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020 _a9781441985927
_9978-1-4419-8592-7
024 7 _a10.1007/978-1-4419-8592-7
_2doi
050 4 _aQA241-247.5
072 7 _aPBH
_2bicssc
072 7 _aMAT022000
_2bisacsh
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082 0 4 _a512.7
_223
100 1 _aKoblitz, Neal.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_931649
245 1 2 _aA Course in Number Theory and Cryptography
_h[electronic resource] /
_cby Neal Koblitz.
250 _a2nd ed. 1994.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c1994.
300 _aX, 235 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGraduate Texts in Mathematics,
_x2197-5612 ;
_v114
505 0 _aI. 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. .
520 _a. . . 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.
650 0 _aNumber theory.
_913208
650 1 4 _aNumber Theory.
_913208
710 2 _aSpringerLink (Online service)
_931650
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
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776 0 8 _iPrinted edition:
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776 0 8 _iPrinted edition:
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830 0 _aGraduate Texts in Mathematics,
_x2197-5612 ;
_v114
_931651
856 4 0 _uhttps://doi.org/10.1007/978-1-4419-8592-7
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