Thesis (M. Sc.)(Mathematics)--University of Pretoria, 2006. / Includes bibliographical references. Available on the Internet via the World Wide Web.

No description available.

Quantum mechanics, which describes the behaviour of matter and energy on very small scales, is one of the most successful theories in the history of science. Einstein's theory of special relativity, which describes the relationship between space and time, is likewise a highly successful and widely accepted theory. And yet there is a well-documented tension between the two theories, to the extent that it is still not clear that the two can ever be reconciled. This thesis is concerned with furthering the current understanding of the relationship between quantum mechanics and special relativity. In the first part of the thesis we study the behaviour of quantum information in relativistic spacetime. The field of quantum information arose from the realisation that quantum information has a number of crucial properties that distinguish it from classical information, such as the no-cloning property, quantum contextuality, and quantum discord. More recently, it has been realised that placing quantum information under relativistic constraints leads to the emergence of further unique features which are not exhibited by either non-relativistic quantum information or relativistic classical information; as part of this ongoing research programme we develop a new relativistic quantum `paradox' which puts pressure on conventional views about the spatiotemporal persistence of quantum states over time. We then study a new set of relativistic quantum protocols which involve the distribution of entangled states over spacetime, defining one task involving the distribution of the two halves of a known entangled state, and another task involving the distribution of the two halves of an unknown entangled state. The second part of the thesis deals with relativistic quantum cryptography, a field which first began attracting serious attention when it was realised that a cryptographic task known as `bit commitment,' can be implemented with perfect security under relativistic constraints. This result was highly significant, since it is provably impossible to implement bit commitment with perfect security in a purely classical or purely quantum context, and hence bit commitment is an ideal starting point for probing the power of relativistic quantum cryptography. In this thesis we propose several new relativistic quantum bit commitment protocols which have notable advantages over previously known protocols. We then move to a related task, a generalization of zero-knowledge proving which we refer to as knowledge-concealing evidencing of knowledge of a quantum state; we prove no-go theorems concerning the possibility of implementing this task with perfect security, and then set out a relativistic protocol for the task which is asymptotically secure as the dimension of the state in question becomes large. These results have interesting foundational significance above and beyond their applications in the field of cryptography, providing a new perspective on the connections between knowledge, realism and quantum states.

O papel das eleições tem crescido de importância na sociedade moderna. Se, por um lado, é necessário garantir a universalização do voto, por outro lado é fundamental garantir a qualidade e a lisura do processo eleitoral. Neste sentido, muitos trabalhos têm sido apresentados com o objetivo de usar recursos computacionais no processo eleitoral. Computadores podem facilitar o acesso dos eleitores aos sistemas e processos de votação, como também aceleram a apuração dos resultados. Entretanto, redes de computadores são alvos de ataques sistemáticos. Esses ataques podem afetar a disponibilidade do processo e, além disso, interferir nos resultados da eleição ou afetar seus fundamentos. Garantir que os princípios exigidos para uma eleição segura sejam respeitados é a finalidade dos sistemas baseados em protocolos criptográficos. Muitas propostas de sistemas têm sido feitas. Algumas utilizam certo grau de obscuridade de funcionamento como garantia contra ataques; outras utilizam técnicas amplamente conhecidas, embora com grau elevado de complexidade. O presente trabalho apresenta a proposta de um sistema completo para execução de uma votação digital segura. O sistema é baseado em um protocolo simples, porém completo, que utiliza técnicas criptográficas amplamente conhecidas. O protocolo é descrito gradativamente, e é provada a sua eficiência contra os ataques possíveis. O texto ainda apresenta alguns outros protocolos criados para esse mesmo propósito. Finalmente, é apresentado o protótipo de um sistema de software que emprega o protocolo considerado. / The role of the elections has grown of importance in the modern society. If it is necessary to guarantee the universalization of the vote, on the other hand it is basic to guarantee the quality and the correctness of the electoral process. In this direction, many works have been presented with the objective to use computational resources in the electoral process. Computers can facilitate to the access of the voters to the voting systems and processes, as also they speed up the verification of the results. However, computer networks are target of systematic attacks. These attacks can affect the availability of the process and, moreover, intervene with the results of the election or affect its fundamentals. To guarantee that the principles demanded for a safe election are respected is the purpose of the systems based on cryptographic protocols. Many proposals of systems have been made. Some use certain degree of functional obscurity as warranty against attacks; others use widely known techniques, even so with high degree of complexity. The present work presents the proposal of a complete system for execution of a secure digital voting. The system is based on a simple protocol, however complete, that uses widely known cryptographic techniques. The protocol is gradually described, and its efficiency against the possible attacksis proven. The text still presents some other protocols created for this same purpose. Finally, the prototype of a software system that uses the considered protocol is presented .

Confusion and Diffusion are two properties of a secure cipher, identified by Claude Shannon. Confusion refers to making the relationship between the ciphertext and the symmetric key as complex and involved as possible. We try to achieve more confusion by creating a ciphertext of different length for a given plaintext when key is changed. As per our knowledge, all the existing symmetric encryption techniques will generate cipher text of same length for a given plaintext with different keys. The technique we are implementing here, will create ciphertext with different length for a given plaintext if we change the appropriate values in the key. This symmetric encryption technique will also possibly make the recovery of key very hard for the attacker.

