An improved low-density subset sum algorithm

M. J. Coster; B. A. LaMacchia; A. M. Odlyzko; C. P. Schnorr

doi:10.1007/3-540-46416-6_4

An improved low-density subset sum algorithm

M. J. Coster, B. A. LaMacchia, A. M. Odlyzko, C. P. Schnorr

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

58 Scopus citations

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 < 0.6463 … in polynomial time if it could invoke a polynomial-time algorithm for finding the shortest non-zero vector in a lattice. This note shows that a simple modification of that algorithm would solve almost all problems of density < 0.9408 … if it could find shortest non-zero vectors in lattices. This modification also yields dramatic improvements in practice when it is combined with known lattice basis reduction algorithms.

Original language	English (US)
Title of host publication	Advances in Cryptology—EUROCRYPT 1991 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings
Editors	Donald W. Davies
Publisher	Springer Verlag
Pages	54-67
Number of pages	14
ISBN (Print)	9783540546207
DOIs	https://doi.org/10.1007/3-540-46416-6_4
State	Published - 1991
Event	Workshop on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1991 - Brighton, United Kingdom Duration: Apr 8 1991 → Apr 11 1991

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	547 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	Workshop on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1991
Country/Territory	United Kingdom
City	Brighton
Period	4/8/91 → 4/11/91

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1991.

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Coster, M. J., LaMacchia, B. A., Odlyzko, A. M., & Schnorr, C. P. (1991). An improved low-density subset sum algorithm. In D. W. Davies (Ed.), Advances in Cryptology—EUROCRYPT 1991 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings (pp. 54-67). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 547 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-46416-6_4

An improved low-density subset sum algorithm. / Coster, M. J.; LaMacchia, B. A.; Odlyzko, A. M. et al.
Advances in Cryptology—EUROCRYPT 1991 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings. ed. / Donald W. Davies. Springer Verlag, 1991. p. 54-67 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 547 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Coster, MJ, LaMacchia, BA, Odlyzko, AM & Schnorr, CP 1991, An improved low-density subset sum algorithm. in DW Davies (ed.), Advances in Cryptology—EUROCRYPT 1991 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 547 LNCS, Springer Verlag, pp. 54-67, Workshop on the Theory and Application of Cryptographic Techniques, EUROCRYPT 1991, Brighton, United Kingdom, 4/8/91. https://doi.org/10.1007/3-540-46416-6_4

Coster MJ, LaMacchia BA, Odlyzko AM, Schnorr CP. An improved low-density subset sum algorithm. In Davies DW, editor, Advances in Cryptology—EUROCRYPT 1991 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings. Springer Verlag. 1991. p. 54-67. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-46416-6_4

Coster, M. J. ; LaMacchia, B. A. ; Odlyzko, A. M. et al. / An improved low-density subset sum algorithm. Advances in Cryptology—EUROCRYPT 1991 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings. editor / Donald W. Davies. Springer Verlag, 1991. pp. 54-67 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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An improved low-density subset sum algorithm

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