Based on its definition, it appears that primality testing should inherently involve a division operation. Even the popular primality testing procedure which involves modular exponentiations has a division essence. Montgomery arithmetic facilitates modular exponentiation without divisions, provided that certain precalculations which involve proper divisions are first performed. In primality testing these precalculations have to be re-done for each number whose candidacy for primality is tested. It is shown in this paper how primality testing can still be based on Montgomery arithmetic, such that no operation, including the precalculation, involves proper divisions. That is, it is shown that a complete primality testing process can be based on divisionless operations only.
ASJC Scopus subject areas
- Computer Science (all)