Open AccessProbabilistic and deterministic analogues of the Miller – Rabin algorithm for ideals of rings of integer algebraic elements of finite extensions of the field
Author(s) -
Н. П. Прохоров
Publication year - 2020
Publication title -
vescì nacyânalʹnaj akadèmìì navuk belarusì. seryâ fìzìka-matèmatyčnyh navuk
Language(s) - English
Resource type - Journals
eISSN - 2524-2415
pISSN - 1561-2430
DOI - 10.29235/1561-2430-2020-56-2-144-156
Subject(s) - primality test , mathematics , finite field , integer (computer science) , field (mathematics) , prime (order theory) , discrete mathematics , algebraic number , ring (chemistry) , algebra over a field , pure mathematics , combinatorics , computer science , mathematical analysis , programming language , chemistry , organic chemistry
In this paper, we obtained the primality criteria for ideals of rings of integer algebraic elements of finite extensions of the field Q, which are analogues of Miller and Euler’s primality criteria for rings of integers. Also advanced analogues of these criteria were obtained, assuming the extended Riemann hypothesis. Arithmetic and modular operations for ideals of rings of integer algebraic elements of finite extensions of the field Q were elaborated. Using these criteria, the polynomial probabilistic and deterministic algorithms for the primality testing in rings of integer algebraic elements of finite extensions of the field Q were offered.