Pairing lattices. (English) Zbl 1186.94444

Hess, Florian

Galbraith, Steven D. (ed.) et al., Pairing-based cryptography – Pairing 2008. Second international conference, Egham, UK, September 1–3, 2008. Proceedings. Berlin: Springer (ISBN 978-3-540-85503-3/pbk). Lecture Notes in Computer Science 5209, 18-38 (2008).

Summary: We provide a convenient mathematical framework that essentially encompasses all known pairing functions based on the Tate pairing and also applies to the Weil pairing. We prove non-degeneracy and bounds on the lowest possible degree of these pairing functions and show how endomorphisms can be used to achieve a further degree reduction.
For the entire collection see [Zbl 1155.94002].

MSC:

94A60	Cryptography
11T71	Algebraic coding theory; cryptography (number-theoretic aspects)
14G50	Applications to coding theory and cryptography of arithmetic geometry