Cryptology and Error Correction An Algebraic Introduction and Real-World Applications /

• Main Author: Childs, Lindsay N. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2019.
• Edition: 1st ed. 2019.
• Series: Springer Undergraduate Texts in Mathematics and Technology,
• Subjects: Algebra.; Data encryption (Computer science).; Number theory.; Cryptology.; Number Theory.

This text presents a careful introduction to methods of cryptology and error correction in wide use throughout the world and the concepts of abstract algebra and number theory that are essential for understanding these methods. The objective is to provide a thorough understanding of RSA, Diffie-Hell...

Table of Contents:

• Preface
• 1. Secure, Reliable Information
• 2. Modular Arithmetic
• 3. Linear Equations Modulo m
• 4. Unique Factorization in Z
• 5. Rings and Fields
• 6. Polynomials
• 7. Matrices and Hamming Codes
• 8. Orders and Euler's theorem
• 9. RSA Cryptography and Prime Numbers
• 10. Groups, Cosets, and Lagrange's theorem
• 11. Solving Systems of Congruences
• 12. Homomorphisms and Euler's Phi function
• 13. Cyclic Groups and Cryptography
• 14. Applications of Cosets
• 15. An Introduction to Reed-Solomon codes
• 16. Blum-Goldwasser Cryptography
• 17. Factoring by the Quadratic Sieve
• 18. Polynomials and Finite Fields
• 19. Reed-Solomon Codes II
• Bibliography. .