Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity

by Manfred Schroeder

I. A Few Fundamentals.- 1. Introduction.- 2. The Natural Numbers.- 3. Primes.- 4. The Prime Distribution.- II. Some Simple Applications.- 5. Continued, Egyptian and Farey.- III. Congruences and the Like.- 6. Linear Congruences.- 7. Diophantine Equations.- 8. The Theorems of Fermat, Wilson and Euler.- IV. Cryptography and Divisors.- 9. Euler Trap Doors and Public-Key Encryption.- 10. The Divisor Functions.- 11. The Prime Divisor Functions.- 12. Certified Signatures.- 13. Primitive Roots.- 14. Knapsack Encryption.- V. Residues and Diffraction.- 15. Quadratic Residues.- VI. Chinese and Other Fast Algorithms.- 16. The Chinese Remainder Theorem and Simultaneous Congruences.- 17. Fast Transformation and Kronecker Products.- 18. Quadratic Congruences.- VII. Pseudoprimes, Möbius Transform, and Partitions.- 19. Pseudoprimes, Poker and Remote Coin Tossing.- 20. The Möbius Function and the Möbius Transform.- 21. Generating Functions and Partitions.- VIII. Cyclotomy and Polynomials.- 22. Cyclotomic Polynomials.- 23. Linear Systems and Polynomials.- 24. Polynomial Theory.- IX. Galois Fields and More Applications.- 25. Galois Fields.- 26. Spectral Properties of Galois Sequences.- 27. Random Number Generators.- 28. Waveforms and Radiation Patterns.- 29. Number Theory, Randomness and "Art".- X. Self-Similarity, Fractals and Art.- 30. Self-Similarity, Fractals, Deterministic Chaos and a New State of Matter.- Glossary of Symbols.- References.- Name Index.

Genres: Mathematics

388 pages, Paperback

First published February 1, 1986