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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Cryptology and Error Correction978-3-030-15453-0Series ISSN 1867-5506 Series E-ISSN 1867-5514

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Human Skin Equivalents: When and How to Use, product of rings or of groups. These concepts provide a suitable setting for proofs of the Chinese Remainder Theorem and for the formula satisfied by Euler’s phi function, which counts the number of units of the ring . in terms of the factorization of .. Ideas in this chapter will also be used in some of the analyses in Chaps.?. and ..

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Polynomials,of degree . with coefficients in a field can have no more than . roots in the field. D’Alembert’s Theorem will become highly useful for explaining Reed-Solomon error correction in Chap.., and for understanding algorithms for factoring large numbers in cryptology. Polynomials will be revisited in Chap.?..

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,Orders and Euler’s Theorem,h is given a proof using the Binomial Theorem. The final section describes an efficient algorithm for computing a high power of a number modulo .. This algorithm will have both an obvious use in using the cryptosystems presented in Chaps.?. and . and a less obvious use to help construct cryptosystems in the last section of Chap.?..

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Solving Systems of Congruences,ed up the decryption of messages in an RSA cryptosystem. For the general case of systems of congruences to non-coprime moduli, we show how to decide if solutions exist, and if so, how to find all of the solutions.

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