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Applied Sciences
Volume 15
Issue 13
10.3390/app15137492
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Article

An Improved GN-AK Protocol Using Double-Base Scalar Multiplication and Point Halving over Elliptic Curves

by
Nicolae Constantinescu
*,†,
Ioan Daniel Hunyadi
† and
Oana-Adriana Ticleanu
†
Mathematics and Informatics Department, Lucian Blaga University of Sibiu, Dr. I. Ratiu Str., No. 5-7, 550012 Sibiu, Romania
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Appl. Sci. 2025, 15(13), 7492; https://doi.org/10.3390/app15137492
Submission received: 5 June 2025 / Revised: 29 June 2025 / Accepted: 1 July 2025 / Published: 3 July 2025
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Abstract

Starting from the basic form of GN-authenticated key agreement (GN-AK), the current research proposes an improved protocol by integrating a new scalar multiplication technique based on a dual-base chain representation with bases 1/2 and 3. This representation allows the use of pointwise halving operations, significantly reducing the complexity of elliptic curve calculations. The resulting protocol maintains cryptographic security based on the elliptic curve discrete logarithm problem (ECDLP) while providing improved performance for key establishment in constrained environments.
Keywords: elliptic curve cryptography; scalar multiplication; point halving; double-base chain; key agreement; authentication elliptic curve cryptography; scalar multiplication; point halving; double-base chain; key agreement; authentication

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MDPI and ACS Style

Constantinescu, N.; Hunyadi, I.D.; Ticleanu, O.-A. An Improved GN-AK Protocol Using Double-Base Scalar Multiplication and Point Halving over Elliptic Curves. Appl. Sci. 2025, 15, 7492. https://doi.org/10.3390/app15137492

AMA Style

Constantinescu N, Hunyadi ID, Ticleanu O-A. An Improved GN-AK Protocol Using Double-Base Scalar Multiplication and Point Halving over Elliptic Curves. Applied Sciences. 2025; 15(13):7492. https://doi.org/10.3390/app15137492

Chicago/Turabian Style

Constantinescu, Nicolae, Ioan Daniel Hunyadi, and Oana-Adriana Ticleanu. 2025. "An Improved GN-AK Protocol Using Double-Base Scalar Multiplication and Point Halving over Elliptic Curves" Applied Sciences 15, no. 13: 7492. https://doi.org/10.3390/app15137492

APA Style

Constantinescu, N., Hunyadi, I. D., & Ticleanu, O.-A. (2025). An Improved GN-AK Protocol Using Double-Base Scalar Multiplication and Point Halving over Elliptic Curves. Applied Sciences, 15(13), 7492. https://doi.org/10.3390/app15137492

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