000			03804nam a22005775i 4500
001			978-3-642-02295-1
003			DE-He213
005			20140220084523.0
007			cr nn 008mamaa
008			100301s2010 gw | s |||| 0|eng d
020			_a9783642022951 _9978-3-642-02295-1
024	7		_a10.1007/978-3-642-02295-1 _2doi
050		4	_aQA76.9.D35
072		7	_aUMB _2bicssc
072		7	_aURY _2bicssc
072		7	_aCOM031000 _2bisacsh
082	0	4	_a005.74 _223
100	1		_aNguyen, Phong Q. _eeditor.
245	1	4	_aThe LLL Algorithm _h[electronic resource] : _bSurvey and Applications / _cedited by Phong Q. Nguyen, Brigitte Vallée.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2010.
300			_aXIV, 496 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aInformation Security and Cryptography, _x1619-7100
505	0		_aThe History of the LLL-Algorithm -- Hermite’s Constant and Lattice Algorithms -- Probabilistic Analyses of Lattice Reduction Algorithms -- Progress on LLL and Lattice Reduction -- Floating-Point LLL: Theoretical and Practical Aspects -- LLL: A Tool for Effective Diophantine Approximation -- Selected Applications of LLL in Number Theory -- The van Hoeij Algorithm for Factoring Polynomials -- The LLL Algorithm and Integer Programming -- Using LLL-Reduction for Solving RSA and Factorization Problems -- Practical Lattice-Based Cryptography: NTRUEncrypt and NTRUSign -- The Geometry of Provable Security: Some Proofs of Security in Which Lattices Make a Surprise Appearance -- Cryptographic Functions from Worst-Case Complexity Assumptions -- Inapproximability Results for Computational Problems on Lattices -- On the Complexity of Lattice Problems with Polynomial Approximation Factors.
520			_aThe LLL algorithm is a polynomial-time lattice reduction algorithm, named after its inventors, Arjen Lenstra, Hendrik Lenstra and László Lovász. The algorithm has revolutionized computational aspects of the geometry of numbers since its introduction in 1982, leading to breakthroughs in fields as diverse as computer algebra, cryptology and algorithmic number theory. This book consists of 15 survey chapters on computational aspects of Euclidean lattices and their main applications. Topics covered include polynomial factorization, lattice reduction algorithms, applications in number theory, integer programming, provable security, lattice-based cryptography and complexity. The authors include many detailed motivations, explanations and examples, and the contributions are largely self-contained. The book will be of value to a wide range of researchers and graduate students working in related fields of theoretical computer science and mathematics.
650		0	_aComputer science.
650		0	_aData structures (Computer science).
650		0	_aComputer software.
650		0	_aComputational complexity.
650		0	_aAlgorithms.
650		0	_aNumber theory.
650		0	_aMathematical optimization.
650	1	4	_aComputer Science.
650	2	4	_aData Structures, Cryptology and Information Theory.
650	2	4	_aAlgorithms.
650	2	4	_aAlgorithm Analysis and Problem Complexity.
650	2	4	_aDiscrete Mathematics in Computer Science.
650	2	4	_aNumber Theory.
650	2	4	_aOptimization.
700	1		_aVallée, Brigitte. _eeditor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783642022944
830		0	_aInformation Security and Cryptography, _x1619-7100
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-642-02295-1
912			_aZDB-2-SCS
999			_c111403 _d111403