## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

AMC

We extend the notion of an invalid-curve attack from elliptic curves
to genus 2 hyperelliptic curves. We also show that invalid singular (hyper)elliptic
curves can be used in mounting invalid-curve attacks on (hyper)elliptic curve
cryptosystems, and make quantitative estimates of the practicality of these
attacks. We thereby show that proper key validation is necessary even in cryptosystems
based on hyperelliptic curves. As a byproduct, we enumerate the
isomorphism classes of genus g hyperelliptic curves over a finite field by a new
counting argument that is simpler than the previous methods.

AMC

For symmetric pairings $e : \mathbb{G} \times \mathbb{G} \rightarrow \mathbb{G}_T$, Verheul proved
that the existence of an efficiently-computable isomorphism $\phi : \mathbb{G}_T
\rightarrow \mathbb{G}$ implies that the Diffie-Hellman problems in $\mathbb{G}$ and $\mathbb{G}_T$
can be efficiently solved. In this paper, we explore the implications of
the existence of efficiently-computable isomorphisms $\phi_1 : \mathbb{G}_T
\rightarrow \mathbb{G}_1$ and $\phi_2 : \mathbb{G}_T \rightarrow \mathbb{G}_2$ for asymmetric
pairings $e : \mathbb{G}_1 \times \mathbb{G}_2 \rightarrow \mathbb{G}_T$. We also give a simplified
proof of Verheul's theorem.

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