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Pairings in Cryptology: efficiency, security and applications

Charlemagne, Manuel (2010) Pairings in Cryptology: efficiency, security and applications. PhD thesis, Dublin City University.

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Abstract The study of pairings can be considered in so many dierent ways that it may not be useless to state in a few words the plan which has been adopted, and the chief objects at which it has aimed. This is not an attempt to write the whole history of the pairings in cryptology, or to detail every discovery, but rather a general presentation motivated by the two main requirements in cryptology; eciency and security. Starting from the basic underlying mathematics, pairing maps are con- structed and a major security issue related to the question of the minimal embedding eld [12]1 is resolved. This is followed by an exposition on how to compute eciently the nal exponentiation occurring in the calculation of a pairing [124]2 and a thorough survey on the security of the discrete log- arithm problem from both theoretical and implementational perspectives. These two crucial cryptologic requirements being fullled an identity based encryption scheme taking advantage of pairings [24]3 is introduced. Then, perceiving the need to hash identities to points on a pairing-friendly elliptic curve in the more general context of identity based cryptography, a new technique to efficiently solve this practical issue is exhibited. Unveiling pairings in cryptology involves a good understanding of both mathematical and cryptologic principles. Therefore, although rst pre- sented from an abstract mathematical viewpoint, pairings are then studied from a more practical perspective, slowly drifting away toward cryptologic applications.

Item Type:Thesis (PhD)
Date of Award:20 December 2010
Supervisor(s):Scott, Michael
Subjects:Computer Science > Computer security
DCU Faculties and Centres:DCU Faculties and Schools > Faculty of Engineering and Computing > School of Computing
Use License:This item is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 3.0 License. View License
ID Code:16000
Deposited On:06 Apr 2011 16:56 by Michael Scott. Last Modified 06 Apr 2011 16:56

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