Simon R. Blackburn

Bio: Simon R. Blackburn is an academic researcher from Royal Holloway, University of London. The author has contributed to research in topics: Cryptography & Cryptanalysis. The author has an hindex of 27, co-authored 136 publications receiving 1943 citations. Previous affiliations of Simon R. Blackburn include University of Oxford & University College London.

Connectivity of the Uniform Random Intersection Graph

Abstract: A \emph{uniform random intersection graph} $G(n,m,k)$ is a random graph constructed as follows. Label each of $n$ nodes by a randomly chosen set of $k$ distinct colours taken from some finite set of possible colours of size $m$. Nodes are joined by an edge if and only if some colour appears in both their labels. These graphs arise in the study of the security of wireless sensor networks. Such graphs arise in particular when modelling the network graph of the well known key predistribution technique due to Eschenauer and Gligor. The paper determines the threshold for connectivity of the graph $G(n,m,k)$ when $n\to \infty$ with $k$ a function of $n$ such that $k\geq 2$ and $m=\lfloor n^\alpha\rfloor$ for some fixed positive real number $\alpha$. In this situation, $G(n,m,k)$ is almost surely connected when \[ \liminf k^2n/m\log n>1, \] and $G(n,m,k)$ is almost surely disconnected when \[ \limsup k^2n/m\log n<1. \]

Comments on "Theory and applications of cellular automata in cryptography" [with reply]

Abstract: This paper argues that the cipher systems based on cellular automata (CA) proposed by S. Nandi et al. (1994) are affine and are insecure. A reply by S. Nandi and P. Pal Chaudhuri is given. The reply emphasizes the point that the regular, modular, cascadable structure of local neighborhood CA can be employed for building low cost cipher system hardware. This cost effective engineering solution can achieve desired level of security with larger size CA.

Comments on “Theory and applications of cellular automata in cryptography”

Abstract: The cipher systems based on Cellular Automata proposed by Nandi et al are a ne and are insecure Index Terms Cryptography block ciphers stream ciphers cellular automata

Handbook of Applied Cryptography

Abstract: From the Publisher: A valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography, this book provides easy and rapid access of information and includes more than 200 algorithms and protocols; more than 200 tables and figures; more than 1,000 numbered definitions, facts, examples, notes, and remarks; and over 1,250 significant references, including brief comments on each paper.

Character Theory of Finite Groups

Abstract: 1. (i) Suppose K is a conjugacy class of Sn contained in An; then K is called split if K is a union of two conjugacy classes of An. Show that the number of split conjugacy classes contained in An is equal to the number of characters χ ∈ Irr(Sn) such that χAn is not irreducible. (Hint. Consider the vector space of class functions on An which are invariant under conjugation by the transposition (12).)

Introduction to random graphs

Abstract: From social networks such as Facebook, the World Wide Web and the Internet, to the complex interactions between proteins in the cells of our bodies, we constantly face the challenge of understanding the structure and development of networks. The theory of random graphs provides a framework for this understanding, and in this book the authors give a gentle introduction to the basic tools for understanding and applying the theory. Part I includes sufficient material, including exercises, for a one semester course at the advanced undergraduate or beginning graduate level. The reader is then well prepared for the more advanced topics in Parts II and III. A final part provides a quick introduction to the background material needed. All those interested in discrete mathematics, computer science or applied probability and their applications will find this an ideal introduction to the subject.