TY - JOUR
T1 - Scaling security of elliptic curves with fast pairing using efficient endomorphisms
AU - Takashima, Katsuyuki
PY - 2007/1
Y1 - 2007/1
N2 - Cryptosystems using pairing computation on elliptic curves have various applications including ID-based encryption ([9], [29], [30] etc.). Scott [33] 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 <Fopf>p ([34]). In this paper, we present an implementation method of the pairing computation with both of the security scaling in [33] and the efficiency in [34]. 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 [34] to achieve flexible scalability of security level.
AB - Cryptosystems using pairing computation on elliptic curves have various applications including ID-based encryption ([9], [29], [30] etc.). Scott [33] 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 <Fopf>p ([34]). In this paper, we present an implementation method of the pairing computation with both of the security scaling in [33] and the efficiency in [34]. 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 [34] to achieve flexible scalability of security level.
KW - Elliptic curve cryptography
KW - ID-based cryptography
KW - Pairing
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U2 - 10.1093/ietfec/e90-a.1.152
DO - 10.1093/ietfec/e90-a.1.152
M3 - Article
AN - SCOPUS:33846448551
VL - E90-A
SP - 152
EP - 158
JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
SN - 0916-8508
IS - 1
ER -