03483nam a22004815i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001400153072001600167072002300183082001200206100003300218245011800251264006100369300003400430336002600464337002600490338003600516347002400552490006400576505033200640520157300972650001702545650004002562650003502602650001302637650001902650650001702669650001302686650001902699650003002718650002102748700003002769710003402799773002002833776003602853830006402889856004802953978-3-540-46368-9DE-He21320180115171700.0cr nn 008mamaa100301s2007 gw | s |||| 0|eng d a97835404636897 a10.1007/978-3-540-46368-92doi 4aQA150-272 7aPBF2bicssc 7aMAT0020002bisacsh04a5122231 aBuchmann, Johannes.eauthor.10aBinary Quadratic Formsh[electronic resource] :bAn Algorithmic Approach /cby Johannes Buchmann, Ulrich Vollmer. 1aBerlin, Heidelberg :bSpringer Berlin Heidelberg,c2007. aXIV, 318 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aAlgorithms and Computation in Mathematics,x1431-1550 ;v200 aBinary Quadratic Forms -- Equivalence of Forms -- Constructing Forms -- Forms, Bases, Points, and Lattices -- Reduction of Positive Definite Forms -- Reduction of Indefinite Forms -- Multiplicative Lattices -- Quadratic Number Fields -- Class Groups -- Infrastructure -- Subexponential Algorithms -- Cryptographic Applications. aThis 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. 0aMathematics. 0aData encryption (Computer science). 0aComputer sciencexMathematics. 0aAlgebra. 0aNumber theory.14aMathematics.24aAlgebra.24aNumber Theory.24aMathematics of Computing.24aData Encryption.1 aVollmer, Ulrich.eauthor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9783540463672 0aAlgorithms and Computation in Mathematics,x1431-1550 ;v2040uhttp://dx.doi.org/10.1007/978-3-540-46368-9