A hierarchy of polynomial time lattice basis reduction algorithms
Theoretical Computer Science
A more efficient algorithm for lattice basis reduction
Journal of Algorithms
Lattice basis reduction: improved practical algorithms and solving subset sum problems
Mathematical Programming: Series A and B
Generating hard instances of lattice problems (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
The shortest vector problem in L2 is NP-hard for randomized reductions (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A sieve algorithm for the shortest lattice vector problem
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Proceedings of the 11th Colloquium on Automata, Languages and Programming
NTRU: A Ring-Based Public Key Cryptosystem
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Segment LLL-Reduction of Lattice Bases
CaLC '01 Revised Papers from the International Conference on Cryptography and Lattices
Improved algorithms for integer programming and related lattice problems
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Finding short lattice vectors within mordell's inequality
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
H-LLL: using householder inside LLL
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
An LLL Algorithm with Quadratic Complexity
SIAM Journal on Computing
The LLL Algorithm: Survey and Applications
The LLL Algorithm: Survey and Applications
Attacking the Chor-Rivest cryptosystem by improved lattice reduction
EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques
Improved analysis of Kannan's shortest lattice vector algorithm
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
Proceedings of the forty-second ACM symposium on Theory of computing
Faster exponential time algorithms for the shortest vector problem
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Lattice enumeration using extreme pruning
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Rankin's constant and blockwise lattice reduction
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Closest point search in lattices
IEEE Transactions on Information Theory
A complexity analysis of a Jacobi method for lattice basis reduction
Proceedings of the Fifth International C* Conference on Computer Science and Software Engineering
Sub-linear root detection, and new hardness results, for sparse polynomials over finite fields
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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Lattice reduction algorithms have surprisingly many applications in mathematics and computer science, notably in cryptology. On the one hand, lattice reduction algorithms are widely used in public-key cryptanalysis, for instance to attack special settings of RSA and DSA/ECDSA. On the other hand, there are more and more cryptographic schemes whose security require that certain lattice problems are hard. In this talk, we survey lattice reduction algorithms, present their performances, and discuss the differences between theory and practice.