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RT Book, Whole SR Electronic DC OPAC T1 Binary Quadratic Forms : An Algorithmic Approach / by Johannes Buchmann, Ulrich Vollmer T2 Algorithms and Computation in Mathematics A1 Buchmann, Johannes A1 Vollmer, Ulrich A1 SpringerLink (Online service) YR 2007 FD 2007 SP XIV, 318 p K1 Mathematics K1 Data encryption (Computer science) K1 Computer science -- Mathematics K1 Algebra K1 Number theory K1 Mathematics K1 Algebra K1 Number Theory K1 Mathematics of Computing K1 Data Encryption PB Springer Berlin Heidelberg PP Berlin, Heidelberg SN 9783540463689 LA English (英語) CL DC23:512 NO This book deals with algorithmic problems concerning binary quadratic forms 2 2 f(X,Y)= aX +bXY +cY with integer coe?cients a, b, c, the mathem- ical theories that permit the solution of these problems, and applications to cryptography. A considerable part of the theory is developed for forms with real coe?cients and it is shown that forms with integer coe?cients appear in a natural way. Much of the progress of number theory has been stimulated by the study of concrete computational problems. Deep theories were developed from the classic time of Euler and Gauss onwards to this day that made the solutions ofmanyof theseproblemspossible.Algorithmicsolutionsandtheirproperties became an object of study in their own right. Thisbookintertwinestheexpositionofoneveryclassicalstrandofnumber theory with the presentation and analysis of algorithms both classical and modern which solve its motivating problems. This algorithmic approach will lead the reader, we hope, not only to an understanding of theory and solution methods, but also to an appreciation of the e?ciency with which solutions can be reached. The computer age has led to a marked advancement of algorithmic - search. On the one hand, computers make it feasible to solve very hard pr- lems such as the solution of Pell equations with large coe?cients. On the other, the application of number theory in public-key cryptography increased the urgency for establishing the complexity of several computational pr- lems: many a computer system stays only secure as long as these problems remain intractable NO 書誌ID=1003001780; LK [E Book]http://dx.doi.org/10.1007/978-3-540-46368-9 OL 30