Matrix-Based Digital Signatures using the Generalized k-Chebyshev p−Sequences

Document Type : Original Article

Authors

1 Associate Professor of Dep. of Computer Engineering, Faculty of Engineering University of Guilan, Rasht, Iran.

2 Mathematics Research Center, Near East University TRNC, Mersin 10 99138, Nicosia,Turkey

Abstract

Digital signatures are a fundamental cryptographic primitive ensuring integrity, authenticity, and non-repudiation in digital communications. This paper introduces two novel generalizations of the classical k-Chebyshev sequences: the k-Chebyshev p-sequences and the (k,t) -Chebyshev p-sequences. These generalizations yield companion matrices of dimension p+1 and p+t, respectively, providing a flexible algebraic framework with tunable security parameters. Applying the cyclic subgroup structure of these matrices, we propose a matrix-based digital signature scheme following a dual-challenge Fiat-Shamir construction that extends the Schnorr paradigm. Unlike naive matrix exponentiation signatures, our scheme employs parameter-dependent hashing to cryptographically bind the message to the nonce, preventing algebraic forgeries. We formally analyze the scheme within the standard EUF-CMA security framework and prove its existential unforgeability under adaptive chosen-message attacks in the random oracle model, reducing its security to the hardness of the Matrix Discrete Logarithm Problem (MDLP). The security analysis demonstrates resistance to brute-force, index-calculus, Pohlig--Hellman, and linear recurrence attacks. The results establish generalized Chebyshev sequence theory as a fertile foundation for designing provably secure public-key cryptosystems, extending the landscape of algebraic methods in digital signatures.

Keywords

References

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Contributions of Science and Technology for Engineering
Volume 3, Issue 3
August 2026
Pages 46-60

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History

  • Receive Date: 18 January 2026
  • Revise Date: 24 July 2026
  • Accept Date: 03 November 2026
  • First Publish Date: 08 November 2026
  • Publish Date: 08 November 2026

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