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In this paper, we propose a new method for constructing a bilinear pairing over (hyper)elliptic curves, which we call the Rate pairing. This pairing is a generalization of the Ate and Ate i pairing, and also improves efficiency of the pairing computation. Using the Rate pairing, the loop length in Miller's algorithm can be as small as log(r 1/φ(k)) for some(More)
New battery systems having high energy density are actively being researched in order to satisfy the rapidly developing market for longer-lasting mobile electronics and hybrid electric vehicles. Here, we report a new Li-Te secondary battery system with a redox potential of ~1.7 V (vs. Li(+)/Li) adapted on a Li metal anode and an advanced Te/C nanocomposite(More)
We define a polynomial generating pairing (PGP) and propose a method to construct a family of pairing friendly curves from PGP. We show that a bilinear map over the family is directly determined by the coefficients of the PGP and the map is non-degenerate under a minor condition which is satisfied with cryptographic parameters. Finally, we provide a(More)