Accelerating Cross Twisted Ate Pairing with Ordinary Pairing Friendly Curve of Composite Order That Has Two Large Prime Factors

摘要

Recently, pairing-based cryptographic applications such as ID-based cryptography have received much attention. On the other hand, RSA cryptography has been widely used and is defined over a certain composite order as the modulus. In detail, it generally needs to be a product of two large prime numbers. In order to apply RSA-based techniques to pairing-based cryptography, the authors have proposed a method for generating ordinary pairing-friendly curves of such a composite order especially when the embedding degree k is equal to 3 and the order of curve is given as a polynomial of degree 2 with an integer variable. Then, as the next problem, its pairing calculation needs to be efficiently carried out. This paper shows the implementation of {???cross twisted} Ate pairing using the obtained composite order curve and some experimental results.