An Application of XTR for the Discrete Logarithm Problem on Barreto -- Naehrig Curve

This paper considers the discrete logarithm problem (DLP) appeared in the context of pairing - based cryptography with Barreto - Naehrig (BN) curve. Since the embedding degree of BN curve is 12, the DLP is defined in the extension field F_p12, where p is the characteristic. This paper first points out that efficient and compact subgroup trace representation (ECSTR:XTR) is available for representing the DLP. Then, XTR-based rho method for solving the DLP is proposed. After that, its efficiency with and without tag tracing technique is evaluated by a small experiment.