Paper 2007/322
Identifying Ideal Lattices
Jintai Ding and Richard Lindner
Abstract
Micciancio defined a generalization of cyclic lattices, called ideal lattices. These lattices can be used in cryptosystems to decrease the number of parameters necessary to describe a lattice by a square root, making them more efficient. He proves that the computational intractability of classic lattice problems for these lattices gives rise to provably secure one-way and collision-resistant hash functions. This provable security relies on the assumption that reducing bases of ideal lattices is similar to reducing bases of random lattices. We give an indication that lattice problems in ideal lattices do not represent the general case by providing a distinguisher, which decides in time $O(n^4)$ whether a given basis of rank $n$ spans an ideal lattice or not. Using this algorithm we perform a statistical analysis for several dimensions and show that randomly generated lattices are practically never ideal.
Metadata
- Available format(s)
-
PDF
PS
- Category
- Foundations
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- decision problemslatticescomplexityNTRU
- Contact author(s)
- rlindner @ cdc informatik tu-darmstadt de
- History
- 2007-08-16: received
- Short URL
- https://ia.cr/2007/322
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2007/322,
author = {Jintai Ding and Richard Lindner},
title = {Identifying Ideal Lattices},
howpublished = {Cryptology ePrint Archive, Paper 2007/322},
year = {2007},
note = {\url{https://eprint.iacr.org/2007/322}},
url = {https://eprint.iacr.org/2007/322}
}
