17 research outputs found
Constructing Optimal Authentication Codes with Perfect Multi-fold Secrecy
We establish a construction of optimal authentication codes achieving perfect
multi-fold secrecy by means of combinatorial designs. This continues the
author's work (ISIT 2009) and answers an open question posed therein. As an
application, we present the first infinite class of optimal codes that provide
two-fold security against spoofing attacks and at the same time perfect two-
fold secrecy.Comment: 4 pages (double-column); to appear in Proc. 2010 International Zurich
Seminar on Communications (IZS 2010, Zurich
Combinatorial Bounds and Characterizations of Splitting Authentication Codes
We present several generalizations of results for splitting authentication
codes by studying the aspect of multi-fold security. As the two primary
results, we prove a combinatorial lower bound on the number of encoding rules
and a combinatorial characterization of optimal splitting authentication codes
that are multi-fold secure against spoofing attacks. The characterization is
based on a new type of combinatorial designs, which we introduce and for which
basic necessary conditions are given regarding their existence.Comment: 13 pages; to appear in "Cryptography and Communications
Authentication Codes Based on Resilient Boolean Maps
We introduce new constructions of systematic authentication codes over finite fields and Galois rings. One code is built over finite fields using resilient functions and it provides optimal impersonation and substitution probabilities. Other two proposed codes are defined over Galois rings, one is based on resilient maps and it attains optimal probabilities as well, while the other uses maps whose Fourier transforms get higher values. Being the finite fields special cases of Galois rings, the first code introduced for Galois rings apply also at finite fields. For the special case of characteristic , the maps used at the second case in Galois rings are bent indeed, and this case is subsumed by our current general construction of characteristic , with
Difference Covering Arrays and Pseudo-Orthogonal Latin Squares
Difference arrays are used in applications such as software testing,
authentication codes and data compression. Pseudo-orthogonal Latin squares are
used in experimental designs. A special class of pseudo-orthogonal Latin
squares are the mutually nearly orthogonal Latin squares (MNOLS) first
discussed in 2002, with general constructions given in 2007. In this paper we
develop row complete MNOLS from difference covering arrays. We will use this
connection to settle the spectrum question for sets of 3 mutually
pseudo-orthogonal Latin squares of even order, for all but the order 146
Perfect Secrecy Systems Immune to Spoofing Attacks
We present novel perfect secrecy systems that provide immunity to spoofing
attacks under equiprobable source probability distributions. On the theoretical
side, relying on an existence result for -designs by Teirlinck, our
construction method constructively generates systems that can reach an
arbitrary high level of security. On the practical side, we obtain, via cyclic
difference families, very efficient constructions of new optimal systems that
are onefold secure against spoofing. Moreover, we construct, by means of
-designs for large values of , the first near-optimal systems that are 5-
and 6-fold secure as well as further systems with a feasible number of keys
that are 7-fold secure against spoofing. We apply our results furthermore to a
recently extended authentication model, where the opponent has access to a
verification oracle. We obtain this way novel perfect secrecy systems with
immunity to spoofing in the verification oracle model.Comment: 10 pages (double-column); to appear in "International Journal of
Information Security
Mutually unbiased maximally entangled bases from difference matrices
Based on maximally entangled states, we explore the constructions of mutually
unbiased bases in bipartite quantum systems. We present a new way to construct
mutually unbiased bases by difference matrices in the theory of combinatorial
designs. In particular, we establish mutually unbiased bases with
maximally entangled bases and one product basis in for arbitrary prime power . In addition, we construct
maximally entangled bases for dimension of composite numbers of non-prime
power, such as five maximally entangled bases in and , which improve the
known lower bounds for , with in . Furthermore, we construct mutually unbiased bases with
maximally entangled bases and one product basis in for arbitrary prime number .Comment: 24 page