Normal Elliptic Bases and Torus-Based Cryptography

We consider representations of algebraic tori $T_n(F_q)$ over finite fields. We make use of normal elliptic bases to show that, for infinitely many squarefree integers $n$ and infinitely many values of $q$, we can encode $m$ torus elements, to a small fixed overhead and to $m$ $\phi(n)$-tuples of $F_q$ elements, in quasi-linear time in $\log q$. This improves upon previously known algorithms, which all have a quasi-quadratic complexity. As a result, the cost of the encoding phase is now negligible in Diffie-Hellman cryptographic schemes

On Modular Inverses of Cyclotomic Polynomials and the Magnitude of their Coefficients

Let p and r be two primes and n, m be two distinct divisors of pr. Consider the n-th and m-th cyclotomic polynomials. In this paper, we present lower and upper bounds for the coefficients of the inverse of one of them modulo the other one. We mention an application to torus-based cryptography.Comment: 21 page

Parameterizable Byzantine Broadcast in Loosely Connected Networks

We consider the problem of reliably broadcasting information in a multihop asynchronous network, despite the presence of Byzantine failures: some nodes are malicious and behave arbitrarly. We focus on non-cryptographic solutions. Most existing approaches give conditions for perfect reliable broadcast (all correct nodes deliver the good information), but require a highly connected network. A probabilistic approach was recently proposed for loosely connected networks: the Byzantine failures are randomly distributed, and the correct nodes deliver the good information with high probability. A first solution require the nodes to initially know their position on the network, which may be difficult or impossible in self-organizing or dynamic networks. A second solution relaxed this hypothesis but has much weaker Byzantine tolerance guarantees. In this paper, we propose a parameterizable broadcast protocol that does not require nodes to have any knowledge about the network. We give a deterministic technique to compute a set of nodes that always deliver authentic information, for a given set of Byzantine failures. Then, we use this technique to experimentally evaluate our protocol, and show that it significantely outperforms previous solutions with the same hypotheses. Important disclaimer: these results have NOT yet been published in an international conference or journal. This is just a technical report presenting intermediary and incomplete results. A generalized version of these results may be under submission

Chaotic dynamical systems associated with tilings of RN\R^N

In this chapter, we consider a class of discrete dynamical systems defined on the homogeneous space associated with a regular tiling of $\R^N$, whose most familiar example is provided by the $N-$dimensional torus \T ^N. It is proved that any dynamical system in this class is chaotic in the sense of Devaney, and that it admits at least one positive Lyapunov exponent. Next, a chaos-synchronization mechanism is introduced and used for masking information in a communication setup

Secret Sharing Schemes with a large number of players from Toric Varieties

A general theory for constructing linear secret sharing schemes over a finite field \Fq from toric varieties is introduced. The number of players can be as large as $(q-1)^r-1$ for $r\geq 1$. We present general methods for obtaining the reconstruction and privacy thresholds as well as conditions for multiplication on the associated secret sharing schemes. In particular we apply the method on certain toric surfaces. The main results are ideal linear secret sharing schemes where the number of players can be as large as $(q-1)^2-1$. We determine bounds for the reconstruction and privacy thresholds and conditions for strong multiplication using the cohomology and the intersection theory on toric surfaces.Comment: 15 pages, 4 figures. arXiv admin note: text overlap with arXiv:1203.454

