213 research outputs found
A Brief Retrospective Look at the Cayley-Purser Public-key Cryptosystem, 19 Years Later
The purpose of this paper is to describe and analyze the Cayley-Purser
algorithm, which is a public-key cryptosystem proposed by Flannery in 1999. I
will present two attacks on it, one of which is apparently new. I will also
examine a variant of the Cayley-Purser algorithm that was patented by Slavin in
2008, and show that it is also insecure.Comment: submitted for publicatio
Optimal Ramp Schemes and Related Combinatorial Objects
In 1996, Jackson and Martin proved that a strong ideal ramp scheme is
equivalent to an orthogonal array. However, there was no good characterization
of ideal ramp schemes that are not strong. Here we show the equivalence of
ideal ramp schemes to a new variant of orthogonal arrays that we term augmented
orthogonal arrays. We give some constructions for these new kinds of arrays,
and, as a consequence, we also provide parameter situations where ideal ramp
schemes exist but strong ideal ramp schemes do not exist
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
Extended Combinatorial Constructions for Peer-to-peer User-Private Information Retrieval
We consider user-private information retrieval (UPIR), an interesting
alternative to private information retrieval (PIR) introduced by Domingo-Ferrer
et al. In UPIR, the database knows which records have been retrieved, but does
not know the identity of the query issuer. The goal of UPIR is to disguise user
profiles from the database. Domingo-Ferrer et al.\ focus on using a
peer-to-peer community to construct a UPIR scheme, which we term P2P UPIR. In
this paper, we establish a strengthened model for P2P UPIR and clarify the
privacy goals of such schemes using standard terminology from the field of
privacy research. In particular, we argue that any solution providing privacy
against the database should attempt to minimize any corresponding loss of
privacy against other users. We give an analysis of existing schemes, including
a new attack by the database. Finally, we introduce and analyze two new
protocols. Whereas previous work focuses on a special type of combinatorial
design known as a configuration, our protocols make use of more general
designs. This allows for flexibility in protocol set-up, allowing for a choice
between having a dynamic scheme (in which users are permitted to enter and
leave the system), or providing increased privacy against other users.Comment: Updated version, which reflects reviewer comments and includes
expanded explanations throughout. Paper is accepted for publication by
Advances in Mathematics of Communication
Some new results on skew frame starters in cyclic groups
In this paper, we study skew frame starters, which are strong frame starters
that satisfy an additional "skew" property. We prove three new non-existence
results for cyclic skew frame starters of certain types. We also construct
several small examples of previously unknown cyclic skew frame starters by
computer
- β¦