## An Improved Worst-Case to Average-Case Connection for Lattice Problems (extended abstract) (1997)

Venue: | In FOCS |

Citations: | 56 - 11 self |

### BibTeX

@INPROCEEDINGS{Cai97animproved,

author = {Jin-yi Cai and Ajay P. Nerurkar},

title = {An Improved Worst-Case to Average-Case Connection for Lattice Problems (extended abstract)},

booktitle = {In FOCS},

year = {1997},

pages = {468--477},

publisher = {IEEE}

}

### Years of Citing Articles

### OpenURL

### Abstract

We improve a connection of the worst-case complexity and the average-case complexity of some well-known lattice problems. This fascinating connection was first discovered by Ajtai [1] in 1996. We improve the exponent of this connection from 8 to 3:5 + ffl. Department of Computer Science, State University of New York at Buffalo, Buffalo, NY 14260. Research supported in part by NSF grants CCR-9319393 and CCR-9634665, and an Alfred P. Sloan Fellowship. Email: cai@cs.buffalo.edu y Department of Computer Science, State University of New York at Buffalo, Buffalo, NY 14260. Research supported in part by NSF grants CCR-9319393 and CCR-9634665. Email: apn@cs.buffalo.edu 1 Introduction A lattice L is a discrete additive subgroup of R n . There are many fascinating problems concerning lattices, both from a structural and from an algorithmic point of view [12, 20, 11, 13]. The study of lattice problems can be traced back to Gauss, Dirichlet and Hermite, among others [8, 6, 14]. The subje...

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