Construction of Akushsky Core Functions Without Critical Cores

The residue number system is widely used in cryptography, digital signal processing, image processing systems, and other areas where high-performance computing is required. One of the main tools used in the residue number system is the Akushsky core function. However, its use is limited due to the existence of so-called critical cores. This study aims to develop Akushsky core functions that effectively eliminate the occurrence of critical cores, thereby enhancing their applicability in real-world scenarios. We introduce a fundamental approach to critical core detection that reduces the average time for critical core detection by 99.48% compared to the brute force algorithm. The results of our analysis indicate not only a substantial improvement in the speed of core detection but also an enhancement in the overall performance of systems utilizing the Akushsky core function. Our findings provide important insights into optimizing residue number systems and encourage further exploration into advanced computational techniques within this domain.