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Side-Channel Analysis of Multiplications in GF(2 128 ) Application to AES-GCM

Abstract : In this paper, we study the side-channel security of the field multiplication in GF(2^n). We particularly focus on GF(2^{128}) multiplication which is the one used in the authentication part of AES-GCM but the proposed attack also applies to other binary extensions. In a hard-ware implementation using a 128-bit multiplier, the full 128-bit secret is manipulated at once. In this context, classical DPA attacks based on the divide and conquer strategy cannot be applied. In this work, the algebraic structure of the multiplication is leveraged to recover bits of information about the secret multiplicand without having to perform any key-guess. To do so, the leakage corresponding to the writing of the multiplication output into a register is considered. It is assumed to follow a Hamming weight/distance leakage model. Under these particular, yet easily met, assumption we exhibit a nice connection between the key recovery problem and some classical coding and Learning Parities with Noise problems with certain instance parameters. In our case, the noise is very high, but the length of the secret is rather short. In this work we investigate different solving techniques corresponding to different attacker models and eventually refine the attack when considering particular implementations of the multiplication.
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https://hal.inria.fr/hal-01093987
Contributor : Pierre-Alain Fouque <>
Submitted on : Thursday, December 11, 2014 - 2:39:57 PM
Last modification on : Thursday, July 1, 2021 - 5:32:37 PM
Long-term archiving on: : Saturday, April 15, 2017 - 7:49:36 AM

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  • HAL Id : hal-01093987, version 1

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Sonia Belaid, Pierre-Alain Fouque, Benoit Gérard. Side-Channel Analysis of Multiplications in GF(2 128 ) Application to AES-GCM. Advances in Cryptology - ASIACRYPT 2014 - 20th International Conference on the Theory and Application of Cryptology and Information Security, Palash Sarkar, Tetsu Iwata, Dec 2014, Kaoshiung, Taiwan. pp.20. ⟨hal-01093987⟩

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