Ring Learning With Errors: A crossroads between postquantum cryptography, machine learning and number theory

The present survey reports on the state of the art of the different cryptographic functionalities built upon the ring learning with errors problem and its interplay with several classical problems in algebraic number theory. The survey is based to a certain extent on an invited course given by the author at the Basque Center for Applied Mathematics in September 2018.Comment: arXiv admin note: text overlap with arXiv:1508.01375 by other authors/ comment of the author: quotation has been added to Theorem 5.

Nonuniform Fuchsian codes for noisy channels

We develop a new transmission scheme for additive white Gaussian noisy (AWGN) channels based on Fuchsian groups from rational quaternion algebras. The structure of the proposed Fuchsian codes is nonlinear and nonuniform, hence conventional decoding methods based on linearity and symmetry do not apply. Previously, only brute force decoding methods with complexity that is linear in the code size exist for general nonuniform codes. However, the properly discontinuous character of the action of the Fuchsian groups on the complex upper half-plane translates into decoding complexity that is logarithmic in the code size via a recently introduced point reduction algorithm

Determinación del potencial y los requerimientos para aplicar la tecnología de gasificación por plasma en el tratamiento de desechos y la producción de energía eléctrica en el país

Proyecto de Investigación. Instituto Tecnológico de Costa Rica. Vicerrectoría de Investigación y Extensión (VIE). Escuela de Física, 2012Este informe se enfoca en la implementación de tratamientos con plasmas térmicos como una alternativa o complemento para métodos existentes para el manejo de desechos en Costa Rica. Se tomó en cuenta varios desechos posibles y se evaluó la factibilidad de comprar sistemas existentes o crear versiones locales de estas tecnologías