Research Article

A blind signature scheme based on new cyclic groups

Published in: Quaestiones Mathematicae
Volume 49 , issue 6 , 2026 , pages: 843–856

DOI: 10.2989/16073606.2026.2625348

Author(s): Elahe Mehraban Mathematics Research Center, Near East University TRNC, Turkey , T. Aaron Gulliver Department of Electrical and Computer Engineering, University of Victoria, Canada , Evren Hincal Mathematics Research Center, Near East University TRNC, Turkey

Keywords: Primary: Primary: 11B39 , 20F05 , Secondary: Secondary: 20D60 , 68R01 , 68P30 , Period , Fibonacci sequence , Lehmer sequence , Mersenne sequence , blind signature

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Abstract

In this paper, the Fibonacci, Lehmer, and Mersenne sequences are used to define new sequences named the Hadamard-type Fibonacci-Lehmer sequences and Mersenne-Lehmer sequences, and some results regarding them are given. Then these sequences are employed to introduce new cyclic groups. As an application, a blind signature scheme is presented which uses these groups. This is a new use of group theory in cryptography.

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