A course in number theory and cryptography.

KOBLITZ, Neal (1948-).

ISBN 10: 0387942939 / ISBN 13: 9780387942933

Editore: Springer, 1987., New York:, 1987

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8vo. x, 208 pp. Index. Blind-embossed stamped on title of Joseph W. Ouellette. Very good. ISBN 10: 0387942939 ISBN 13: 9780387942933 "Neal I. Koblitz is a Professor of Mathematics at the University of Washington. He is also an adjunct professor with the Centre for Applied Cryptographic Research at the University of Waterloo. He is the creator of hyperelliptic curve cryptography and the independent co-creator of elliptic curve cryptography.". Codice articolo S13759

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Titolo: A course in number theory and cryptography.

Casa editrice: Springer, 1987., New York:

Data di pubblicazione: 1987

Legatura: Rilegato

Edizione: seconda edizione

Descrizione articolo

Riassunto:

. . . both Gauss and lesser mathematicians may be justified in rejoic­ ing that there is one science [number theory] at any rate, and that their own, whose very remoteness from ordinary human activities should keep it gentle and clean. - G. H. Hardy, A Mathematician's Apology, 1940 G. H. Hardy would have been surprised and probably displeased with the increasing interest in number theory for application to "ordinary human activities" such as information transmission (error-correcting codes) and cryptography (secret codes). Less than a half-century after Hardy wrote the words quoted above, it is no longer inconceivable (though it hasn't happened yet) that the N. S. A. (the agency for U. S. government work on cryptography) will demand prior review and clearance before publication of theoretical research papers on certain types of number theory. In part it is the dramatic increase in computer power and sophistica­ tion that has influenced some of the questions being studied by number theorists, giving rise to a new branch of the subject, called "computational number theory. " This book presumes almost no background in algebra or number the­ ory. Its purpose is to introduce the reader to arithmetic topics, both ancient and very modern, which have been at the center of interest in applications, especially in cryptography. For this reason we take an algorithmic approach, emphasizing estimates of the efficiency of the techniques that arise from the theory.

Contenuti:

I. Some Topics in Elementary Number Theory.- 1. Time estimates for doing arithmetic.- 2. Divisibility and the Euclidean algorithm.- 3. Congruences.- 4. Some applications to factoring.- II. Finite Fields and Quadratic Residues.- 1. Finite fields.- 2. Quadratic residues and reciprocity.- III. Cryptography.- 1. Some simple cryptosystems.- 2. Enciphering matrices.- IV. Public Key.- 1. The idea of public key cryptography.- 2. RSA.- 3. Discrete log.- 4. Knapsack.- 5 Zero-knowledge protocols and oblivious transfer.- V. Primality and Factoring.- 1. Pseudoprimes.- 2. The rho method.- 3. Fermat factorization and factor bases.- 4. The continued fraction method.- 5. The quadratic sieve method.- VI. Elliptic Curves.- 1. Basic facts.- 2. Elliptic curve cryptosystems.- 3. Elliptic curve primality test.- 4. Elliptic curve factorization.- Answers to Exercises.