arXiv subjects

L. Hernández Encinas

Publications and source records attributed to L. Hernández Encinas.

4 recordsLinked to original sources

arXiv2025

Post-Quantum Wireless-based Key Encapsulation Mechanism via CRYSTALS-Kyber for Resource-Constrained Devices

We consider the problem of adapting a Post-Quantum cryptosystem to be used in resource-constrained devices, such as those typically used in Device-to-Device and Internet of Things systems. In particular, we propose leveraging the characteristics of wireless communications channels to minimize the complexity of implementation of a Post-Quantum public key encryption scheme, without diminishing its security. To that end, we focus on the adaptation of a well-known cryptosystem, namely CRYSTALS-Kyber, so as to enable its direct integration into the lowest layer of the communication stack, the physical layer, defining two new transport schemes for CRYSTALS-Kyber to be used in Device-to-Device communications, both of which are modeled under a wireless channel subject to Additive White Gaussian Noise, using a 4 Quadrature Amplitude Modulation constellation and a BCH-code to communicate CRYSTALSKyber's polynomial coefficients. Simulation results demonstrate the viability of the adapted Kyber algorithm due to its low key error probability, while maintaining the security reductions of the original Kyber by considering the error distribution imposed by the channel on the cipher.

eess.SP↗

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↗