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Titlebook: Cryptology and Error Correction; An Algebraic Introdu Lindsay N. Childs Textbook 2019 Springer Nature Switzerland AG 2019 Caeser ciphers.Ch

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书目名称Cryptology and Error Correction
副标题An Algebraic Introdu
编辑Lindsay N. Childs
视频video
概述Exercises in each chapter are real-world application based.Provides solid mathematical preparation for more specialized applied courses on cryptography/error correction.Presents some of the remarkable
丛书名称Springer Undergraduate Texts in Mathematics and Technology
图书封面Titlebook: Cryptology and Error Correction; An Algebraic Introdu Lindsay N. Childs Textbook 2019 Springer Nature Switzerland AG 2019 Caeser ciphers.Ch
描述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 suitable for classroom or online use or for independent study. Aimed at students in mathematics, computer science, and engineering, the prerequisite includes one or two year
出版日期Textbook 2019
关键词Caeser ciphers; Chinese Remainder Theorem; El Gamal cryptography; Lagrange‘s Theorem; Luhn‘s formula; Ver
版次1
doihttps://doi.org/10.1007/978-3-030-15453-0
isbn_ebook978-3-030-15453-0Series ISSN 1867-5506 Series E-ISSN 1867-5514
issn_series 1867-5506
copyrightSpringer Nature Switzerland AG 2019
The information of publication is updating

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Factoring by the Quadratic Sieve,of units modulo a large prime. These methods are examined in sects. 4 and 5. Both methods described in this chapter are models for methods currently used in practice to try to crack those cryptosystems. An appendix compares the speed of Fermat’s original method of factoring with the grade school met
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Water Institutions in the Middle East,r combinations of the two numbers. Matrices play a similar role in isolating and working efficiently with the coefficients of a system of linear equations in order to find solutions of the system. So they will show up again in Chaps. ., . and .. The chapter ends with a brief description of Hill cryp
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Textbook 2019e well prepared, both in concepts and in motivation, to pursue more advanced study in algebra and number theory...This text is suitable for classroom or online use or for independent study. Aimed at students in mathematics, computer science, and engineering, the prerequisite includes one or two year
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Water Institutions in the Middle East,o find the greatest common divisor, and the Extended Euclidean Algorithm to write the greatest common divisor of two numbers as an integer linear combination of the two numbers (Bezout’s Identity). We show how to solve linear congruences and find all integer solutions of integer linear equations in
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Werkstoffgruppen und Werkstoffeigenschaften, to prove the existence and uniqueness of factorization of any number > 1 into a product of prime numbers (the so-called Fundamental Theorem of Arithmetic), to prove the Division Theorem, and to prove the existence of Bezout’s Identity. Uniqueness of factorization permits an alternative description
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,Zerstörungsfreie Werkstoffprüfung,quotient rings. The immediate objective is to describe modular arithmetic as addition and multiplication in the ring ., of cosets of integers modulo the ideal consisting of all multiples of the modulus .. Doing so places modular arithmetic on a firm theoretical foundation. One consequence is to show
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