Mugurel Barcau

collaborators

4 papers

math.NT2026

Iterated extensions and the ramification dichotomy

Mugurel Barcau, VicenÅ£iu PaÅol

Let $K / Q_{p}$ be finite and let $f \in O_{K} [X]$ be monic, of degree at least two, with $f^{'} (X) \in m_{K} O_{K} [X]$ , equivalently $f ˉ \in k [X^{p}]$ . For a co…

math.NT2026

Transversal Difference Numbers in Finite Abelian Quotients

Mugurel Barcau, VicenÅ£iu PaÅol, George C. Å¢urcaÅ

Given $H\leq G$ finite abelian groups, a transversal $T\subseteq G$ for $G/H$ has fixed size $|G/H|$, but its ambient difference support $D(T)=T-T$ can vary with the embe…

math.NT2026

Logarithmic Density of Rank $\geq 1$ and Rank $\geq 2$ Genus-2 Jacobians and Applications to Hyperelliptic Curve Cryptography

Razvan Barbulescu, Mugurel Barcau, Vicentiu Pasol +1

In this work we study quantitative existence results for genus- $2$ curves over $Q$ whose Jacobians have Mordell--Weil rank at least $1$ or $2$ , ordering the curves by the…

cs.CR2026

Bridges connecting Encryption Schemes

Mugurel Barcau, Cristian Lupascu, Vicentiu Pasol +1

The present work investigates a type of morphisms between encryption schemes, called bridges. By associating an encryption scheme to every such bridge, we define and examine their…

Iterated extensions and the ramification dichotomy

Transversal Difference Numbers in Finite Abelian Quotients

Logarithmic Density of Rank ≥1 and Rank ≥2 Genus-2 Jacobians and Applications to Hyperelliptic Curve Cryptography

Bridges connecting Encryption Schemes

Logarithmic Density of Rank $\geq 1$ and Rank $\geq 2$ Genus-2 Jacobians and Applications to Hyperelliptic Curve Cryptography