The Realm of the Pairings

  • Diego F. Aranha
  • Paulo S. L. M. Barreto
  • Patrick Longa
  • Jefferson E. Ricardini
Conference paper

DOI: 10.1007/978-3-662-43414-7_1

Volume 8282 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Aranha D.F., Barreto P.S.L.M., Longa P., Ricardini J.E. (2014) The Realm of the Pairings. In: Lange T., Lauter K., Lisoněk P. (eds) Selected Areas in Cryptography -- SAC 2013. SAC 2013. Lecture Notes in Computer Science, vol 8282. Springer, Berlin, Heidelberg

Abstract

Bilinear maps, or pairings, initially proposed in a cryptologic context for cryptanalytic purposes, proved afterward to be an amazingly flexible and useful tool for the construction of cryptosystems with unique features. Yet, they are notoriously hard to implement efficiently, so that their effective deployment requires a careful choice of parameters and algorithms. In this paper we review the evolution of pairing-based cryptosystems, the development of efficient algorithms and the state of the art in pairing computation, and the challenges yet to be addressed on the subject, while also presenting some new algorithmic and implementation refinements in affine and projective coordinates.

Keywords

Pairing-based cryptosystems Efficient algorithms 

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Diego F. Aranha
    • 1
  • Paulo S. L. M. Barreto
    • 2
  • Patrick Longa
    • 3
  • Jefferson E. Ricardini
    • 2
  1. 1.Department of Computer ScienceUniversity of BrasíliaBrasíliaBrazil
  2. 2.Departamento de Engenharia de Computação e Sistemas DigitaisEscola Politécnica, University of São PauloSão PauloBrazil
  3. 3.Microsoft ResearchOne Microsoft WayRedmondUSA