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Pairings are useful tools in isogeny-based cryptography and have been used in SIDH/SIKE
and other protocols. As a general technique, pairings can be used to move problems about …

While the Weil pairing is geometric, the Tate pairing is arithmetic: its value depends on the
base field considered. Nevertheless, the étale topology allows to interpret the Galois action …

This paper presents a new projective coordinate system and new explicit algorithms which
together boost the speed of arithmetic in the divisor class group of genus 2 curves. The …

A Kummer variety is obtained as the quotient of an abelian variety by the automorphism (− 1)
acting on it. Kummer varieties can be seen as a higher dimensional generalisation of the x …

Let A be an abelian variety of dimension g together with a principal polarization ϕ: A→ ˆA
defined over a field k. Let l be an odd integer prime to the characteristic of k and let K be a …

Pairings are useful tools in cryptography and efficient implementations play a critical role in
their usage, where Miller's algorithms are the main method for all pairings. As an alternative …

This paper presents an algorithm to construct cryptographically strong genus curves and
their Kummer surfaces via Rosenhain invariants and related Kummer parameters. The most …

Nowadays, one area of research in cryptanalysis is solving the Discrete Logarithm Problem
(DLP) in finite groups whose group representation is not yet exploited. For such groups, the …

In Cogdell et al., LMS Lecture Notes Series 459, 393–427 (2020), the authors proved a type
of Kronecker's limit formula associated to any divisor D on any smooth Kähler manifold X …