Computing and mathematical modeling

Computing and

Mathematical Modeling

Computing and

Mathematical Modeling

E d ito rs

K. Thangavel

P. Balasubramaniam

Narosa Publishing House

N ew Delhi Chennai M umbai Kolkata

E d ito rs

K . T h angavel

P. B alasu b ram an iam

Department of Mathematics

Gandhigram Rural Institute (Deemed University)

Gandhigram, India

Copyright €> 2006, Narosa Publishing House Pvt. Ltd.

N A R O S A P U B L I S H I N G H O U S E PVT. LTD.

22 Daryaganj, Delhi Medical Association Road, New Delhi 110 002

35-36 Greams Road, Thousand Lights, Chennai 600 006

306 Shiv Centre, D.B.C. Sector 17, K.U. Bazar P.O., Navi Mumbai 400 703

2F-2G Shivam Chambers, 53 Syed Amir Ali Avenue, Kolkata 700 019

w w w .narosa.com

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system,

or transmitted in any form or by any means, electronic, mechanical, photocopying,

recording or otherwise, without prior written permission of the publisher.

All export rights for this book vest exclusively with Narosa Publishing House.

Unauthorised export is a violation of terms of sale and is subject to legal action.

Printed from the camera-ready copy provided by the Editors.

ISBN 81-7319-720-2

Published by N.K. Mehra for Narosa Publishing House Pvt. Ltd.,

22 Daryaganj, Delhi Medical Association Road, New Delhi 110 002

and printed at Rajkamal Electric Press, New Delhi 110 033, India

Preface

M athem atics is the com m on language o f m odem science, engineering, and business. T echniques

o f m athem atical m odeling and data analysis are key instrum ents in the tool kit o f m odern

practitioners and researchers in a w ide array o f disciplines.

C om puting and M athem atical m odeling is a prom ising and hot area o f current research

and developm ent, w hich can provide im portant advantages to the users. It can yield substantial

know ledge from m odeling prim arily gathered for a w ide range o f different applications. A lm ost

all industrialists, scientists, engineers and science disciplines are applying the com puting and

m athem atical m odeling to increasing effect.

T he D epartm ent o f M athem atics o f G andhigram R ural Institute-D eem ed U niversity,

G andhigram had organized a tw o day N ational C onference on C om puting and M athem atical

M odeling(N C C M M -2005) under U niversity G rants Com m ission-Special A ssistance Program m e

(U G C -SA P). T he conference facilitated the tools for the researchers w orking in soft com puting/

com putational in telligence and application d evelopers from m any differen t areas, to share

state-of-the-art research results and practical developm ent experiences. T h is volum e contains

38 papers presented after peer review . T he D epartm ent o f M athem atics ex presses its sincere

thanks and regards for all the help and assistance it received from various organizations, Institutions

and individuals.

We ow e our deep sense o f gratitude to the U G C for having sanctioned SA P (D R S ) to

the D epartm ent o f M athem atics from 2004 to 2009 and for having perm itted us to organize the

conference under th is program m e.

E ditors

K. Thangavel

P. Balasubramaniam

Table of Contents

Preface

Cryptography

Information Security and Threshold Cryptography

M.K. Viswanath and K P. Vidya

A Public Distribution Model Using the Feige-Fiat-Shamir Scheme

M K Viswanath and A R Deepti

Neural vs Genetic in Steganography to Indirectly Hide Sensitive Data

T Subha Jayanthi and V. Kavitha

Data M ining

Rule Identification in HIV Data Using Rough Set Strategies

A. Pethalakshmi and K. Thangavel

Grid Based Performance Enhancement of the Mathematical Application

K.S. Ravichandran and M.G. Lakshmi Kanna

Reducts in Information System with Conditional Decision Attributes

G Ganesan and C. Raghavendra Rao

Extended ID3 Algorithm for G enerating Decision Rules Directly for

Rule Post Pruning in Data M ining

S. S. VijayaSri, P. Jaganathan and V Alagarsamy

Im age Processing

Performance Study on Segmentation of Mammogram Image Using

GLRL Texture Features

C. Veiayutham and K. Thangavel

Design and Implementation of Noisy Image Restoration System:

