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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Maximizing Small Root Bounds by Linearization and Applications to Small Secret Exponent RSA
verfasst von : Mathias Herrmann, Alexander May
Erschienen in: Public Key Cryptography – PKC 2010
Verlag: Springer Berlin Heidelberg
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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
≤
N
0.292
. Moreover, we identify a sublattice structure behind the Jochemsz-May attack for small CRT-RSA exponents
$d_p, d_q \leq N^{0.073}$
. 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
d
p
,
d
q
in practice by LLL reducing smaller dimensional lattices.