Improvement of Miller Loop for a Pairing on FK12 Curve and its Implementation

Ikesaka, Kazuma; Nanjo, Yuki; Kodera, Yuta; Kusaka, Takuya; Nogami, Yasuyuki

doi:10.1109/candar57322.2022.00021

Cited by 1 publication

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“…Table 2 shows the experimental environment and Table 3 shows the results of the execution time. Note that these results are remeasured for this paper from [10]. In the experiment, the authors measured 1000000 trials of the execution time of the Miller loop and obtained the average execution time.…”

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confidence: 62%

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

Ikesaka

Nanjo

Kodera

et al. 2023

IJNC

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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 the 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 a 3.71% reduction in the number of multiplications and a 3.03% reduction in the execution time. In addition, the authors implement other STNFS secure curves and evaluate these curves from viewpoint of execution time.

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confidence: 62%

“…This paper is an extended version of the authors' previous work [10] in CANDAR'22. The previous version provided Xate pairing on the FK12 curve and evaluate their efficiency of them.…”

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confidence: 99%