Speeding up the Bilinear Pairings Computation on Curves with Automorphisms

Speeding up Pairing Computation Using Non-adjacent Form and ELM Method

The bilinear pairings such as Weil pairing and Tate pairing on elliptic curves have recently found many applications in cryptography. The first efficient algorithm for computing pairing was originally proposed by Miller and much subsequent research has been directed at many different aspects in order to improve efficiency. In 2003, Eisenträger, Lauter and Montgomery proposed a new point-double-...

Speeding Up Pairing Computations on Genus 2 Hyperelliptic Curves with Efficiently Computable Automorphisms

Pairings on the Jacobians of (hyper-)elliptic curves have received considerable attention not only as a tool to attack curve based cryptosystems but also as a building block for constructing cryptographic schemes with new and novel properties. Motivated by the work of Scott, we investigate how to use efficiently computable automorphisms to speed up pairing computations on two families of non-su...

Speeding up the Discrete Log Computation on Curves with Automorphisms

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 sh...

On Compressible Pairings and Their Computation

In this paper we provide explicit formulæ to compute bilinear pairings in compressed form, and indicate families of curves where particularly generalised versions of the Eta and Ate pairings due to Zhao et al. are especially efficient. With the new formulæ it is possible to entirely avoid F pk arithmetic during pairing computation on elliptic curves over Fp with even embedding degree k. Using o...