On the Randomness of Bits Generated by Sufficiently Smooth Functions
Identifieur interne : 000086 ( Istex/Curation ); précédent : 000085; suivant : 000087On the Randomness of Bits Generated by Sufficiently Smooth Functions
Auteurs : Damien Stehlé [France, Australie]Source :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: Elementary functions such as sin or exp may naively be considered as good generators of random bits: the bit-runs output by these functions are believed to be statistically random most of the time. Here we investigate their computational hardness: given a part of the binary expansion of exp x, can one recover x? We describe a heuristic technique to address this type of questions. It relies upon Coppersmith’s heuristic technique — itself based on lattice reduction — for finding the small roots of multivariate polynomials modulo an integer. For our needs, we improve the lattice construction step of Coppersmith’s method: we describe a way to find a subset of a set of vectors that decreases the Minkowski theorem bound, in a rather general setup including Coppersmith-type lattices.
Url:
DOI: 10.1007/11792086_19
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