Determinant-preserving blind signatures from Hadamard-type t-Jacobsthal–Leonardo sequences

Elahe Mehraban, Reza Ebrahimi Atani, Ömür Deveci and Ghadir Golkarian
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 32, 2026, Number 1, Pages 96–111
DOI: 10.7546/nntdm.2026.32.1.96-111
Full paper (PDF, 272 Kb)

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Authors and affiliations

Elahe Mehraban
Mathematics Research Center, Near East University TRNC
Mersin 10, 99138 Nicosia, Türkiye

Reza Ebrahimi Atani
Department of Computer Engineering, Faculty of Engineering, University of Guilan
Rasht, Iran

Ömür Deveci
Department of Mathematics, Faculty of Science and Letters, Kafkas University
36100 Kars, Türkiye

Ghadir Golkarian
Art & Sciences Faculty, Eurasia Reserach Center, Near East University
Lefkosia, Cyprus

Abstract

In this paper, we introduce a new class of sequences called the termed Hadamard-type t-Jacobsthal Leonardo sequence which is generated by applying a Hadamard-type product to the characteristic polynomials of the t-Jacobsthal and Leonardo sequences. We derive fundamental algebraic properties of these sequences including determinant formulas, combinatorial identities, and exponential representations, and building on these mathematical results, we construct a novel blind signature scheme in which the public and secret keys are represented as companion matrices derived from the new sequences. The proposed scheme ensures correctness through determinant-preserving transformations and achieves blindness and unforgeability under matrix- based key assumptions. We provide security analysis within the standard cryptographic framework and discuss efficiency aspects compared with existing blind signature constructions. Our results demonstrate that Hadamard-type t-Jacobsthal–Leonardo matrices can serve as a new algebraic foundation for cryptographic protocols, thereby linking structured number-theoretic sequences with provably secure digital signature mechanisms.

Keywords

• Jacobsthal sequence
• Leonardo sequence
• Blind signature

2020 Mathematics Subject Classification

• 11K31
• 11C20
• 68P25
• 68R01
• 68P30
• 15A15

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Manuscript history

• Received: 4 October 2025
• Revised: 17 February 2026
• Accepted: 22 February 2026
• Online First: 24 February 2026

Copyright information

Ⓒ 2026 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).