Pairing-Friendly Primes for Abelian Varieties

Article type: Research Article

Authors: Grześkowiak, Maciej^*

Affiliations: Adam Mickiewicz University, Faculty of Mathematics and Computer Science, Umultowska 87, 61-614 Poznań, Poland. [email protected]

Correspondence: [*] The author was partially supported by the grant no. 2013/11/B/ST1/02799 from National Science Centre. Address for correspondence: Faculty of Mathematics and Computer Science, Umultowska 87, 61-614 Poznań, Poland.

Abstract: We present a method of generating primes r ≡ 1 (mod n), q and a Weil q-number π such that r divides Φn(q) and r divides |A(𝔽q)|, where A/𝔽q is an ordinary abelian variety defined over a finite 𝔽q corresponding to π. Such primes can be used for implementing pairing-based cryptographic systems.

Keywords: Abelian vrieties over finite field, public key cryptography

DOI: 10.3233/FI-2016-1453

Journal: Fundamenta Informaticae, vol. 149, no. 4, pp. 385-400, 2016