Algorithmic number theory: lattices, number fields, curves by J.P. Buhler, P. Stevenhagen PDF

By J.P. Buhler, P. Stevenhagen

ISBN-10: 0521808545

ISBN-13: 9780521808545

Quantity thought is without doubt one of the oldest and so much beautiful components of arithmetic. Computation has continually performed a task in quantity idea, a job which has elevated dramatically within the final 20 or 30 years, either as a result of introduction of contemporary pcs, and thanks to the invention of bizarre and strong algorithms. as a result, algorithmic quantity concept has progressively emerged as a tremendous and exact box with connections to laptop technology and cryptography in addition to different components of arithmetic. this article presents a entire advent to algorithmic quantity concept for starting graduate scholars, written through the best specialists within the box. It comprises numerous articles that disguise the fundamental themes during this quarter, resembling the basic algorithms of hassle-free quantity conception, lattice foundation relief, elliptic curves, algebraic quantity fields, and strategies for factoring and primality proving. furthermore, there are contributions pointing in broader instructions, together with cryptography, computational classification box thought, zeta features and L-series, discrete logarithm algorithms, and quantum computing.

Show description

Read or Download Algorithmic number theory: lattices, number fields, curves and cryptography PDF

Best algorithms and data structures books

Graph algorithms and applications 4 - download pdf or read online

This booklet comprises quantity 7 of the "Journal of Graph Algorithms and functions" (JGAA). JGAA is a peer-reviewed clinical magazine dedicated to the book of top of the range examine papers at the research, layout, implementation, and purposes of graph algorithms. components of curiosity contain computational biology, computational geometry, special effects, computer-aided layout, laptop and interconnection networks, constraint platforms, databases, graph drawing, graph embedding and format, wisdom illustration, multimedia, software program engineering, telecommunications networks, person interfaces and visualization, and VLSI circuit layout.

Download e-book for kindle: A VU-algorithm for convex minimization by Mifflin R., Sagastizabal C.

For convex minimization we introduce an set of rules in keeping with VU-space decomposition. the strategy makes use of a package subroutine to generate a series of approximate proximal issues. whilst a primal-dual music resulting in an answer and nil subgradient pair exists, those issues approximate the primal music issues and provides the algorithm's V, or corrector, steps.

Read e-book online Practical Industrial Data Networks: Design, Installation and PDF

There are lots of facts communications titles masking layout, set up, and so on, yet virtually none that particularly specialise in commercial networks, that are a vital a part of the daily paintings of business keep an eye on platforms engineers, and the main target of an more and more huge workforce of community experts.

Extra resources for Algorithmic number theory: lattices, number fields, curves and cryptography

Sample text

G b /a . More generally, the eavesdropper can succeed if he or she can find g ab knowing g, g a , and g b . ‫ކ‬p / on a suitable elliptic curve E over a finite field ‫ކ‬p WD ‫=ޚ‬p ‫ޚ‬. The representation of a cyclic group in the group of points of an elliptic curve seems particularly opaque, and in this case no sub-exponential discrete logarithm algorithms are known at all. For details on these cases, see [Pomerance 2008; Poonen 2008; Schirokauer 2008]. The difficulty of the abstract discrete logarithm problem in a group is dominated by the difficulty of the problem in the largest cyclic subgroup of prime order [Pomerance 2008].

In either case we then use recursion. 40 JOE BUHLER AND STAN WAGON P ROBLEM 10. S QUARE ROOTS M ODULO A P RIME : Given an odd prime p and a quadratic residue a, find an x such that x 2 Á a mod p. We start by showing how to efficiently reduce this problem to Q UADRATIC N ONRESIDUES. This means that modular square roots can be found efficiently once a quadratic nonresidue is known. Let a be a quadratic nonresidue. Write p 1 D 2t q, where q is odd. ‫=ޚ‬p ‫ޚ‬/ of order 2t , and b D g q is a generator of that group.

Grosjean and De Meyer 1991] C. C. Grosjean and H. E. De Meyer, “A new contribution to the mathematical study of the cattle-problem of Archimedes”, pp. 404–453 in Constantin Carath´eodory: an international tribute, vol. I, edited by T. M. Rassias, World Sci. Publishing, Teaneck, NJ, 1991. SOLVING THE PELL EQUATION 21 [Hallgren 2002] S. Hallgren, “Polynomial-time quantum algorithms for Pell’s equation and the principal ideal problem”, pp. 653–658 in Proceedings of the Thirty-Fourth Annual ACM Symposium on Theory of Computing, ACM, New York, 2002.

Download PDF sample

Algorithmic number theory: lattices, number fields, curves and cryptography by J.P. Buhler, P. Stevenhagen


by Kevin
4.5

Rated 4.75 of 5 – based on 46 votes