In this paper, we introduce the concept of an optimal pairing, which by definition can be
computed using only log 2 r/¿(k) basic Miller iterations, with r the order of the groups …

In this paper we study non-trivial self-pairings with cyclic domains that are compatible with
isogenies between elliptic curves oriented by an imaginary quadratic order O. We prove that …

In this paper, we propose a new method for constructing a bilinear pairing over (hyper)
elliptic curves, which we call the R-ate pairing. This pairing is a generalization of the Ate and …

We implement asymmetric pairings derived from Kachisa-Schaefer-Scott (KSS), Barreto-
Naehrig (BN), and Barreto-Lynn-Scott (BLS) elliptic curves at the 192-bit security level …

We address three main open problems concerning the use of radical isogenies, as
presented by Castryck, Decru and Vercauteren at Asiacrypt 2020, in the computation of long …

Aspects of Pairing Inversion Page 1 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL.
54, NO. 12, DECEMBER 2008 5719 Aspects of Pairing Inversion S. Galbraith, F. Hess, and F …

Let x be a curve in positive characteristic. A Hasse–Witt matrix for x is a matrix that
represents the action of the Frobenius operator on the cohomology group H1 (x, OX) with …

Pairings on genus 2 hyperelliptic curves are believed to be far less efficient compared to
elliptic curve ones. The main reason is the structure of their Jacobian which leads to slower …

With the recent advances in mobile technologies, biometric verification is being adopted in
many smart devices as a means for authenticating their owners. As biometric data leakage …

The recent introduction of Edwards curves has significantly reduced the cost of addition on
elliptic curves. This paper presents new explicit formulae for pairing implementation in …