Low Complexity Cubing and Cube Root Computation over $\F_{3^m}$ in Polynomial Basis
Omran Ahmadi, Francisco Rodríguez Henríquez · IEEE Transactions on Computers · 2010
We present low complexity formulae for the computation of cubing and cube root over IF3mconstructed using special classes of irreducible trinomials, tetranomials and pentanomials. We show that for all those special classes of polynomials, field cubing and field cube root operation have the same computational complexity when implemented in hardware or software platforms. As one of the main applications of these two field arithmetic operations lies in pairing-based cryptography, we also give in this paper a selection of irreducible polynomials that lead to low cost field cubing and field cube root computations for supersingular elliptic curves defined over IF3m, where m is a prime number in the pairing-based cryptographic range of interest, namely, m ∈ [47, 541].