The Realm of the Pairings

• Published in: Selected Areas in Cryptography -- SAC 2013 pp. 3 - 25
• Main Authors: Aranha, Diego F., Barreto, Paulo S. L. M., Longa, Patrick, Ricardini, Jefferson E.
• Format: Book Chapter
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg
• Series: Lecture Notes in Computer Science
• Subjects: Efficient algorithms; Pairing-based cryptosystems
• ISBN: 9783662434130; 366243413X
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-662-43414-7_1

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.