Accelerating Beta Weil Pairing with Precomputation and Multi-pairing Techniques

摘要

In this paper, we present the efficient computation methods of β Weil pairing with the precomputation and multi-pairing techniques. We use the following two ideas to facilitate applying those techniques to β Weil pairing. 1.Elimination of denominators of β Weil pairing: The original β Weil pairing proposed by Aranha et al. is the products of quotients of extended Miller functions. Then, we propose the method to eliminate denominators of β Weil pairing. 2. Elimination of exponents of β Weil pairing: The original β Weil pairing has distinct exponent in each term. Then, we propose the method to eliminate exponents of the β Weil pairing. Thereby, we can apply the precomputation and multi-pairing technique to β Weil pairing in order to accelerate the computation. Moreover, we estimate the computational costs of the proposed methods for the BLS-48 curve with 256 bit level of security against the Kim-Barbulescu attack, proposed by Kiyomura et al. Then, we compare the results with the normal β Weil pairing and the optimal ate pairing. Furthermore, we also provide implementation results.