Boolean Gröbner bases

Abstract

In recent years, Boolean Gröbner bases have attracted the attention of many researchers, mainly in connection with cryptography. Several sophisticated methods have been developed for the computation of Boolean Gröbner bases. However, most of them only deal with Boolean polynomial rings over the simplest coefficient Boolean ring GF2. Boolean Gröbner bases for arbitrary coefficient Boolean rings were first introduced by two of the authors almost two decades ago. While the work is not well-known among computer algebra researchers, recent active work on Boolean Gröbner bases inspired us to return to their development. In this paper, we introduce our work on Boolean Gröbner bases with arbitrary coefficient Boolean rings. © 2010 Elsevier Ltd.