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.
Bibliographical noteFunding 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 ).
© 2014 Elsevier Inc. All rights reserved.
- Cyclotomic polynomial
- Elliptic curve
- Pairing-based cryptosystem