This study analyzes the computational efficiency of parametric exponentiation operations in parametric algebra and proposes an algorithmic approach for their fast computation. By leveraging the properties of parametric algebra, the possibility of reducing parametric exponentiation to fast exponentiation methods is established, and a corresponding computational algorithm is developed. The proposed approach enables more efficient computation of parametric exponentiation and reduces the computational impact of the system parameter. The obtained results provide a basis for reconsidering approaches to the efficiency of parametric algebra-based computations, demonstrating that the slowness of exponentiation often stems from the computational methods employed rather than the algebraic structure itself. This research establishes a significant foundation for the efficient organization of cryptographic computations based on parametric algebra and for addressing algorithmic optimization challenges.
Zarifjon et al. (Thu,) studied this question.