with the help of visual
aids, humans can carry out addition correctly with a 99\% degree of
accuracy. We introduce an unconditionally secure MIX based on the combinatorics
of set systems.
Given that end users of our proposed voting scheme construction are humans we
\emph{cannot use} classical Secure Multi Party Computation protocols.
Our solutions are for both single and multi-seat elections achieving:
\begin{enumerate}[i)]
\item An anonymous and perfectly secure communication network secure against
a -bounded passive adversary used to deliver voting,
\item The end step of the protocol can be handled by a human to evade the
threat of malware. \end{enumerate} We do not focus on active adversaries
More is Less: Perfectly Secure Oblivious Algorithms in the Multi-Server Setting
The problem of Oblivious RAM (ORAM) has traditionally been studied in a
single-server setting, but more recently the multi-server setting has also been
considered. Yet it is still unclear whether the multi-server setting has any
inherent advantages, e.g., whether the multi-server setting can be used to
achieve stronger security goals or provably better efficiency than is possible
in the single-server case.
In this work, we construct a perfectly secure 3-server ORAM scheme that
outperforms the best known single-server scheme by a logarithmic factor. In the
process, we also show, for the first time, that there exist specific algorithms
for which multiple servers can overcome known lower bounds in the single-server
setting.Comment: 36 pages, Accepted in Asiacrypt 201
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