Schroeder Number Theory in Science and Communication

With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity
3rd Auflage 1997
ISBN: 978-3-662-03430-9
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 7, 364 Seiten, eBook

Reihe: Springer Series in Information Sciences

Number Theory in Science and Communication is an introduction for non-mathematicians. The book stresses intuitive understanding rather than abstract theory and highlights important concepts such as continued fractions, the golden ratio, quadratic residues and Chinese remainders, trapdoor functions, pseudoprimes and primitive elements. Their applications to problems in the real world is one of the main themes of the book. This third edition is augmented by recent advances in primes in progressions, twin primes, prime triplets, prime quadruplets and quintruplets, factoring with elliptic curves, quantum factoring, Golomb rulers and "baroque" integers.

Zielgruppe

Research

Autoren/Hrsg.

Schroeder, Manfred

Inhaltsverzeichnis

I. A Few Fundamentals.- 1. Introduction.- 2. The Natural Numbers.- 3. Primes.- 4. The Prime Distribution.- II. Some Simple Applications.- 5. Fractions: 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.