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Speeding-Up Elliptic Curve Cryptography Algorithms

Author

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  • Diana Maimuţ

    (Advanced Technologies Institute, 10 Dinu Vintilă Street, 021102 Bucharest, Romania
    Faculty of Computer Systems and Cybersecurity, Military Technical Academy, 39-49 George Coşbuc Street, 050141 Bucharest, Romania
    These authors contributed equally to this work.)

  • Alexandru Cristian Matei

    (Advanced Technologies Institute, 10 Dinu Vintilă Street, 021102 Bucharest, Romania
    Faculty of Mathematics and Computer Science, University of Bucharest, 14 Academiei Street, 010014 Bucharest, Romania
    These authors contributed equally to this work.)

Abstract

In recent decades there has been an increasing interest in Elliptic curve cryptography (ECC) and, especially, the Elliptic Curve Digital Signature Algorithm (ECDSA) in practice. The rather recent developments of emergent technologies, such as blockchain and the Internet of Things (IoT), have motivated researchers and developers to construct new cryptographic hardware accelerators for ECDSA. Different types of optimizations (either platform dependent or algorithmic) were presented in the literature. In this context, we turn our attention to ECC and propose a new method for generating ECDSA moduli with a predetermined portion that allows one to double the speed of Barrett’s algorithm. Moreover, we take advantage of the advancements in the Artificial Intelligence (AI) field and bring forward an AI-based approach that enhances Schoof’s algorithm for finding the number of points on an elliptic curve in terms of implementation efficiency. Our results represent algorithmic speed-ups exceeding the current paradigm as we are also preoccupied by other particular security environments meeting the needs of governmental organizations.

Suggested Citation

  • Diana Maimuţ & Alexandru Cristian Matei, 2022. "Speeding-Up Elliptic Curve Cryptography Algorithms," Mathematics, MDPI, vol. 10(19), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3676-:d:935852
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