International Association for Cryptologic Research

International Association
for Cryptologic Research


Jiwu Huang


All Pairings Are in a Group
In this paper, we suggest that all pairings be in a group from an abstract angle. It is possible that our observation can be applied into other aspects of pairing-based cryptosystems.
A Note on the Ate Pairing
The Ate pairing has been suggested since it can be computed efficiently on ordinary elliptic curves with small values of the traces of Frobenius $t$. However, not all pairing-friendly elliptic curves have this property. In this paper, we generalize the Ate pairing and find a series of variations of the Ate pairing. We show that the shortest Miller loop of the variations of the Ate pairing can possibly be as small as $r^{1/\varphi(k)}$ on more pairing-friendly curves generated by the method of complex multiplications, and hence speed up the pairing computation significantly.
Efficient Tate Pairing Computation Using Double-Base Chains
Pairing-based cryptosystems have been developing very fast in the last few years. The efficiencies of the cryptosystems are determined by the computation of the Tate pairing. In this paper a new efficient algorithm based on double-base chain for computing the Tate pairing is proposed for odd characteristic $p>3$. The inherent sparseness of double-base number system reduces the computational cost for computing the Tate pairing evidently. It is $9\%$ faster than the previous fastest method for MOV degree k=6.
Speeding up the Bilinear Pairings Computation on Curves with Automorphisms
In this paper we present an algorithm for computing the bilinear pairings on a family of non-supersingular elliptic curves with non-trivial automorphisms. We obtain a short iteration loop in Miller's algorithm using non-trivial ecient automorphisms. The proposed algorithm is as ecient as Scott's algorithm in [12].


Fangguo Zhang (4)
Chang'an Zhao (1)
Chang-An Zhao (3)