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Generating shorter bases for hard random lattices. (English) Zbl 1217.94092
Summary: 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 M. Ajtai [Lect. Notes Comput. Sci. 1644, 1–9 (1999; Zbl 0987.94021)]. Second, we improve the construction and its analysis in several ways, most notably by making the output basis asymptotically as short as possible.

##### MSC:
 94A60 Cryptography 11H06 Lattices and convex bodies (number-theoretic aspects) 68Q25 Analysis of algorithms and problem complexity
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##### References:
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