Year: 2024
Type: article
Abstract: The feasibility of considering quasi-Mersenne numbers represented in the form p = 3k + 2 is justi- fied. The first prime numbers represented in this form are 11, 29, 83, 6563, i.e. there exist specific Galois fields corresponding to such numbers. It is shown that computations in such Galois fields can be reduced to computations in finite algebraic rings, specifically, in rings of subtraction classes modulo 3k + 1. It is found that the numbers under consideration have a property similar to that possessed by the Mersenne prime numbers in binary representation. Specifically, when multiplying numbers of the considered type written in ternary representation by 3, there is a cyclic rearrangement of ternary symbols with a change of sign. The highlighted case is an exception: in rings of subtraction classes modulo 3k + 1 there exists a highlighted element whose multiplication by three modulo 3k + 1 remains unchanged. We discuss the pos- sibilities of application of the found property for realisation of computational systems operating in Galois fields and finite algebraic rings.
Language: English
Subfield: Information Systems
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4410125343