Improving Modular Inversion in RNS using the Plus-Minus Method

Karim Bigou 1 Arnaud Tisserand 1, *
* Corresponding author
1 CAIRN - Energy Efficient Computing ArchItectures with Embedded Reconfigurable Resources
Inria Rennes – Bretagne Atlantique , IRISA-D3 - ARCHITECTURE
Abstract : The paper describes a new RNS modular inversion algorithm based on the extended Euclidean algorithm and the plus-minus trick. In our algorithm, comparisons over large RNS values are replaced by cheap computations modulo 4. Comparisons to an RNS version based on Fermat's little theorem were carried out. The number of elementary modular operations is signi cantly reduced: a factor 12 to 26 for multiplications and 6 to 21 for additions. Virtex 5 FPGAs implementations show that for a similar area, our plus-minus RNS modular inversion is 6 to 10 times faster.
Keywords : Residue Number System Modular Representation Extended Euclidean Algorithm Hardware Implementation ECC RSA
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Conference papers
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Submitted on : Friday, May 24, 2013 - 2:36:36 PM
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Karim Bigou, Arnaud Tisserand. Improving Modular Inversion in RNS using the Plus-Minus Method. CHES - 15th Workshop on Cryptographic Hardware and Embedded Systems - 2013, Aug 2013, Santa Barbara, United States. pp.233-249, ⟨10.1007/978-3-642-40349-1_14⟩. ⟨hal-00825745⟩

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