High-speed constant-time division module for Elliptic Curve Cryptography based on GF(2m)

To achieve high performance scalar multiplication arithmetic in Elliptic Curve Cryptography (ECC) based on GF(2^m), a high-speed constant-time division module with optimized architecture is proposed in this paper. Modified from the traditional extended Euclidean Great Common Divisor (GCD) division algorithm, the presented algorithm computes a single multiplicative inverse or division in constant m iterations, i.e. m clock cycles, in GF(2^m), which obtains a tremendous reduction (specifically more than 50%) on computing time compared with previous works. Combined with the meticulously optimized architecture, this novel division module achieves lower area-time complexity, which makes it an excellent option for high performance ECC design.