Optimizations in the computation of pairings and cryptographic applications

En la criptografía de clave pública actual el uso de curvas elípticas es cada vez más habitual debido a que ofrecen una seguridad similar a los ya utilizados cuerpos finitos, pero con unas claves más cortas. Por otra parte, la introducción de los apareamientos sobre curvas elípticas ha hecho posible, a cambio de un coste computacional más alto, el desarrollo de soluciones a nuevos escenarios criptográficos. En este trabajo final de máster describimos y completamos el trabajo hecho por Costello et al. sobre una optimización en el cálculo de apareamientos basada en precálculos, especialmente útil en la criptografía de clave pública donde un argumento del apareamiento es fijo. Hemos completado detalles sobre el análisis computacional e implementado la optimización en una librería ya existente para poder comparar y analizar el coste de los precálculos y de cada evaluación.. Es tractaria de fer una anàlisi, tant teòrica com pràctica, d'algunes optimitzacions existents (o variacions que trobi l'estudiant) per millorar el temps de càlcul dels "bilinear pairing", un objecte matemàtic definit sobre corbes el·líptiques que està trobant un gran número d'aplicacions en l'àrea de la criptografi

Optimal Pairings on BN Curves

Bilinear pairings are being used in ingenious ways to solve various protocol problems. Much research has been done on improving the efficiency of pairing computations. This thesis gives an introduction to the Tate pairing and some variants including the ate pairing, Vercauteren's pairing, and the R-ate pairing. We describe the Barreto-Naehrig (BN) family of pairing-friendly curves, and analyze three different coordinates systems (affine, projective, and jacobian) for implementing the R-ate pairing. Finally, we examine some recent work for speeding the pairing computation and provide improved estimates of the pairing costs on a particular BN curve

Delaying mismatched field multiplications in pairing computations

Miller’s algorithm for computing pairings involves perform- ing multiplications between elements that belong to different finite fields. Namely, elements in the full extension field Fpk are multiplied by elements contained in proper subfields F pk/d , and by elements in the base field Fp . We show that significant speedups in pairing computations can be achieved by delaying these “mismatched” multiplications for an optimal number of iterations. Importantly, we show that our technique can be easily integrated into traditional pairing algorithms; implementers can exploit the computational savings herein by applying only minor changes to existing pairing code

Bibliography of Lewis Research Center technical publications announced in 1988

This bibliography contains abstracts of the technical reports that resulted from the scientific and engineering work performed and managed by the Lewis Research Center in 1988. Subject, author, and corporate source indexes are also included. All the publications were announced in the 1988 issues of STAR (Scientific and Technical Aerospace Reports) and/or IAA (International Aerospace Abstracts). Included are research reports, journal articles, conference presentations, patents and patent applications, and theses

Programming Languages and Systems

This open access book constitutes the proceedings of the 30th European Symposium on Programming, ESOP 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 24 papers included in this volume were carefully reviewed and selected from 79 submissions. They deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems

Cumulative index to NASA Tech Briefs, 1986-1990, volumes 10-14

Tech Briefs are short announcements of new technology derived from the R&D activities of the National Aeronautics and Space Administration. These briefs emphasize information considered likely to be transferrable across industrial, regional, or disciplinary lines and are issued to encourage commercial application. This cumulative index of Tech Briefs contains abstracts and four indexes (subject, personal author, originating center, and Tech Brief number) and covers the period 1986 to 1990. The abstract section is organized by the following subject categories: electronic components and circuits, electronic systems, physical sciences, materials, computer programs, life sciences, mechanics, machinery, fabrication technology, and mathematics and information sciences

A comparison of the CAR and DAGAR spatial random effects models with an application to diabetics rate estimation in Belgium

When hierarchically modelling an epidemiological phenomenon on a finite collection of sites in space, one must always take a latent spatial effect into account in order to capture the correlation structure that links the phenomenon to the territory. In this work, we compare two autoregressive spatial models that can be used for this purpose: the classical CAR model and the more recent DAGAR model. Differently from the former, the latter has a desirable property: its ρ parameter can be naturally interpreted as the average neighbor pair correlation and, in addition, this parameter can be directly estimated when the effect is modelled using a DAGAR rather than a CAR structure. As an application, we model the diabetics rate in Belgium in 2014 and show the adequacy of these models in predicting the response variable when no covariates are available

A Statistical Approach to the Alignment of fMRI Data

Multi-subject functional Magnetic Resonance Image studies are critical. The anatomical and functional structure varies across subjects, so the image alignment is necessary. We define a probabilistic model to describe functional alignment. Imposing a prior distribution, as the matrix Fisher Von Mises distribution, of the orthogonal transformation parameter, the anatomical information is embedded in the estimation of the parameters, i.e., penalizing the combination of spatially distant voxels. Real applications show an improvement in the classification and interpretability of the results compared to various functional alignment methods

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum