Improvement of Miller Loop for a Pairing on FK12 Curve and Evaluation with other STNFS Curves

Pairing is carried out by two steps, Miller loop and final exponentiation. In this manuscript, the authors propose an efficient for a pairing on FK12 curve. A Hamming weight bit-length of parameter have great effect computational cost loop. Optimal-ate used as most curve currently. The optimal-ate 6z + 2 where z integer to make parameter. Our method uses which has shorter than previous Usually, low exponentiation efficient. Therefore, in our lower one many cases. evaluate number multiplications execution time. As result, proposed algorithm leads 3.71% reduction 3.03% addition, implement other STNFS secure curves these from viewpoint