Cryptography Reference
In-Depth Information
One can perform lattice basis reduction and apply the nearest plane algorithm. For
improved methods and experimental results see Lindner and Peikert [
352
]. As in Exam-
ple
19.7.5
, one can work with a subset of
m
rows of
A
; see Section 5.1 of [
352
]for
details.
19.8 Further applications of lattice reduction
There are a number of other applications of lattices in cryptography. We briefly list some
of them.
The improvement by Boneh and Durfee of Wiener's attack on small private exponent
RSA. This is briefly mentioned in Section
24.5.1
.
Solving the hidden number problem in finite fields and its applications to bit security of
Diffie-Hellman key exchange. See Section
21.7.1
.
The attack by Howgrave-Graham and Smart on digital signature schemes in finite fields
when there is partial information available about the random nonces. See Section
22.3
.
The deterministic reduction by Coron and May from knowing
Ï•
(
N
) to factoring
N
.This
is briefly mentioned in Section
24.1.3
.
