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2020-06-26
Babenko, Mikhail, Redvanov, Aziz Salimovich, Deryabin, Maxim, Chervyakov, Nikolay, Nazarov, Anton, Al-Galda, Safwat Chiad, Vashchenko, Irina, Dvoryaninova, Inna, Nepretimova, Elena.  2019.  Efficient Implementation of Cryptography on Points of an Elliptic Curve in Residue Number System. 2019 International Conference on Engineering and Telecommunication (EnT). :1—5.

The article explores the question of the effective implementation of arithmetic operations with points of an elliptic curve given over a prime field. Given that the basic arithmetic operations with points of an elliptic curve are the operations of adding points and doubling points, we study the question of implementing the arithmetic operations of adding and doubling points in various coordinate systems using the weighted number system and using the Residue Number System (RNS). We have shown that using the fourmodule RNS allows you to get an average gain for the operation of adding points of the elliptic curve of 8.67% and for the operation of doubling the points of the elliptic curve of 8.32% compared to the implementation using the operation of modular multiplication with special moduli from NIST FIPS 186.

2017-11-27
Fournaris, A. P., Papachristodoulou, L., Batina, L., Sklavos, N..  2016.  Residue Number System as a side channel and fault injection attack countermeasure in elliptic curve cryptography. 2016 International Conference on Design and Technology of Integrated Systems in Nanoscale Era (DTIS). :1–4.

Implementation attacks and more specifically Power Analysis (PA) (the dominant type of side channel attack) and fault injection (FA) attacks constitute a pragmatic hazard for scalar multiplication, the main operation behind Elliptic Curve Cryptography. There exists a wide variety of countermeasures attempting to thwart such attacks that, however, few of them explore the potential of alternative number systems like the Residue Number System (RNS). In this paper, we explore the potential of RNS as an PA-FA countermeasure and propose an PA-FA resistant scalar multiplication algorithm and provide an extensive security analysis against the most effective PA-FA techniques. We argue through a security analysis that combining traditional PA-FA countermeasures with lightweight RNS countermeasures can provide strong PA-FA resistance.