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Master's Dissertation
DOI
https://doi.org/10.11606/D.3.2014.tde-25112014-144116
Document
Author
Full name
Jefferson Evandi Ricardini Fernandes de Oliveira
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2014
Supervisor
Committee
Barreto, Paulo Sérgio Licciardi Messeder (President)
Rosset, Valério
Simplicio Junior, Marcos Antonio
Title in Portuguese
Emparelhamentos e reticulados: estado-da-arte em algoritmos e parâmetros para as famílias mais flexíveis de sistemas criptográficos.
Keywords in Portuguese
Algoritmos
Criptologia
Reticulados
Abstract in Portuguese
A criptografia de chave pública é uma área do conhecimento sujeita que é tema de intensa atividade contemporânea de pesquisa. Novos protocolos, primitivas e ataques são propostos com frequência, com semelhanças e diferenças mútuas que podem ser mais ou menos evidentes. Algumas primitivas criptográficas de chave pública mostram-se extremamente férteis em termos de flexibilidade, eficiência e segurança. Duas vertentes que se enquadram nesta categoria são os emparelhamentos e os reticulados. Por possuírem semelhanças em suas funcionalidades a despeito de possuírem naturezas completamente díspares, além de exibirem uma versatilidade rara em toda a área de criptografia de chave pública, alguns autores propuseram chamar os reticulados de os novos emparelhamentos, conforme a ordem cronológica em que essas primitivas passaram a atrair interesse mais vívido de pesquisa. Neste cenário, um estudo comparativo entre elas é de razoável interesse, em particular sobre vantagens e desvantagens que o estado da arte revela sobre a eficiência de cada uma delas. A pesquisa aqui relatada contempla esse estudo, e contribui técnicas de implementação eficiente de emparelhamentos (com ênfase no uso de coordenadas afins, pouco exploradas na literatura), novos parâmetros para a construção de reticulados compactos (na forma das chamadas álgebras discretas de Rojo) e uma técnica inovadora para instanciar reticulados na prática (especificamente, um algoritmo simples e natural para amostrar vetores normalmente distribuídos nos reticulados comumente adotados em sistemas criptográficos).
Title in English
Pairings and lattices: the state-of-art of algorithms and parameters for the most flexible families of cryptographic systems.
Keywords in English
Algorithms
Cryptology
Lattices
Abstract in English
Public key cryptography is an area of knowledge undergoing intense research at present. New protocols, primitives and attacks are often proposed, with mutual similarities and differences that may be more or less evident. Some public key cryptographic primitives tend to be extremely prolific in terms of flexibility, efficiency and security. Two trends that fit this category are pairings and lattices. Because of their similar functionalities despite their completely disparate nature, and because of their rare versatility within the whole area of public key cryptography, some authors proposed to call lattices "the new pairings," according to the chronological order by which these primitives began to attract more vivid research interest. In this scenario, a comparative study between them is of reasonable interest, in particular on the advantages and disadvantages that the state of the art reveals about the efficiency of each one. The research reported herein addresses this study, and also contributes efficient pairing implementation techniques (focusing on affine coordinates, which are scarcely explored in literature), new parameters for building compact lattices (in the form of the so-called discrete Rojo algebras) and an innovative technique to instantiate lattices in practical (specifically, a simple and natural algorithm for sampling normally distributed vectors in the lattices that are commonly adopted in cryptographic systems).
 
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Publishing Date
2014-12-05
 
WARNING: The material described below relates to works resulting from this thesis or dissertation. The contents of these works are the author's responsibility.
  • ARANHA, D. F., et al. The Realm of the Pairings. In Selected Areas in Cryptography (SAC 2013), Burnaby, British Columbia, 2013. Selected Areas in Cryptography (SAC 2013). : Springer, 2013.
All rights of the thesis/dissertation are from the authors
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