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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)
We provide a simple and exact formula for the minimum Miller loop length in Ate i pairing based on Brezing-Weng curves, in terms of the involved parameters, under a mild condition on the parameters. It will be also shown that almost all cryptographically useful/meaningful parameters satisfy the mild condition. Hence the simple and exact formula is valid for(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)
The development of new anode materials having high electrochemical performances and interesting reaction mechanisms is highly required to satisfy the need for long-lasting mobile electronic devices and electric vehicles. Here, we report a layer crystalline structured SnP3 and its unique electrochemical behaviors with Li. The SnP3 was simply synthesized(More)