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2023-07-18
Ikesaka, Kazuma, Nanjo, Yuki, Kodera, Yuta, Kusaka, Takuya, Nogami, Yasuyuki.  2022.  Improvement of Miller Loop for a Pairing on FK12 Curve and its Implementation. 2022 Tenth International Symposium on Computing and Networking (CANDAR). :104—109.
Pairing is carried out by two steps, Miller loop and final exponentiation. In this manuscript, the authors propose an efficient Miller loop for a pairing on the FK12 curve. A Hamming weight and bit-length of loop parameter have a great effect on the computational cost of Miller loop. Optimal-ate pairing is used as the most efficient pairing on the FK12 curve currently. The loop parameter of optimal-ate pairing is 6z+2 where z is the integer to make the FK12 curve parameter. Our method uses z which has a shorter bit-length than the previous optimal-ate pairing as the loop parameter. Usually, z has a low Hamming weight to make final exponentiation efficient. Therefore, the loop parameter in our method has a lower Hamming weight than the loop parameter of the previous one in many cases. The authors evaluate our method by the number of multiplications and execution time. As a result, the proposed algorithm leads to the 3.71% reduction in the number of multiplications and the 3.38% reduction in the execution time.