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Ebrahimi Atani, Reza, Mehraban, Elahe. (1405). Matrix-Based Digital Signatures using the Generalized k-Chebyshev p−Sequences. پژوهشنامه مدیریت اجرایی, 3(3), 46-60. doi: 10.22080/cste.2026.31071.1113
Reza Ebrahimi Atani; Elahe Mehraban. "Matrix-Based Digital Signatures using the Generalized k-Chebyshev p−Sequences". پژوهشنامه مدیریت اجرایی, 3, 3, 1405, 46-60. doi: 10.22080/cste.2026.31071.1113
Ebrahimi Atani, Reza, Mehraban, Elahe. (1405). 'Matrix-Based Digital Signatures using the Generalized k-Chebyshev p−Sequences', پژوهشنامه مدیریت اجرایی, 3(3), pp. 46-60. doi: 10.22080/cste.2026.31071.1113
Ebrahimi Atani, Reza, Mehraban, Elahe. Matrix-Based Digital Signatures using the Generalized k-Chebyshev p−Sequences. پژوهشنامه مدیریت اجرایی, 1405; 3(3): 46-60. doi: 10.22080/cste.2026.31071.1113

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

Contributions of Science and Technology for Engineering
دوره 3، شماره 3، آبان 2026، صفحه 46-60    اصل مقاله (1.45 M)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22080/cste.2026.31071.1113
نویسندگان
Reza Ebrahimi Atani* 1؛ Elahe Mehraban2
1Associate Professor of Dep. of Computer Engineering, Faculty of Engineering University of Guilan, Rasht, Iran.
2Mathematics Research Center, Near East University TRNC, Mersin 10 99138, Nicosia,Turkey
تاریخ دریافت: 28 دی 1404،  تاریخ بازنگری: 02 مرداد 1405،  تاریخ پذیرش: 12 آبان 1405 
چکیده
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.
کلیدواژه‌ها
k-Chebyshev sequences؛ Digital signature؛ Public key Cryptosystem؛ EUF-CMA؛ Matrix Discrete Logarithm Problem
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