Number Theory and Cryptography

J. H. Loxton

• Publisher: Cambridge University Press
• Year: 1990
• Print ISBN:
  9780521398770
• eBook ISBN:
  9781107108288
• Topic: Mathematics
• Subtopic: Number Theory
• Index: Mathematics

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'.

Table of contents

• Cover
• Series Page
• Title
• Copyright
• CONTENTS
• CONTRIBUTORS
• INTRODUCTION
• 1 SOME MATHEMATICAL ASPECTS OF RECENT ADVANCES IN CRYPTOLOGY
• 2 QUADRATIC FIELDS AND CRYPTOGRAPHY
• 3 PARALLEL ALGORITHMS FOR INTEGER FACTORISATION
• 4 AN OPEN ARCHITECTURE NUMBER SIEVE
• 5 ALGORITHMS FOR FINITE FIELDS
• 6 NOTES ON CONTINUED FRACTIONS AND RECURRENCE SEQUENCES
• 7 SECURITY IN TELECOMMUNICATION SERVICES OVER THE NEXT DECADE
• 8 LINEAR FEEDBACK SHIFT REGISTERS AND STREAM CIPHERS
• 9 APPLYING RANDOMNESS TESTS TO COMMERCIAL LEVEL BLOCK CIPHERS
• 10 PSEUDO-RANDOM SEQUENCE GENERATORS USING STRUCTURED NOISE
• 11 PRIVACY FOR MACNET
• 12 AUTHENTICATION
• 13 INSECURITY OF THE KNAPSACK ONE-TIME PAD
• 14 THE TACTICAL FREQUENCY MANAGEMENT PROBLEM: HEURISTIC SEARCH AND SIMULATED ANNEALING
• 15 REED-SOLOMON CODING IN THE COMPLEX FIELD
• 16 CLASS NUMBER PROBLEMS FOR REAL QUADRATIC FIELDS
• 17 NUMBER THEORETIC PROBLEMS INVOLVING TWO INDEPENDENT BASES
• 18 A CLASS OF NORMAL NUMBERS II
• 19 NOTES ON UNIFORM DISTRIBUTION
• 20 THUE EQUATIONS AND MULTIPLICATIVE INDEPENDENCE
• 21 A NUMBER THEORETIC CRANK ASSOCIATED WITH OPEN BOSONIC STRINGS
• 22 UNIVERSAL FAMILIES OF ABELIAN VARIETIES