# Contributions aux opérateurs arithmétiques GF$(2^m)$ et leurs applications à la cryptographie sur courbes elliptiques

1 CAIRN - Energy Efficient Computing ArchItectures with Embedded Reconfigurable Resources
Inria Rennes – Bretagne Atlantique , IRISA-D3 - ARCHITECTURE
Abstract : Cryptography and security market is growing up at a annual rate of 17% according to some recent studies. Cryptography is known to be the science of secret. It is based on mathematical hard problems as integer factorization, the well-known discrete logarithm problem. Although those problems are trusted, software or hardware implementations of cryptographic algorithms can suffer from inherent weaknesses. Execution time, power consumption (...) can differ depending on secret informations such as the secret key. Because of that, some malicious attacks could be used to exploit these weak points and therefore can be used to break the whole crypto-system. In this thesis, we are interested in protecting our physical device from the so called side channel attacks as well as interested in proposing new GF(2^m) multiplication algorithms used over elliptic curves cryptography. As a protection, we first thought that parallel scalar multiplication (using halve-and-add and double-and-add algorithms both executed at the same time) would be a great countermeasure against template attacks. We showed that it was not the case and that parallelism could not be used as protection by itself : it had to be combined with more conventional countermeasures. We also proposed two new GF(2^m) representations we respectively named permuted normal basis (PNB) and Phi-RNS. Those two representations, under some requirements, can offer a great time-area trade-off.
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Cited literature [80 references]

https://hal.archives-ouvertes.fr/tel-01324924
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Submitted on : Wednesday, June 1, 2016 - 4:06:23 PM
Last modification on : Thursday, October 10, 2019 - 10:49:15 AM
Long-term archiving on : Friday, September 2, 2016 - 10:39:40 AM

### Identifiers

• HAL Id : tel-01324924, version 1

### Citation

Jérémy Métairie. Contributions aux opérateurs arithmétiques GF$(2^m)$ et leurs applications à la cryptographie sur courbes elliptiques . Arithmétique des ordinateurs. Université Rennes 1, 2016. Français. ⟨tel-01324924⟩

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