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Algorithmic number theory. Lattices, number fields, curves and cryptography. (English) Zbl 1154.11002
Mathematical Sciences Research Institute Publications 44. Cambridge: Cambridge University Press (ISBN 978-0-521-80854-5/hbk). x, 652 p. £ 50.00; $ 99.00 (2008).
The articles of this volume will be reviewed individually. Indexed articles: {\it Lenstra, Hendrik W.jun.}, Solving the Pell equation, 1-23 [Zbl 1178.11077] {\it Buhler, Joe; Wagon, Stan}, Basic algorithms in number theory, 25-68 [Zbl 1196.11170] {\it Pomerance, Carl}, Smooth numbers and the quadratic sieve, 69-81 [Zbl 1188.11065] {\it Stevenhagen, Peter}, The number field sieve, 83-100 [Zbl 1188.11066] {\it Schoof, René}, Four primality testing algorithms, 101-126 [Zbl 1196.11169] {\it Lenstra, Hendrik W.jun.}, Lattices, 127-181 [Zbl 1200.11046] {\it Poonen, Bjorn}, Elliptic curves, 183-207 [Zbl 1214.11073] {\it Stevenhagen, Peter}, The arithmetic of number rings, 209-266 [Zbl 1216.11099] {\it Granville, Andrew}, Smooth numbers: computational number theory and beyond, 267-323 [Zbl 1230.11157] {\it Bernstein, Daniel J.}, Fast multiplication and it applications, 325-384 [Zbl 1208.68239] {\it Pomerance, Carl}, Elementary thoughts on discrete logarithms, 385-396 [Zbl 1188.11070] {\it Schirokauer, Oliver}, The impact of the number field sieve on the discrete logarithm problem in finite fields, 397-420 [Zbl 1188.11071] {\it Bernstein, Daniel J.}, Reducing lattice bases to find small-height values of univariate polynomials, 421-446 [Zbl 1188.11068] {\it Schoof, René}, Computing Arakelov class groups, 447-495 [Zbl 1188.11076] {\it Cohen, Henri; Stevenhagen, Peter}, Computational class field theory, 497-534 [Zbl 1177.11095] {\it Bernstein, Daniel J.}, Protecting communications against forgery, 535-549 [Zbl 1157.94355] {\it Wan, Daqing}, Algorithmic theory of zeta functions over finite fields, 551-578 [Zbl 1188.11075] {\it Lauder, Alan G.B.; Wan, Daqing}, Counting points on varieties over finite fields of small characteristic, 579-612 [Zbl 1188.11069] {\it Top, Jaap; Yui, Noriko}, Congruent number problems and their variants, 613-639 [Zbl 1161.11014] {\it Stein, William A.}, An introduction to computing modular forms using modular symbols, 641-652 [Zbl 1188.11074]

MSC:
11-06Proceedings of conferences (number theory)
14-06Proceedings of conferences (algebraic geometry)
00B15Collections of articles of miscellaneous specific interest
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