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Titlebook: Algorithmic Number Theory; 8th International Sy Alfred J. Poorten,Andreas Stein Conference proceedings 2008 Springer-Verlag Berlin Heidelbe

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期刊全称Algorithmic Number Theory
期刊简称8th International Sy
影响因子2023Alfred J. Poorten,Andreas Stein
视频video
学科分类Lecture Notes in Computer Science
图书封面Titlebook: Algorithmic Number Theory; 8th International Sy Alfred J. Poorten,Andreas Stein Conference proceedings 2008 Springer-Verlag Berlin Heidelbe
影响因子This 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.
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Almost Prime Orders of CM Elliptic Curves Modulo ,cd. splits in ., where . is the size of the group of rational . points, and prove that it can be bigger than the common factor that comes from the torsion of the curve. Then, we prove that #{. ≤ ., . splits in . hence extending the results in [16]. This is the best known result in the direction of t
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Efficiently Computable Distortion Maps for Supersingular Curves that there exists a distortion map in a specific set of efficiently computable endomorphisms for every pair of nontrivial divisors . for two types of curves. In this paper, we prove that this result holds using a different method . for both curves with . > 5 and . > 19 respectively, where . is the
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Some Improvements to 4-Descent on an Elliptic Curvef 4-descent in the search for generators of large height on elliptic curves of rank at least 2, we explain how to cut down the number of class group and unit group calculations required, by using the group law on the 4-Selmer group.
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Predicting the Sieving Effort for the Number Field Sieveng test as input and simulates relations according to this test. After removing singletons, we decide how many relations we need for the factorization according to the simulation and this gives a good estimate for the real sieving. Experiments show that our estimate is within 2 % of the real data.
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Improved Stage 2 to P ± 1 Factoring Algorithmsn lengths around 2. and stage 2 limit around 10. while attempting to factor 230-digit numbers on modern PC’s. We describe arithmetic algorithms on reciprocal polynomials. We present adjustments for the P+1 algorithm. We list some new findings.
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