@article{71098addf85b4c1da9677f5480d1e4f9,
title = "Explicit formula for optimal ate pairing over cyclotomic family of elliptic curves",
abstract = "Pairings on elliptic curves play an important role in cryptography. We provide an explicit formula for vectors of polynomials describing optimal ate pairings over cyclotomic family of elliptic curves. The explicit formula is simple in that it only involves partitioning a certain cyclotomic polynomial. The simplicity of the formula allows us to analyze the sparsity of the vector.",
keywords = "Cyclotomic polynomial, Elliptic curve, Pairing-based cryptosystem",
author = "Hoon Hong and Eunjeong Lee and Lee, {Hyang Sook}",
note = "Funding Information: Eunjeong Lee and Hyang-Sook Lee were supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (Grant Number: 2012R1A2A1A03006706 ). Publisher Copyright: {\textcopyright} 2014 Elsevier Inc. All rights reserved.",
year = "2015",
month = jul,
doi = "10.1016/j.ffa.2014.12.007",
language = "English",
volume = "34",
pages = "45--74",
journal = "Finite Fields and their Applications",
issn = "1071-5797",
publisher = "Academic Press Inc.",
}