Cryptology and Error Correction : An Algebraic Introduction and Real-World Applications. 1st ed. 2019

種類:

電子ブック

責任表示:

by Lindsay N. Childs

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2019

著者名:

• Childs, Lindsay N.
• SpringerLink (Online service)

シリーズ名:

Springer Undergraduate Texts in Mathematics and Technology ;

ISBN:

9783030154530 [303015453X]    

注記:

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. .
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–Hellman, and Blum–Goldwasser cryptosystems and Hamming and Reed–Solomon error correction: how they are constructed, how they are made to work efficiently, and also how they can be attacked. To reach that level of understanding requires and motivates many ideas found in a first course in abstract algebra—rings, fields, finite abelian groups, basic theory of numbers, computational number theory, homomorphisms, ideals, and cosets. Those who complete this book will have gained a solid mathematical foundation for more specialized applied courses on cryptology or error correction, and should also be well prepared, both in concepts and in motivation, to pursue more advanced study in algebra and number theory. This text is sui

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