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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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 1 is resolved. This is followed by an exposition on how
to compute eciently the nal exponentiation occurring in the calculation
of a pairing 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 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
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