Guest editorial : In Journal of networks, v.7 n.3

Networking of computing devices has been going through rapid evolution and thus continuing to be an ever expanding area of importance in recent years. New technologies, protocols, services and usage patterns have contributed to the major research interests in this area of computer science. The current special issue is an effort to bring forward some of these interesting developments that are being pursued by researchers at present in different parts of the globe. Our objective is to provide the readership with some insight into the latest innovations in computer networking through this. This Special Issue presents selected papers from the thirteenth conference of the series (ICCIT 2010) held during December 23-25, 2010 at the Ahsanullah University of Science and Technology. The first ICCIT was held in Dhaka, Bangladesh, in 1998. Since then the conference has grown to be one of the largest computer and IT related research conferences in the South Asian region, with participation of academics and researchers from many countries around the world. Starting in 2008 the proceedings of ICCIT are included in IEEExplore. In 2010, a total of 410 full papers were submitted to the conference of which 136 were accepted after reviews conducted by an international program committee comprising 81 members from 16 countries. This was tantamount to an acceptance rate of 33%. From these 136 papers, 14 highly ranked manuscripts were invited for this Special Issue. The authors were advised to enhance their papers significantly and submit them to undergo review for suitability of inclusion into this publication. Of those, eight papers survived the review process and have been selected for inclusion in this Special Issue. The authors of these papers represent academic and/or research institutions from Australia, Bangladesh, Japan, Korea and USA. These papers address issues concerning different domains of networks namely, optical fiber communication, wireless and interconnection networks, issues related to networking hardware and software and network mobility. The paper titled “Virtualization in Wireless Sensor Network: Challenges and Opportunities” argues in favor of bringing in different heterogeneous sensors under a common virtual framework so that the issues like flexibility, diversity, management and security can be handled practically. The authors Md. Motaharul Islam and Eui-Num Huh propose an architecture for sensor virtualization. They also present the current status and the challenges and opportunities for further research on the topic. The manuscript “Effect of Polarization Mode Dispersion on the BER Performance of Optical CDMA” deals with impact of polarization mode dispersion on the bit error rate performance of direct sequence optical code division multiple access. The authors, Md. Jahedul Islam and Md. Rafiqul Islam present an analytical approach toward determining the impact of different performance parameters. The authors show that the bit error rate performance improves significantly by the third order polarization mode dispersion than its first or second order counterparts. The authors Md. Shohrab Hossain, Mohammed Atiquzzaman and William Ivancic of the paper “Cost and Efficiency Analysis of NEMO Protocol Entities” present an analytical model for estimating the cost incurred by major mobility entities of a NEMO. The authors define a new metric for cost calculation in the process. Both the newly developed metric and the analytical model are likely to be useful to network engineers in estimating the resource requirement at the key entities while designing such a network. The article titled “A Highly Flexible LDPC Decoder using Hierarchical Quasi-Cyclic Matrix with Layered Permutation” deals with Low Density Parity Check decoders. The authors, Vikram Arkalgud Chandrasetty and Syed Mahfuzul Aziz propose a novel multi-level structured hierarchical matrix approach for generating codes of different lengths flexibly depending upon the requirement of the application. The manuscript “Analysis of Performance Limitations in Fiber Bragg Grating Based Optical Add-Drop Multiplexer due to Crosstalk” has been contributed by M. Mahiuddin and M. S. Islam. The paper proposes a new method of handling crosstalk with a fiber Bragg grating based optical add drop multiplexer (OADM). The authors show with an analytical model that different parameters improve using their proposed OADM. The paper “High Performance Hierarchical Torus Network Under Adverse Traffic Patterns” addresses issues related to hierarchical torus network (HTN) under adverse traffic patterns. The authors, M.M. Hafizur Rahman, Yukinori Sato, and Yasushi Inoguchi observe that dynamic communication performance of an HTN under adverse traffic conditions has not yet been addressed. The authors evaluate the performance of HTN for comparison with some other relevant networks. It is interesting to see that HTN outperforms these counterparts in terms of throughput and data transfer under adverse traffic. The manuscript titled “Dynamic Communication Performance Enhancement in Hierarchical Torus Network by Selection Algorithm” has been contributed by M.M. Hafizur Rahman, Yukinori Sato, and Yasushi Inoguchi. The authors introduce three simple adapting routing algorithms for efficient use of physical links and virtual channels in hierarchical torus network. The authors show that their approaches yield better performance for such networks. The final title “An Optimization Technique for Improved VoIP Performance over Wireless LAN” has been contributed by five authors, namely, Tamal Chakraborty, Atri Mukhopadhyay, Suman Bhunia, Iti Saha Misra and Salil K. Sanyal. The authors propose an optimization technique for configuring the parameters of the access points. In addition, they come up with an optimization mechanism in order to tune the threshold of active queue management system appropriately. Put together, the mechanisms improve the VoIP performance significantly under congestion. Finally, the Guest Editors would like to express their sincere gratitude to the 15 reviewers besides the guest editors themselves (Khalid M. Awan, Mukaddim Pathan, Ben Townsend, Morshed Chowdhury, Iftekhar Ahmad, Gour Karmakar, Shivali Goel, Hairulnizam Mahdin, Abdullah A Yusuf, Kashif Sattar, A.K.M. Azad, F. Rahman, Bahman Javadi, Abdelrahman Desoky, Lenin Mehedy) from several countries (Australia, Bangladesh, Japan, Pakistan, UK and USA) who have given immensely to this process. They have responded to the Guest Editors in the shortest possible time and dedicated their valuable time to ensure that the Special Issue contains high-quality papers with significant novelty and contributions