Basis Reduction Algorithms and Subset Sum Problems

LaMacchia, Brian A.

Basis Reduction Algorithms and Subset Sum Problems

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Author(s)

LaMacchia, Brian A.

Date Issued

June 1, 1991

Series/Report no.

AITR-1283

Abstract

This thesis investigates a new approach to lattice basis reduction suggested by M. Seysen. Seysen's algorithm attempts to globally reduce a lattice basis, whereas the Lenstra, Lenstra, Lovasz (LLL) family of reduction algorithms concentrates on local reductions. We show that Seysen's algorithm is well suited for reducing certain classes of lattice bases, and often requires much less time in practice than the LLL algorithm. We also demonstrate how Seysen's algorithm for basis reduction may be applied to subset sum problems. Seysen's technique, used in combination with the LLL algorithm, and other heuristics, enables us to solve a much larger class of subset sum problems than was previously possible.

Subjects

subset sum problems

knapsack cryptosystems

public keyscryptography

integer lattice

Seysen's algorithm

lattice basissreduction

Persistent DSpace Link

http://hdl.handle.net/1721.1/6813