An Area-Efficient Design for Modular Inversion in GF(2m)

Modular inversion is one of the kernel arithmetic operations in error control codes and cryptography, so the design of the low-cost and high-speed hardware implementation is absolutely necessary. A novel algorithm and hardware implementation for modular inversion in finite fields GF(2^m) with the standard basis representation is presented. The algorithm used is based on a modification of the extended Euclid's algorithm. The proposed architecture is O(m) area complexity and O(m) time complexity. It is highly regular, modular and thus well suited to VLSI implementation. Compared with two related architectures with the same time complexity, it can save at least 22.5% combinational area