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2010
Springer

Maximizing Small Root Bounds by Linearization and Applications to Small Secret Exponent RSA

9 years 6 months ago
Maximizing Small Root Bounds by Linearization and Applications to Small Secret Exponent RSA
We present an elementary method to construct optimized lattices that are used for finding small roots of polynomial equations. Former methods first construct some large lattice in a generic way from a polynomial f and then optimize via finding suitable smaller dimensional sublattices. In contrast, our method focuses on optimizing f first which then directly leads to an optimized small dimensional lattice. Using our method, we construct the first elementary proof of the Boneh-Durfee attack for small RSA secret exponents with d ≤ N0.292 . Moreover, we identify a sublattice structure behind the Jochemsz-May attack for small CRT-RSA exponents dp, dq ≤ N0.073 . Unfortunately, in contrast to the Boneh-Durfee attack, for the Jochemsz-May attack the sublattice does not help to improve the bound asymptotically. Instead, we are able to attack much larger values of dp, dq in practice by LLL reducing smaller dimensional lattices.
Mathias Herrmann, Alexander May
Added 14 Aug 2010
Updated 14 Aug 2010
Type Conference
Year 2010
Where PKC
Authors Mathias Herrmann, Alexander May
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