Changan Zhao

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 the 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 r1/φ(k) on some special pairing-friendly curves with large values of Frobenius trace, and hence speed up the pairing computation significantly.

Computing bilinear pairings on elliptic curves with automorphisms

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.

Faster Computation of Self-Pairings

Self-pairings have found interesting applications in cryptographic schemes. In this paper, we present a novel method for constructing a self-pairing on supersingular elliptic curves with even embedding degrees, which we call the Ateil pairing. This new pairing improves the efficiency of the self-pairing computation on supersingular curves over finite fields with large characteristic. Based on the ηT pairing, we propose a generalization of the Ateil pairing, which we call the Ateili pairing. The optimal Ateili pairing which has the shortest Miller loop is faster than previously known self-pairings on supersingular elliptic curves over finite fields with small characteristic. We also present a new self-pairing based on the Weil pairing which is faster than the self-pairing based on the Tate pairing on ordinary elliptic curves with embedding degree one.

All Pairings Are in a Group

In this paper, we suggest that all pairings are in a group from an abstract angle. Based on the results, some new pairings with the short Miller loop are constructed for great efficiency. It is possible that our observation can be applied into other aspects of pairing-based cryptosystems.