Cryptology ePrint Archive: Report 2020/875

Efficient Final Exponentiation via Cyclotomic Structure for Pairings over Families of Elliptic Curves

Daiki Hayashida and Kenichiro Hayasaka and Tadanori Teruya

Abstract: The final exponentiation, which is the exponentiation by a fixed large exponent, must be performed in the Tate and (optimal) Ate pairing computation to ensure output uniqueness, algorithmic correctness, and security for pairing-based cryptography. In this paper, we propose a new framework of efficient final exponentiation for pairings over families of elliptic curves. Our framework provides two methods: the first method supports families of elliptic curves with arbitrary embedding degrees, and the second method supports families with specific embedding degrees of providing even faster algorithms. Applying our framework to several Barreto-Lynn-Scott families, we obtain faster final exponentiation than the previous state-of-the-art constructions.

Category / Keywords: public-key cryptography / pairings, final exponentiation, cyclotomic polynomial

Date: received 11 Jul 2020

Contact author: Hayashida Daiki at df MitsubishiElectric co jp

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Version: 20200712:130033 (All versions of this report)

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