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Scaling Security of Elliptic Curves with Fast Pairing Using Efficient Endomorphisms
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2007/01/01
Online ISSN: 1745-1337
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
Category: Elliptic Curve Cryptography
elliptic curve cryptography, pairing, ID-based cryptography,
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Cryptosystems using pairing computation on elliptic curves have various applications including ID-based encryption (,, etc.). Scott  proposed a scaling method of security by a change of the embedding degree k. On the other hand, he also presented an efficient pairing computation method on an ordinary (non-supersingular) elliptic curve over a large prime field Fp (). In this paper, we present an implementation method of the pairing computation with both of the security scaling in  and the efficiency in . First, we will investigate the mathematical nature of the set of the paremeter r (the order of cyclic group used) so as to support many k's. Then, based on it, we will suggest some modification to the algorithm of Scott in  to achieve flexible scalability of security level.