Generating Shorter Bases for Hard Random Lattices
We revisit the problem of generating a ``hard'' random lattice together with a basis of relatively short vectors. This problem has gained in importance lately due to new cryptographic schemes that use such a procedure for generating public/secret key pairs. In these applications, a shorter basis directly corresponds to milder underlying complexity assumptions and smaller key sizes.
The contributions of this work are twofold. First, using the \emph{Hermite normal form} as an organizing principle, we simplify and generalize an approach due to Ajtai (ICALP 1999). Second, we improve the construction and its analysis in several ways, most notably by tightening the length of the output basis essentially to the optimum value.
Lattices
Random
Short basis
Average-case hardness
Hermite normal form
Cryptography
75-86
Regular Paper
Joel
Alwen
Joel Alwen
Chris
Peikert
Chris Peikert
10.4230/LIPIcs.STACS.2009.1832
Creative Commons Attribution-NoDerivs 3.0 Unported license
https://creativecommons.org/licenses/by-nd/3.0/legalcode