MATHEMATICAL ANALYSIS OF THE R-PARAMETRIC OPERATION PRESENTED IN THE O'ZMST 286:2024 STANDARD
DOI:
https://doi.org/10.51699/sx8rqc40Keywords:
Electronic Digital Signature, Cryptography, Parametric Multiplication, Modular Arithmetic, Discrete Logarithm, Cryptographic AlgorithmsAbstract
This article mathematically analyzes the R parametric multiplication operation introduced in the national standard of the Republic of Uzbekistan O'zMSt 286:2024 "Processes of generating and verifying electronic digital signatures". The theoretical foundations of the parametric multiplication and exponentiation operations presented in the standard are considered, and the computational processes generated on the basis of these operations are analyzed using examples. In particular, the commutativity of the parametric multiplication operation, the determination of the inverse element, and the exponentiation processes are mathematically considered. Additionally, the computational efficiency of the method recommended in the standard is analyzed during the calculation of large powers, and the possibility of optimizing this calculation is demonstrated. The research results determine that certain computational processes related to the R-parametric operation can be simplified.
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