A hierarchy of polynomial time lattice basis reduction algorithms
Theoretical Computer Science
Polynomial time algorithms for finding integer relations among real numbers
SIAM Journal on Computing
A random polynomial-time algorithm for approximating the volume of convex bodies
Journal of the ACM (JACM)
Improved low-density subset sum algorithms
Computational Complexity
Lattice basis reduction: improved practical algorithms and solving subset sum problems
Mathematical Programming: Series A and B
A sieve algorithm for the shortest lattice vector problem
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Cryptanalysis of the Goldreich-Goldwasser-Halevi Cryptosystem from Crypto '97
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Improved algorithms for integer programming and related lattice problems
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Sampling Short Lattice Vectors and the Closest Lattice Vector Problem
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Journal of the ACM (JACM)
Simulated annealing in convex bodies and an O*(n4) volume algorithm
Journal of Computer and System Sciences - Special issue on FOCS 2003
Finding short lattice vectors within mordell's inequality
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Rigorous and Efficient Short Lattice Vectors Enumeration
ASIACRYPT '08 Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
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
Closest point search in lattices
IEEE Transactions on Information Theory
Accelerating lattice reduction with FPGAs
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
Parallel enumeration of shortest lattice vectors
Euro-Par'10 Proceedings of the 16th international Euro-Par conference on Parallel processing: Part II
Better key sizes (and attacks) for LWE-based encryption
CT-RSA'11 Proceedings of the 11th international conference on Topics in cryptology: CT-RSA 2011
Analysis of gauss-sieve for solving the shortest vector problem in lattices
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Improved Nguyen-Vidick heuristic sieve algorithm for shortest vector problem
Proceedings of the 6th ACM Symposium on Information, Computer and Communications Security
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
Algorithms for the shortest and closest lattice vector problems
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
A parallel implementation of GaussSieve for the shortest vector problem in lattices
PaCT'11 Proceedings of the 11th international conference on Parallel computing technologies
Extreme enumeration on GPU and in clouds: how many dollars you need to break SVP challenges
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
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
Efficient multiplication over extension fields
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
Solving BDD by enumeration: an update
CT-RSA'13 Proceedings of the 13th international conference on Topics in Cryptology
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Lattice enumeration algorithms are the most basic algorithms for solving hard lattice problems such as the shortest vector problem and the closest vector problem, and are often used in public-key cryptanalysis either as standalone algorithms, or as subroutines in lattice reduction algorithms. Here we revisit these fundamental algorithms and show that surprising exponential speedups can be achieved both in theory and in practice by using a new technique, which we call extreme pruning. We also provide what is arguably the first sound analysis of pruning, which was introduced in the 1990s by Schnorr et al.