Abstract
In this paper, we describe an efficient implementation in Sage of the Tate pairing over ordinary hyperelliptic curves of type \( y^2 = x^5 +a \, x\). First, we describe a method of construction of these curves according to Kawazoe and Takahashi [8]. Then, we describe an efficient formula for computing pairings on such curves over prime fields, and develop algorithms to compute Tate pairing. We provide a faster optimisation of the final exponentiation in particular for the embedding degree \(k = 28\).
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Zitouni, M., Mokrane, F. (2020). Implementing Cryptography Pairings over Ordinary Pairing-Friendly Curves of Type \( y^2 = x^5 +a \, x\). In: Simion, E., Géraud-Stewart, R. (eds) Innovative Security Solutions for Information Technology and Communications. SecITC 2019. Lecture Notes in Computer Science(), vol 12001. Springer, Cham. https://doi.org/10.1007/978-3-030-41025-4_7
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