A refined version of the inverse decomposition theorem for modular multiplicative inverse operators

Abstract

Recently, we started in the IOP Conference Series [1, 2] and in [3] the study of modular multiplicative inverse operators in an algorithmic functional context on (ℤ/ϱℤ)* with ϱ > 3, where it is possible to distinguish different formulas that break up these operators over (ℤ/ϱℤ)*, all this thanks to the so-called “inverse decomposition theorem (IDT)”. In this paper, we will study these issues a little deeper. Though we mainly focus the paper on derived for these operators a refined version of the (IDT), also appear on the scene some additional contributions. Finally, in a brief overview, we compare the differences that exist among the new result here established and the old ones. However, along with this, there are still plenty of questions to be answered in this research field.