Computing bilinear pairings on elliptic curves with automorphisms

Designs Codes and Cryptography (Impact Factor: 0.96). 01/2011; 58(1):35-44. DOI: 10.1007/s10623-010-9383-y
Source: DBLP


In this paper, we present a novel method for constructing a super-optimal pairing with great efficiency, which we call the
omega pairing. The computation of the omega pairing requires the simple final exponentiation and short loop length in Miller’s
algorithm which leads to a significant improvement over the previously known techniques on certain pairing-friendly curves.
Experimental results show that the omega pairing is about 22% faster and 19% faster than the super-optimal pairing proposed
by Scott at security level of AES 80 bits on certain pairing-friendly curves in affine coordinate systems and projective coordinate
systems, respectively.

KeywordsElliptic curves–Automorphism–Pairing based cryptography–Weil pairing

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Available from: Fangguo Zhang, Apr 01, 2014
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    • "Note that we need 2 log r ⎢ ⎥ ⎣ ⎦ basic Miller iterations to compute f r, P (Q). Recall the pairings by q-expansion from [10], [12], [13], [16]. Let π q be the Frobenius endomorphism: "
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    ABSTRACT: 2 DGA sorina.ionica, Abstract. Scott uses an eciently computable isomorphism in order to optimize pairing computation on a particular class of curves with embed- ding degree 2. He points out that pairing implementation becomes thus faster on these curves than on their supersingular equivalent, originally recommended by Boneh and Franklin for Identity Based Encryption. We extend Scott's method to other classes of curves with small embedding degree and eciently computable endomorphism.
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