A Neuro Fuzzy Approach

C. Samraj D aniel, V. Seenivasagam and K. Ramar

Image Restoration Using Radial Basis Function Networks

A K Kumaresh and M. Marudai

A Modified Block Truncation Coding for Image Compression

K. Somasundaram and I. Kaspar Raj

Enhancement of Digital M ammogram Using Hybrid Filtering Techniques

K Thangavel, M. Karnan and R. Sivakumar

Performance Analysis of Haralick Features

R Rose!in and K Thangavel

Comparative Study of Clustering Algorithms Using Statistical Features Extracted

from Mammograms by Spatial Grey Level Dependency Matrix

D Ashok Kumar, C. Velayutham and K. Thangavel

EfTect of Window Size and Weight of Median Filters in Removing Impulse Noise

K. Somasundaram and P. Shanmugavadivu

Design and Implementation of Image Restoration: A Neural Network Based

Comparative Study

S. Prakash, V. Seenivasagam and K Ramar

Mathematical M odeling

Short Term Software Failure Predictions Using Time Series Analysis with

Weightage for Recent Failures

S. Venkateswaran, B Sam, K Ekambavanan, P. Vivekanandan and R Ahmed

A Study on Plasma Confinement by a Computational Model

H.B. Ramalingam and V. Selvarajan

Solutions of a Specific Integral Equation Arising out of

C ertain Classes of Point Processes

A.G. Srinivasan

Optimal Control for Bilinear Singular System with a Generalised Cost

P. Balasubramaniam and N. Kumaresan

Advanced Properties of Brownian Paths in Stochastic Modeling

R Sasikumar and V.S. Sampath Kumar

Expected Time to Recruitment in Man Power Planning-A Shock Model Approach

A Srinivasan and S. Sendhamizhselvi

Expected Time to Recruitment in an Organization with ‘n’ Parallel Branches

A. Srinivasan and V. Saavithri

Facial Expression Recognition through Model Based Face Tracking

R. Bhavani, R. Krishnamoorlhy and P. Gajalakshmi

viii Table o f Contents

93

103

112

121

128

137

139

146

157

163

171

182

189

197

Table o f Contents ix

A Synchronous M ethod of Stream Ciphers Using Genetic Algorithm

N. Nalini and G. Raghavendra Rao

Neural Network

Computational Authorship Using Neural Network

G Manimannan, W. Abdul H am eed and M Bagavandas

Solution of Systems of Linear Equations :A Neural Network Approach Using M atlab

W. Abdul Hameed and M. Bagavandas

Optim al Stabilising Q uadratic Control of an Inverted Pendulum Using Neural Networks

P Balasubramaniam and J Abdul Samath

Operations Research

Algorithm to Solve Separable Non-Linear Fractional Program m ing Problems

R Mohanraj, S. Saravanan and R M. Chandrasekaran

Genetic Algorithm A pproach to the Axial Multidimensional Assignment Problem

K. Thangavel and G. Velammal

An Approximative Solution to Unconstrained Multi-Objective

Stochastic Optimization Problem

V. Charles, D S Bharadwaj and N. Abdul Ali

Transient Analysis of a System with Queue Dependent Servers and

Controllable Arrivals

K Udaya Chandrika and K. P. Uma

Theory of Computation

A rray Contextual G ram m ar and its Relevance in DN A Computing

A Murugan and K S. Easwarakumar

Gram m ar, DFA for and from DTL (Decision Tree Learning)

Dinesh B. Hanchate, Sanjay R. Sutar, Indrabhan S. Borse and S M. Choudhari

Simple Contextual A rray G ram m ars and Languages

P Helen Chandra and K G. Subramanian

On Inference of Uniquely Term inating Linear Languages

S. Kannamma, D.G. Thomas and K. Rangarajan

204

211

213

222

231

239

241

248

253

261

269

271

278

282

291

x Table o f Contents

A rray Token Petri Nets

S. Kannamma, K Rangarajan, D G. Thomas and N. G David

Reliable Design Approach for Communication Networks to

Avoid Denial of Service Attacks

S. Behin Sam, S. Venkateswaran, P. Vivekanandan and A. Kannan

Cryptography

C o m p u tin g and M a th em a tica l M o d elin g

Editors: K. Thangavel and P. Balasubramaniam

Copyright© 2006, Narosa Publishing House, New Delhi, India

Information Security and Threshold Cryptography

M .K . V isw anath and K.P. V idya

Department of Mathematics, Madras Christian College (Autonomous)

Affiliated to University of Madras, Chennai 600 059, Tamil Nadu

ABSTRACT

Secret sharing schemes are multi-party protocols that facilitate shared control o f critical activities.

Threshold schemes are a special class of these schemes, where, only / o f a total of n participants o f the

scheme (t £ n), need to pool in their shares, to trigger the critical action. In this paper, we suggest a

web application of the (I, n) threshold scheme based on the Chinese Remainder Theorem. Our

application offers an efficient solution for online submission o f research papers at Conferences, which

insist on Author anonymity at the time o f submission and the results o f the acceptance/non-acceptance

o f the papers need to be published without compromising on the identity o f the referees.

Keywords Secret Sharing, Threshold Scheme, Chinese Remainder Theorem

1. INTRODUCTION

A Secret sharing scheme is a multi-party protocol where two or more parties derive a shared secret

from information contributed by, or associated with each o f them, such that, no party can predetermine

the resulting value. That is, a dealer D divides a secret 5 into n pieces called shares or shadows and

distributes them to the n participants Ph i= I,...,« of the scheme. Later, the secret S is reconstructed by

pooling in the shares of authorized sets of participants. This reconstruction may be carried out with the

help of a combiner C. Moreover, if <t> denotes the group o f participants and T and A respectively

denote the set o f authorized and unauthorized participants where r and A are assumed to be mutually

disjoint then the collection (/", A) is called the access structure o f the secret sharing scheme. The

access structure is called a monotone access structure if a set P containing r is also a set o f authorized

participants.

A perfect secret sharing scheme is one in which the shares corresponding to each

unauthorized subset provides absolutely no information about the shared secret. In fact, they have a

monotone access structure. The efficiency o f any secret sharing scheme is measured by its information

rate (defined as the minimum such rate over all the participants where information rate fo r a

3