Minkowski's convex body theorem and integer programming
Mathematics of Operations Research
A hierarchy of polynomial time lattice basis reduction algorithms
Theoretical Computer Science
A random polynomial-time algorithm for approximating the volume of convex bodies
Journal of the ACM (JACM)
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
On the complexity of computing short linearly independent vectors and short bases in a lattice
STOC '99 Proceedings of the thirty-first 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
The Shortest Vector in a Lattice is Hard to Approximate to within Some Constant
SIAM Journal on Computing
Closest Vectors, Successive Minima, and Dual HKZ-Bases of Lattices
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Sampling Short Lattice Vectors and the Closest Lattice Vector Problem
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Hardness of approximating the shortest vector problem in lattices
Journal of the ACM (JACM)
Efficient reductions among lattice problems
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Limits on the Hardness of Lattice Problems in lp Norms
Computational Complexity
Noninteractive Statistical Zero-Knowledge Proofs for Lattice Problems
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
Efficient lattice-based signature scheme
International Journal of Applied Cryptography
Lattice-based identification schemes secure under active attacks
PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
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
SCN'10 Proceedings of the 7th international conference on Security and cryptography for networks
A O(1/ε2)n-time sieving algorithm for approximate integer programming
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
| Hi-index | 0.00 |
In this paper we introduce a new lattice problem, the subspace avoiding problem (SAP). We describe a probabilistic single exponential time algorithm for Sap for arbitrary lp norms. We also describe polynomial time reductions for four classical problems from the geometry of numbers, the shortest vector problem (SVP), the closest vector problem (CVP), the successive minima problem (SMP), and the shortest independent vectors problem (SIVP) to Sap, establishing probabilistic single exponential time algorithms for them. The result generalize and extend previous results of Ajtai, Kumar and Sivakumar. The results on Smp and Sivp are new for all norms. The results on Svp and Cvp generalize previous results of Ajtai et al. for the l2 norm to arbitrary lp norms.