Compartición de secretos y votación electrónica: implementación y aplicaciones

En muchos sectores y ámbitos profesionales existe cierta información confidencial que no conviene exponer. Dado que se trata de un tipo de información cuyo acceso podría tener numerosas consecuencias, es necesario utilizar algún método que oculte dicho contenido. En este sentido, la criptografía se encarga de proteger estos datos al convertirlos en secuencias que resulten ilegibles para cualquier elemento que no tenga implicación directa en ellos. El presente documento se centrará en los esquemas de compartición de secretos (ECS) y la computación segura entre múltiples partes (MPC). Hemos realizado un estudio de los diferentes tipos de ECS, dando sentido a todos los conceptos vinculados a ellos. El análisis de los ECS se ha orientado a los esquemas de umbral, con su ejemplo más característico el esquema de Shamir. Además, se ha estudiado la utilización de los códigos lineales para formar un esquema de compartición de secretos a través de la idea de Massey. La idea de Massey se ha extendido para poder trabajar con ficheros más grandes. El estudio de los ECS, ha tenido como finalidad llegar a conseguir un aplicativo de votación electrónica, gracias a la unión con el protocolo de computación segura entre múltiples partes, MPC. Para finalizar hemos explicado todos los conceptos correspondientes para el entendimiento de la votación electrónica, en el que todo el mundo colabora y obtenemos como resultado final la suma de todos los votos de los participantes. Siempre se ha intentado aportar ejemplos numéricos para ilustrar a la perfección los algoritmos que lo componen.In many industries and professional fields there is certain confidential information that should not be exposed. Since this type of information could have many consequences if accessed, it is necessary to use some method to conceal its content. Cryptography protects this data by converting it into sequences that are unreadable to anyone who has no direct involvement with it. This paper will focus on (ECS) secret sharing schemes and (MPC) multiparty secure computing. We have conducted a survey of the different types of ECS, making sense of all the concepts linked to them. The analysis of ECS has been oriented towards threshold schemes, with its most characteristic example being Shamir’s scheme. In addition, the use of linear codes to form a secret sharing scheme has been studied through Massey’s idea. Massey’s idea has been extended to work with larger files. The study of of the ECS was to achieve a electronic voting application, thanks to the union with the secure multi-party computing protocol, MPC. Finally, we have explained all the corresponding concepts for the understanding of the electronic voting, in which everybody collaborates and we obtain as final result the sum of all the votes of the participants.We have always tried to provide numerical examples to understand perfectly the algorithms that compose it.Departamento de Algebra, Geometría y TopologíaGrado en Matemática

Novel Secret Sharing and Commitment Schemes for Cryptographic Applications

In the second chapter, the notion of a social secret sharing (SSS) scheme is introduced in which shares are allocated based on a player's reputation and the way she interacts with other parties. In other words, this scheme renews shares at each cycle without changing the secret, and it allows the trusted parties to gain more authority. Our motivation is that, in real-world applications, components of a secure scheme have different levels of importance (i.e., the number of shares a player has) and reputation (i.e., cooperation with other parties). Therefore, a good construction should balance these two factors accordingly. In the third chapter, a novel socio-rational secret sharing (SRS) scheme is introduced in which rational foresighted players have long-term interactions in a social context, i.e., players run secret sharing while founding and sustaining a public trust network. To motivate this, consider a repeated secret sharing game such as sealed-bid auctions. If we assume each party has a reputation value, we can then penalize (or reward) the players who are selfish (or unselfish) from game to game. This social reinforcement stimulates the players to be cooperative in the secret recovery phase. Unlike the existing protocols in the literature, the proposed solution is stable and it only has a single reconstruction round. In the fourth chapter, a comprehensive analysis of the existing dynamic secret sharing (DSS) schemes is first provided. In a threshold scheme, the sensitivity of the secret and the number of players may fluctuate due to various reasons. Moreover, a common problem with almost all secret sharing schemes is that they are ``one-time'', meaning that the secret and shares are known to everyone after secret recovery. We therefore provide new techniques where the threshold and/or the secret can be changed multiple times to arbitrary values after the initialization. In addition, we introduce a new application of dynamic threshold schemes, named sequential secret sharing (SQS), in which several secrets with increasing thresholds are shared among the players who have different levels of authority. In the fifth chapter, a cryptographic primitive, named multicomponent commitment scheme (MCS) is proposed where we have multiple committers and verifiers. This new scheme is used to construct different sealed-bid auction protocols (SAP) where the auction outcomes are defined without revealing the losing bids. The main reason for constructing secure auctions is the fact that the values of the losing bids can be exploited in future auctions and negotiations if they are not kept private. In our auctioneer-free protocols, bidders first commit to their bids before the auction starts. They then apply a decreasing price mechanism to define the winner and selling price in an unconditionally secure setting