XOR-Counts and Lightweight Multiplication with Fixed Elements in Binary Finite Fields Abstract
XOR-metrics measure the efficiency of certain arithmetic operations in binary finite fields. We prove some new results about two different XOR-metrics that have been used in the past. In particular, we disprove a conjecture from . We consider implementations of multiplication with one fixed element in a binary finite field. Here we achieve a complete characterization of all elements whose multiplication matrix can be implemented using exactly 2 XOR-operations, confirming a conjecture from . Further, we provide new results and examples in more general cases, showing that significant improvements in implementations are possible.