Circular Shift Squarer for Efficiency Improvement of Normal Basis Galois Field Inverter

A performance evaluation on modified structure of square operation in an inverter architecture of Galois Field (GF) has been conducted. The most time-consuming GF multiplicative inversion process has been implemented by constructing a nested square and multiplication operations. The new structure of square operator takes advantage of Normal Basis (NB) representation of GF elements. Although NB parallel multiplication has higher complexity than Polynomial Basis (PB) version, the nature of simple circular shift in NB square operation has reduced the total delay significantly and increased the inversion speed by 43% in average.