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Published in:
2008 | OriginalPaper | Chapter
Integer Variable χ–Based Ate Pairing
Authors : Yasuyuki Nogami, Masataka Akane, Yumi Sakemi, Hidehiro Kato, Yoshitaka Morikawa
Published in: Pairing-Based Cryptography – Pairing 2008
Publisher: Springer Berlin Heidelberg
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In implementing an efficient pairing calculation, it is said that the lower bound of the number of iterations of Miller’s algorithm is log
2
r
/
ϕ
(
k
), where
ϕ
(·) is the Euler’s function. Ate pairing reduced the number of the loops of Miller’s algorithm of Tate pairing from
$\lfloor\log_2r\rfloor$
to
$\lfloor \log_2(t-1)\rfloor$
. Recently, it is known to systematically prepare a pairing–friendly elliptic curve whose parameters are given by a polynomial of integer variable “
χ
”. For the curve, this paper gives
integer variable χ
–based
Ate pairing that achieves the lower bound by reducing it to
$\lfloor\log_2\chi\rfloor$
.