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020 _a9783540794561
_9978-3-540-79456-1
024 7 _a10.1007/978-3-540-79456-1
_2doi
050 4 _aQA76.9.A43
072 7 _aUMB
_2bicssc
072 7 _aCOM051300
_2bisacsh
072 7 _aUMB
_2thema
082 0 4 _a518.1
_223
245 1 0 _aAlgorithmic Number Theory
_h[electronic resource] :
_b8th International Symposium, ANTS-VIII Banff, Canada, May 17-22, 2008 Proceedings /
_cedited by Alf J. van der Poorten, Andreas Stein.
250 _a1st ed. 2008.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2008.
300 _aIX, 458 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aTheoretical Computer Science and General Issues,
_x2512-2029 ;
_v5011
505 0 _aInvited Papers -- Running Time Predictions for Factoring Algorithms -- A New Look at an Old Equation -- Elliptic Curves Cryptology and Generalizations -- Abelian Varieties with Prescribed Embedding Degree -- Almost Prime Orders of CM Elliptic Curves Modulo p -- Efficiently Computable Distortion Maps for Supersingular Curves -- On Prime-Order Elliptic Curves with Embedding Degrees k?=?3, 4, and 6 -- Arithmetic of Elliptic Curves -- Computing in Component Groups of Elliptic Curves -- Some Improvements to 4-Descent on an Elliptic Curve -- Computing a Lower Bound for the Canonical Height on Elliptic Curves over Totally Real Number Fields -- Faster Multiplication in GF(2)[x] -- Integer Factorization -- Predicting the Sieving Effort for the Number Field Sieve -- Improved Stage 2 to P ± 1 Factoring Algorithms -- K3 Surfaces -- Shimura Curve Computations Via K3 Surfaces of Néron-Severi Rank at Least 19 -- K3 Surfaces of Picard Rank One and Degree Two -- Number Fields -- Number Fields Ramified at One Prime -- An Explicit Construction of Initial Perfect Quadratic Forms over Some Families of Totally Real Number Fields -- Functorial Properties of Stark Units in Multiquadratic Extensions -- Enumeration of Totally Real Number Fields of Bounded Root Discriminant -- Point Counting -- Computing Hilbert Class Polynomials -- Computing Zeta Functions in Families of C a,b Curves Using Deformation -- Computing L-Series of Hyperelliptic Curves -- Point Counting on Singular Hypersurfaces -- Arithmetic of Function Fields -- Efficient Hyperelliptic Arithmetic Using Balanced Representation for Divisors -- Tabulation of Cubic Function Fields with Imaginary and Unusual Hessian -- Modular Forms -- Computing Hilbert Modular Forms over Fields with Nontrivial Class Group -- Hecke Operators and Hilbert Modular Forms.-Cryptography -- A Birthday Paradox for Markov Chains, with an Optimal Bound for Collision in the Pollard Rho Algorithm for Discrete Logarithm -- An Improved Multi-set Algorithm for the Dense Subset Sum Problem -- Number Theory -- On the Diophantine Equation x 2?+?2 ? 5 ? 13 ? ?=?y n -- Non-vanishing of Dirichlet L-functions at the Central Point.
520 _aThis book constitutes the refereed proceedings of the 8th International Algorithmic Number Theory Symposium, ANTS 2008, held in Banff, Canada, in May 2008. The 28 revised full papers presented together with 2 invited papers were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on elliptic curves cryptology and generalizations, arithmetic of elliptic curves, integer factorization, K3 surfaces, number fields, point counting, arithmetic of function fields, modular forms, cryptography, and number theory.
650 0 _aAlgorithms.
_93390
650 0 _aComputer science
_xMathematics.
_93866
650 0 _aDiscrete mathematics.
_912873
650 0 _aCryptography.
_91973
650 0 _aData encryption (Computer science).
_99168
650 0 _aNumber theory.
_913208
650 1 4 _aAlgorithms.
_93390
650 2 4 _aDiscrete Mathematics in Computer Science.
_931837
650 2 4 _aCryptology.
_931769
650 2 4 _aSymbolic and Algebraic Manipulation.
_955589
650 2 4 _aNumber Theory.
_913208
700 1 _avan der Poorten, Alf J.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
_9140854
700 1 _aStein, Andreas.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
_9140855
710 2 _aSpringerLink (Online service)
_9140856
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783540794554
776 0 8 _iPrinted edition:
_z9783540849971
830 0 _aTheoretical Computer Science and General Issues,
_x2512-2029 ;
_v5011
_9140857
856 4 0 _uhttps://doi.org/10.1007/978-3-540-79456-1
912 _aZDB-2-SCS
912 _aZDB-2-SXCS
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