Accelerating lattice reduction with FPGAs
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
An LLL-reduction algorithm with quasi-linear time complexity: extended abstract
Proceedings of the forty-third annual ACM symposium on Theory of computing
Recent progress in linear algebra and lattice basis reduction
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Lattice reduction algorithms: theory and practice
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
Making NTRU as secure as worst-case problems over ideal lattices
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
Algorithms for the shortest and closest lattice vector problems
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
Using the inhomogeneous simultaneous approximation problem for cryptographic design
AFRICACRYPT'11 Proceedings of the 4th international conference on Progress in cryptology in Africa
Analyzing blockwise lattice algorithms using dynamical systems
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Random sampling for short lattice vectors on graphics cards
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
Non-linear polynomial selection for the number field sieve
Journal of Symbolic Computation
Lattice enumeration using extreme pruning
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
BKZ 2.0: better lattice security estimates
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
Random walks and bisections in random circulant graphs
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
A complexity analysis of a Jacobi method for lattice basis reduction
Proceedings of the Fifth International C* Conference on Computer Science and Software Engineering
On the optimality of lattices for the coppersmith technique
ACISP'12 Proceedings of the 17th Australasian conference on Information Security and Privacy
Learning a zonotope and more: cryptanalysis of NTRUSign countermeasures
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
Improvements in closest point search based on dual HKZ-bases
Theoretical Computer Science
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The LLL algorithm is a polynomial-time lattice reduction algorithm, named after its inventors, Arjen Lenstra, Hendrik Lenstra and Lszl Lovsz. 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.