Number Theory and Cryptography

J. H. Loxton

doi:10.1017/CBO9781107325838

In this volume, originally published in 1990, are included papers presented at two meetings; one a workshop on Number Theory and Cryptography, and the other, the annual meeting of the Australian Mathematical Society. Questions in number theory are of military and commercial importance for the security of communication, as they are related to codes and code-breaking. Papers in the volume range from problems in pure mathematics whose study has been intensified by this connection, through interesting theoretical and combinatorial problems which arise in the implementation, to practical questions that come from banking and telecommunications. The contributors are prominent within their field. The whole volume will be an attractive purchase for all number theorists, 'pure' or 'applied'.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Contributors
pp vii-viii
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Introduction
pp ix-xii
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I - NUMBER THEORETIC ASPECTS OF CRYPTOLOGY
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1 - Some mathematical aspects of recent advances in cryptology
pp 1-8
- By R. Lidl, University of Tasmania
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2 - Quadratic fields and cryptography
pp 9-25
- By J. Buchmann, Universität des Saarlandes, H. C. Williams, University of Manitoba
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3 - Parallel algorithms for integer factorisation
pp 26-37
- By R. P. Brent, Australian National University
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4 - An open architecture number sieve
pp 38-75
- By A. J. Stephens, University of Manitoba, H. C. Williams, University of Manitoba
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5 - Algorithms for finite fields
pp 76-85
- By H. W. Lenstra, Jr., University of California
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6 - Notes on continued fractions and recurrence sequences
pp 86-97
- By A. J. van der Poorten, Macquarie University
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II - CRYPTOGRAPHIC DEVICES AND APPLICATIONS
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7 - Security in telecommunication services over the next decade
pp 98-105
- By J. Snare, Telecom Australia Research Laboratories
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8 - Linear feedback shift registers and stream ciphers
pp 106-119
- By E. Dawson, Queensland University of Technology
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9 - Applying randomness tests to commercial level block ciphers
pp 120-128
- By H. Gustaphson, Queensland University of Technology, E. Dawson, Queensland University of Technology, W. Caelli, Queensland University of Technology
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10 - Pseudo-random sequence generators using structured noise
pp 129-136
- By R. S. Safavi-Naini, University College, J. R. Seberry, University College, University of New South Wales
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11 - Privacy for MACNET
pp 137-148
- By M. Warner, Telecom Australia Research Laboratory
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12 - Authentication
pp 149-155
- By B. Newman, James Cook University
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13 - Insecurity of the knapsack one-time pad
pp 156-164
- By R. T. Worley, Monash University
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14 - The tactical frequency management problem: heuristic search and simulated annealing
pp 165-174
- By L. Peters, Plessey Australia, Railway Road
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15 - Reed-Solomon coding in the complex field
pp 175-176
- By M. Rudolph, Royal Melbourne Institute of Technology
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PART III - DIOPHANTINE ANALYSIS
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16 - Class number problems for real quadratic fields
pp 177-195
- By R. A. Mollin, University of Calgary, H. C. Williams, University of Manitoba
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17 - Number theoretic problems involving two independent bases
pp 196-203
- By T. Kamae, Osaka City University
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18 - A class of normal numbers II
pp 204-210
- By Y.-N. Nakai, Yamanashi University, I. Shiokawa, Keio University
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19 - Notes on uniform distribution
pp 211-212
- By G. Myerson, Macquarie University, A. Pollington, Brigham Young University
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20 - Thue equations and multiplicative independence
pp 213-220
- By B. Brindza, Macquarie University
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21 - A number theoretic crank associated with open bosonic strings
pp 221-226
- By F. G. Garvan, Macquarie University
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22 - Universal families of abelian varieties
pp 227-236
- By A. Silverberg, Thomas J. Watson Research Centre
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