Algorithmic Number Theory
Springer Berlin (Verlag)
978-3-540-79455-4 (ISBN)
Invited 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.
| Erscheint lt. Verlag | 25.4.2008 |
|---|---|
| Reihe/Serie | Lecture Notes in Computer Science | Theoretical Computer Science and General Issues |
| Zusatzinfo | IX, 458 p. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Gewicht | 718 g |
| Themenwelt | Informatik ► Theorie / Studium ► Algorithmen |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Schlagworte | Algebraic Geometry • Algebraic Number Fields • algebraic number theory • algorithm • Algorithm analysis and problem complexity • Algorithmic Number Theory • algorithms • Computational Number Theory • cryptography • Cryptology • Diophantine equation • discrete Fourier transform • Elliptic Curve Computations • exponential equations • Factoring • Finite Field Computations • Galois groups • Hardcover, Softcover / Informatik, EDV/Informatik • HC/Informatik, EDV/Informatik • Integer Factorization • number-theoretic algorithms • Number Theory • pairing-based cryptosystems • polynomial evaluation • Prime • Zeta functions |
| ISBN-10 | 3-540-79455-7 / 3540794557 |
| ISBN-13 | 978-3-540-79455-4 / 9783540794554 |
| Zustand | Neuware |
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