6 research outputs found
Crossing Hands in the Russian Cards Problem
When communicating using an unconditionally secure protocol, a sender and receiver is able to transmit secret information over a public, insecure channel without fear of the secret being intercepted by a third party. The Russian cards problem is an example of an unconditionally secure protocol where the communication is fully understandable for everyone listening in. Even though everyone can understand what is being said, only the sender and receiver are able to uncover the secrets being transmitted. In this thesis we investigate the interaction among the communicating parties. By extending existing problem-specific software we are able to more efficiently analyze protocols, and we are therefore able to provide an answer to an open problem in the literature. We provide a completely new solution to the Russian cards protocol and show that it fulfills all requirements by the problem. Discovering this new solution provides the person initiating the protocol two new strategies to choose from when constructing the initial announcement of the protocol.Masteroppgave i informasjonsvitenskapINFO39
Combinatorial Solutions Providing Improved Security for the Generalized Russian Cards Problem
We present the first formal mathematical presentation of the generalized
Russian cards problem, and provide rigorous security definitions that capture
both basic and extended versions of weak and perfect security notions. In the
generalized Russian cards problem, three players, Alice, Bob, and Cathy, are
dealt a deck of cards, each given , , and cards, respectively.
The goal is for Alice and Bob to learn each other's hands via public
communication, without Cathy learning the fate of any particular card. The
basic idea is that Alice announces a set of possible hands she might hold, and
Bob, using knowledge of his own hand, should be able to learn Alice's cards
from this announcement, but Cathy should not. Using a combinatorial approach,
we are able to give a nice characterization of informative strategies (i.e.,
strategies allowing Bob to learn Alice's hand), having optimal communication
complexity, namely the set of possible hands Alice announces must be equivalent
to a large set of -designs, where . We also provide some
interesting necessary conditions for certain types of deals to be
simultaneously informative and secure. That is, for deals satisfying
for some , where and the strategy is assumed to satisfy
a strong version of security (namely perfect -security), we show that and hence . We also give a precise characterization of informative
and perfectly -secure deals of the form satisfying involving -designs
Unconditionally Secure Cryptography: Signature Schemes, User-Private Information Retrieval, and the Generalized Russian Cards Problem
We focus on three different types of multi-party cryptographic protocols. The first is in the area of unconditionally secure signature schemes, the goal of which is to provide users the ability to electronically sign documents without the reliance on computational assumptions needed in traditional digital signatures. The second is on cooperative protocols in which users help each other maintain privacy while querying a database, called user-private information retrieval protocols. The third is concerned with the generalized Russian cards problem, in which two card players wish to communicate their hands to each other via public announcements without the third player learning the card deal. The latter two problems have close ties to the field of combinatorial designs, and properly fit within the field of combinatorial cryptography. All of these problems have a common thread, in that they are grounded in the information-theoretically secure or unconditionally secure setting