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2020-06-26
Pandey, Jai Gopal, Mitharwal, Chhavi, Karmakar, Abhijit.  2019.  An RNS Implementation of the Elliptic Curve Cryptography for IoT Security. 2019 First IEEE International Conference on Trust, Privacy and Security in Intelligent Systems and Applications (TPS-ISA). :66—72.

Public key cryptography plays a vital role in many information and communication systems for secure data transaction, authentication, identification, digital signature, and key management purpose. Elliptic curve cryptography (ECC) is a widely used public key cryptographic algorithm. In this paper, we propose a hardware-software codesign implementation of the ECC cipher. The algorithm is modelled in C language. Compute-intensive components are identified for their efficient hardware implementations. In the implementation, residue number system (RNS) with projective coordinates are utilized for performing the required arithmetic operations. To manage the hardware-software codeign in an integrated fashion Xilinx platform studio tool and Virtex-5 xc5vfx70t device based platform is utilized. An application of the implementation is demonstrated for encryption of text and its respective decryption over prime fields. The design is useful for providing an adequate level of security for IoTs.

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.