arXiv subjects

J. Muñoz Masqué

Publications and source records attributed to J. Muñoz Masqué.

5 recordsLinked to original sources

arXiv2019

A group law on the projective plane with applications in Public Key Cryptography

We present a new group law defined on a subset of the projective plane $\mathbb{F}P^2$ over an arbitrary field $\mathbb{F}$, which lends itself to applications in Public Key Cryptography, in particular to a Diffie-Hellman-like key agreement protocol. We analyze the computational difficulty of solving the mathematical problem underlying the proposed Abelian group law and we prove that the security of our proposal is equivalent to the discrete logarithm problem in the multiplicative group of the cubic extension of the finite field considered. Finally, we present a variant of the proposed group law but over the ring $\mathbb{Z}/pq\mathbb{Z}$, and explain how the security becomes enhanced, though at the cost of a longer key length.

cs.CR↗

arXiv2019

Quadratic Maps in Two Variables on Arbitrary Fields

Let $\mathbb{F}$ be a field of characteristic different from $2$ and $3$, and let $V$ be a vector space of dimension $2$ over $\mathbb{F}$. The generic classification of homogeneous quadratic maps $f\colon V\to V$ under the action of the linear group of $V$, is given and efficient computational criteria to recognize equivalence are provided.

math.RT↗

arXiv2018

Square-Zero Basis of Matrix Lie Algebras

A method is obtained to compute the maximum number of functionally independent invariant functions under the action of a linear algebraic group as long as its Lie algebra admits a base of square-zero matrices. Some applications are also given.

math.RT↗

arXiv2015

Second-order Lagrangians admitting a first-order Hamiltonian formalism

Second-order Lagrangian densities admitting a first-order Hamiltonian formalism are studied; namely, i) for each second-order Lagrangian density on an arbitrary fibred manifold $p\colon E\to N$ the Poincaré-Cartan form of which is projectable onto $J^1E$, by using a new notion of regularity previously introduced, a first-order Hamiltonian formalism is developed for such a class of variational problems; ii) the existence of first-order equivalent Lagrangians are discussed from a local point of view as well as global; iii) this formalism is then applied to classical Einstein-Hilbert Lagrangian and a generalization of the BF theory. The results suggest that the class of problems studied is a natural variational setting for GR.

math-ph↗

arXiv2011

Diffeomorphism-invariant Covariant Hamiltonians of a pseudo-Riemannian Metric and a Linear Connection

\noindent Let $M\to N$ (resp.\ $C\to N$) be the fibre bundle of pseudo-Riemannian metrics of a given signature (resp.\ the bundle of linear connections) on an orientable connected manifold $N$. A geometrically defined class of first-order Ehresmann connections on the product fibre bundle $M\times_NC$ is determined such that, for every connection $γ$ belonging to this class and every $\mathrm{Diff}N$-invariant Lagrangian density $Λ$ on $J^1(M\times_NC)$, the corresponding covariant Hamiltonian $Λ^γ$ is also $\mathrm{Diff}N$-invariant. The case of $\mathrm{Diff}N$-invariant second-order Lagrangian densities on $J^2M$ is also studied and the results obtained are then applied to Palatini and Einstein-Hilbert Lagrangians.

math-ph↗