Study of modular inversion in RNS

Jean Claude Bajard; Nicolas Meloni; Thomas Plantard

doi:10.1117/12.617543

16 September 2005 Study of modular inversion in RNS

Jean Claude Bajard, Nicolas Meloni, Thomas Plantard

Proceedings Volume 5910, Advanced Signal Processing Algorithms, Architectures, and Implementations XV; 59100T (2005) https://doi.org/10.1117/12.617543
Event: Optics and Photonics 2005, 2005, San Diego, California, United States

Abstract

Residue Numbers System have some features which are fine for some implementations of cryptographic protocols. The main property of RNS is the distribution of the evaluation on large values on its small residues, allowing parallelization. This last property implies that we can randomize the distribution of the bases elements. Hence, the obtained arithmetic is leak resistant, it is robust against side channel attacks. But one drawback of RNS is that modular inversion is not obvious. Thus, RNS is well suited for RSA but not really for ECC. We analyze in this paper the features of the modular inversion in RNS over GF(P). We propose a RNS Extended Euclidean Algorithm which uses a quotient approximation module.

Citation Download Citation

Jean Claude Bajard, Nicolas Meloni, and Thomas Plantard "Study of modular inversion in RNS", Proc. SPIE 5910, Advanced Signal Processing Algorithms, Architectures, and Implementations XV, 59100T (16 September 2005); https://doi.org/10.1117/12.617543

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