Algorithms to construct Minkowski reduced and Hermite reduced lattice bases
Theoretical Computer Science
A hierarchy of polynomial time lattice basis reduction algorithms
Theoretical Computer Science
Lattice basis reduction: improved practical algorithms and solving subset sum problems
Mathematical Programming: Series A and B
A public-key cryptosystem with worst-case/average-case equivalence
STOC '97 Proceedings of the twenty-ninth 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
Complexity of Lattice Problems
Complexity of Lattice Problems
Lattice Reduction by Random Sampling and Birthday Methods
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
A procedure for determining algebraic integers of given norm
EUROCAL '83 Proceedings of the European Computer Algebra Conference on Computer Algebra
Public-Key Cryptosystems from Lattice Reduction Problems
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Cryptanalysis of the Ajtai-Dwork Cryptosystem
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
NTRU: A Ring-Based Public Key Cryptosystem
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Improved algorithms for integer programming and related lattice problems
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Tensor-based hardness of the shortest vector problem to within almost polynomial factors
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
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
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
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
Cryptography Based on Quadratic Forms: Complexity Considerations
Research in Cryptology
Efficient lattice-based signature scheme
International Journal of Applied Cryptography
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
Sampling methods for shortest vectors, closest vectors and successive minima
Theoretical Computer Science
A digital signature scheme based on CV P∞
PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
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
Accelerating lattice reduction with FPGAs
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
SCN'10 Proceedings of the 7th international conference on Security and cryptography for networks
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
Analyzing blockwise lattice algorithms using dynamical systems
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Implicit factoring with shared most significant and middle bits
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Lattice enumeration using extreme pruning
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Parallel shortest lattice vector enumeration on graphics cards
AFRICACRYPT'10 Proceedings of the Third international conference on Cryptology in Africa
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
Improvements in closest point search based on dual HKZ-bases
Theoretical Computer Science
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The security of lattice-based cryptosystems such as NTRU, GGH and Ajtai-Dwork essentially relies upon the intractability of computing a shortest non-zero lattice vector and a closest lattice vector to a given target vector in high dimensions. The best algorithms for these tasks are due to Kannan, and, though remarkably simple, their complexity estimates have not been improved since over twenty years. Kannan's algorithm for solving the shortest vector problem (SVP) is in particular crucial in Schnorr's celebrated block reduction algorithm, on which rely the best known generic attacks against the lattice-based encryption schemes mentioned above. In this paper we improve the complexity upper-bounds of Kannan's algorithms. The analysis provides new insight on the practical cost of solving SVP, and helps progressing towards providing meaningful key-sizes.