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Generating Shorter Bases for Hard Random Lattices

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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 to generate public/secret key pairs. In these applications, a shorter basis corresponds to milder underlying complexity assumptions and smaller key sizes.

The contributions of this work are twofold. First, we simplify and modularize an approach originally due to Ajtai (ICALP 1999). Second, we improve the construction and its analysis in several ways, most notably by making the output basis asymptotically as short as possible.

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Correspondence to Chris Peikert.

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Work of J. Alwen performed while at SRI International.

Much of work of C. Peikert was performed while at SRI International. This material is based upon work supported by the National Science Foundation under Grants CNS-0716786 and CNS-0749931. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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Alwen, J., Peikert, C. Generating Shorter Bases for Hard Random Lattices. Theory Comput Syst 48, 535–553 (2011).

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