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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Efficient CRT-RSA Decryption for Small Encryption Exponents
verfasst von : Subhamoy Maitra, Santanu Sarkar
Erschienen in: Topics in Cryptology - CT-RSA 2010
Verlag: Springer Berlin Heidelberg
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Consider CRT-RSA with the parameters
p
,
q
,
e
,
d
p
,
d
q
, where
p
,
q
are secret primes,
e
is the public encryption exponent and
d
p
,
d
q
are the private decryption exponents. We present an efficient method to select CRT-RSA parameters in such a manner so that the decryption becomes faster for small encryption exponents. This is the most frequently used situation for application of RSA in commercial domain. Our idea is to choose
e
and the factors (with low Hamming weight) of
d
p
,
d
q
first and then applying the extended Euclidean algorithm, we obtain
p
,
q
of same bit size. For small
e
, we get an asymptotic reduction of the order of
${{1}\over{3}}$
in the decryption time compared to standard CRT-RSA parameters for large
N
=
pq
. In case of practical parameters, with 1024 bits
N
and
e
= 2
16
+ 1, we achieve a reduction of more than 27%. Extensive security analysis is presented for our selected parameters and benchmark examples are also provided.