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High Performance GHASH Function for Long Messages

Nicolas Méloni 1 Christophe Negre 2 M. Anwar Hasan
2 DALI - Digits, Architectures et Logiciels Informatiques
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier, UPVD - Université de Perpignan Via Domitia
Abstract : This work presents a new method to compute the GHASH function involved in the Galois/Counter Mode of operation for block ciphers. If $X= X_1\dots X_n$ is a bit string made of $n$ blocks of 128 bits each, then the GHASH function effectively computes $X_1H^n + X_2H^{n-1} + \dots X_nH$, where $H$ is an element of the binary field $\Fd_{2^{128}}$. This operation is usually computed by using $n$ successive multiply-add operations over $\Fd_{2^{128}}$. 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 $H$.
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Nicolas Méloni, Christophe Negre, M. Anwar Hasan. High Performance GHASH Function for Long Messages. ACNS: Applied Cryptography and Network Security, 2010, Beijing, China. pp.154-167, ⟨10.1007/978-3-642-13708-2_10⟩. ⟨hal-01279437⟩

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