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Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.2020.tde-06012023-194249
Document
Author
Full name
Olívia Terence Saa
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2020
Supervisor
Committee
Popov, Serguei (President)
Gallesco, Christophe Frederic
Iambartsev, Anatoli
Machado, Fabio Prates
Nascimento, Roberto Venegeroles
Title in English
Some mathematical aspects of DAG-based distributed Ledger systems
Keywords in English
Distributed systems
DLT
Nash equilibria
Tangle
Abstract in English
In the first part of this work, we present, model and analyze a randomized automated peering model, that can be implemented to any distributed system. We conclude that the scheme has some desirable properties (specifically, a reasonable message overhead, a reasonable distribution of the numbers of peers of a node, and a negligible probability of an attack by a malicious actor to be successful). In the second part, we present an article published in the volume 136 of the journal Computers & Industrial Engineering, in October of 2019 (DOI 10.1016=j.cie.2019.07.025). In the paper, we analyze the Nash Equilibria of a graph attachment game, defined to represent the different strategies that malicious actors can use to take certain advantages in a DAG-based (i.e., based on Directed Acyclic Graphs) distributed ledger system. We prove the existence of almost symmetric Nash equilibria for the system where a part of players tries to optimize their attachment strategies and another part follows a default one. We also present simulations that show that the selfish players will not choose strategies that are considerably different that the recommended one.
Title in Portuguese
Aspectos matemáticos diversos sobre sistemas de Ledger distribuído baseados em DAGs
Keywords in Portuguese
DLT
Equilíbrio de Nash
Sistemas distribuídos
Tangle
Abstract in Portuguese
Na primeira parte do presente trabalho, um sistema de peering automático e aleatório é apresentado, modelado e analisado. Este sistema pode ser implementado em qualquer sistema distribuído. Concluímos que ele possui certas propriedades desejáveis (especificamente, um fluxo baixo de mensagens entre os agentes, uma distribuição razoável do número de conexões de cada nó e uma probabilidade desprezável de ser atacado). Na segunda parte do trabalho, apresentamos um artigo publicado no volume 136 do periódico Computers & Industrial Engineering, de outubro de 2019 (DOI 10.1016=j.cie.2019.07.025). Neste paper, analisamos os equilíbrios de Nash de um jogo definido de tal maneira a representar as diferentes estratégias que participantes maliciosos podem utilizar para obter certas vantagens em um sistema de Ledger distribuído baseado em DAGs (Directed Acyclic Graphs). Provamos a existência de equilíbrios quase simétricos para o sistema no qual uma parte dos jogadores usa uma estratégia padronizada e a outra parte tenta otimizar sua estratégia. Também são apresentadas simulações que apontam que os atores egoístas não escolherão estratégias excessivamente diferentes das estratégias padrão.
 
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Publishing Date
2023-01-09
 
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