An improved low-density subset sum algorithm

Authors:
M. J. Coster;B. A. LaMacchia;A. M. Odlyzko;C. P. Schnorr
Affiliations:
AT&T Bell Laboratories, Murray Hill, New Jersey;MIT, Cambridge, MA and AT&T Bell Laboratories, Murray Hill, New Jersey;AT&T Bell Laboratories, Murray Hill, New Jersey;Universität Frankfurt, Fachbereich Mathematik, Informatik, Frankfurt am Main, Germany
Venue:
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
Year:
1991

Citing 10
Cited 7

Solving low-density subset sum problems

Journal of the ACM (JACM)
On the Lagarias-Odlyzko algorithm for the subset sum problem

SIAM Journal on Computing
Approximating integer lattices by lattices with cyclic factor groups

14th International Colloquium on Automata, languages and programming
A hierarchy of polynomial time lattice basis reduction algorithms

Theoretical Computer Science
A more efficient algorithm for lattice basis reduction

Journal of Algorithms
Succinct certificates for almost all subset sum problems

SIAM Journal on Computing
Polynomial time algorithms for finding integer relations among real numbers

SIAM Journal on Computing
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
Lattice Basis Reduction: Improved Practical Algorithms and Solving Subset Sum Problems

FCT '91 Proceedings of the 8th International Symposium on Fundamentals of Computation Theory
Improving the Critical Density of the Lagarias-Odlyzko Attack Against Subset Sum Problems

FCT '91 Proceedings of the 8th International Symposium on Fundamentals of Computation Theory

A knapsack-based probabilistic encryption scheme

Information Sciences: an International Journal
Broadcast Attacks against Lattice-Based Cryptosystems

ACNS '09 Proceedings of the 7th International Conference on Applied Cryptography and Network Security
Parallel Lattice Basis Reduction Using a Multi-threaded Schnorr-Euchner LLL Algorithm

Euro-Par '09 Proceedings of the 15th International Euro-Par Conference on Parallel Processing
Factoring integers and computing discrete logarithms via diophantine approximation

EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
Recursive lattice reduction

SCN'10 Proceedings of the 7th international conference on Security and cryptography for networks
Higher order universal one-way hash functions from the subset sum assumption

PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
An efficient LLL gram using buffered transformations

CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

The general subset sum problem is NP-complete. However, there are two algorithms, one due to Brickell and the other to Lagarias and Odlyzko, which in polynomial time solve almost all subset sum problems of sufficiently low density. Both methods rely on basis reduction algorithms to find short non-zero vectors in special lattices. The Lagarias-Odlyzko algorithm would solve almost all subset sum problems of density