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Erschienen in:
2010 | OriginalPaper | Buchkapitel
High Performance GHASH Function for Long Messages
verfasst von : Nicolas Méloni, Christophe Négre, M. Anwar Hasan
Erschienen in: Applied Cryptography and Network Security
Verlag: Springer Berlin Heidelberg
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This work presents a new method to compute the GHASH function involved in the Galois/Counter Mode of operation for block ciphers. If
X
=
X
1
...
X
n
is a bit string made of
n
blocks of 128 bits each, then the GHASH function effectively computes
$X_1H^n + X_2H^{n-1} + \ldots X_nH$
, where
H
is an element of the binary field
${\mathbb{F}}_{2^{128}}$
. This operation is usually computed by using
n
successive multiply-add operations over
${\mathbb{F}}_{2^{128}}$
. In this work, we propose a method to replace all but a fixed number of those multiplications by additions on the field. This is achieved by using the characteristic polynomial of
H
. We present both how to use this polynomial to speed up the GHASH function and how to efficiently compute it for each session that uses a new
H
.