Journal of Cryptology

, Volume 17, Issue 4, pp 321–334

Efficient Implementation of Pairing-Based Cryptosystems


DOI: 10.1007/s00145-004-0311-z

Cite this article as:
Barreto, P., Lynn, B. & Scott, M. J Cryptology (2004) 17: 321. doi:10.1007/s00145-004-0311-z


Pairing-based cryptosystems rely on the existence of bilinear, nondegenerate, efficiently computable maps (called pairings) over certain groups. Currently, all such pairings used in practice are related to the Tate pairing on elliptic curve groups whose embedding degree is large enough to maintain a good security level, but small enough for arithmetic operations to be feasible. In this paper we describe how to construct ordinary (non-supersingular) elliptic curves containing groups with arbitrary embedding degree, and show how to compute the Tate pairing on these groups efficiently.

Pairing-based cryptosystem Elliptic curve construction Efficient implementation Tate pairing 

Copyright information

© International Association for Cryptologic Research 2004

Authors and Affiliations

  1. 1.Escola Politécnica, Universidade de São Paulo, Av. Prof. Luciano Gualberto, tr. 3, n. 158, s. C1-46, BR 05508-900, São Paulo (SP)Brazil
  2. 2.Computer Science Department, Stanford University, Stanford, CA 94305 USA
  3. 3.School of Computer Applications, Dublin City University, Ballymun, Dublin 9 Ireland

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