O papel das eleições tem crescido de importância na sociedade moderna. Se, por um lado, é necessário garantir a universalização do voto, por outro lado é fundamental garantir a qualidade e a lisura do processo eleitoral. Neste sentido, muitos trabalhos têm sido apresentados com o objetivo de usar recursos computacionais no processo eleitoral. Computadores podem facilitar o acesso dos eleitores aos sistemas e processos de votação, como também aceleram a apuração dos resultados. Entretanto, redes de computadores são alvos de ataques sistemáticos. Esses ataques podem afetar a disponibilidade do processo e, além disso, interferir nos resultados da eleição ou afetar seus fundamentos. Garantir que os princípios exigidos para uma eleição segura sejam respeitados é a finalidade dos sistemas baseados em protocolos criptográficos. Muitas propostas de sistemas têm sido feitas. Algumas utilizam certo grau de obscuridade de funcionamento como garantia contra ataques; outras utilizam técnicas amplamente conhecidas, embora com grau elevado de complexidade. O presente trabalho apresenta a proposta de um sistema completo para execução de uma votação digital segura. O sistema é baseado em um protocolo simples, porém completo, que utiliza técnicas criptográficas amplamente conhecidas. O protocolo é descrito gradativamente, e é provada a sua eficiência contra os ataques possíveis. O texto ainda apresenta alguns outros protocolos criados para esse mesmo propósito. Finalmente, é apresentado o protótipo de um sistema de software que emprega o protocolo considerado. / The role of the elections has grown of importance in the modern society. If it is necessary to guarantee the universalization of the vote, on the other hand it is basic to guarantee the quality and the correctness of the electoral process. In this direction, many works have been presented with the objective to use computational resources in the electoral process. Computers can facilitate to the access of the voters to the voting systems and processes, as also they speed up the verification of the results. However, computer networks are target of systematic attacks. These attacks can affect the availability of the process and, moreover, intervene with the results of the election or affect its fundamentals. To guarantee that the principles demanded for a safe election are respected is the purpose of the systems based on cryptographic protocols. Many proposals of systems have been made. Some use certain degree of functional obscurity as warranty against attacks; others use widely known techniques, even so with high degree of complexity. The present work presents the proposal of a complete system for execution of a secure digital voting. The system is based on a simple protocol, however complete, that uses widely known cryptographic techniques. The protocol is gradually described, and its efficiency against the possible attacksis proven. The text still presents some other protocols created for this same purpose. Finally, the prototype of a software system that uses the considered protocol is presented .

This research explores the problem of finding a preimage — an input that, when passed through a particular function, will result in a pre-specified output — for the compression function of the SHA-1 cryptographic hash. This problem is much more difficult than the problem of finding a collision for a hash function, and preimage attacks for very few popular hash functions are known. The research begins by introducing the field and giving an overview of the existing work in the area. A thorough analysis of the compression function is made, resulting in alternative formulations for both parts of the function, and both statistical and theoretical tools to determine the difficulty of the SHA-1 preimage problem. Different representations (And- Inverter Graph, Binary Decision Diagram, Conjunctive Normal Form, Constraint Satisfaction form, and Disjunctive Normal Form) and associated tools to manipulate and/or analyse these representations are then applied and explored, and results are collected and interpreted. In conclusion, the SHA-1 preimage problem remains unsolved and insoluble for the foreseeable future. The primary issue is one of efficient representation; despite a promising theoretical difficulty, both the diffusion characteristics and the depth of the tree stand in the way of efficient search. Despite this, the research served to confirm and quantify the difficulty of the problem both theoretically, using Schaefer's Theorem, and practically, in the context of different representations.

Submitted by Cintia Kohori Rosseto (cintia.kohori@gmail.com) on 2018-02-25T11:37:49Z No. of bitstreams: 1 Criptografia como Recurso Didático.pdf: 16070844 bytes, checksum: f0c68145110bd6df9410e22393237634 (MD5) / Approved for entry into archive by Elza Mitiko Sato null (elzasato@ibilce.unesp.br) on 2018-02-26T18:08:51Z (GMT) No. of bitstreams: 1 rosseto_ck_me_sjrp.pdf: 16065351 bytes, checksum: db5887637166f7613e9af923836aa41d (MD5) / Made available in DSpace on 2018-02-26T18:08:51Z (GMT). No. of bitstreams: 1 rosseto_ck_me_sjrp.pdf: 16065351 bytes, checksum: db5887637166f7613e9af923836aa41d (MD5) Previous issue date: 2018-01-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / A criptografia tem como objetivo básico, transmitir uma mensagem a um destinatário sem que outra pessoa possa conhecer seu conteúdo, para que isso ocorra usa como ferramenta os recursos matemáticas. A preocupação com a privacidade e segurança é muito antiga, ao longo do tempo muitos códigos foram usados e utilizados principalmente para proteger segredos militares. Com o advento da comunicação eletrônica, muitas atividades essenciais passaram a depender do sigilo na troca de mensagens, principalmente aquelas que envolvem transações financeiras e uso seguro da internet. O presente trabalho trata a Criptografia como ferramenta de ensino nas aulas de Matemática, tendo em vista que o ensino da matemática está cada vez mais comprometido, principalmente por conta do desinteresse dos alunos e da grande defasagem com a qual chegam no Ensino Fundamental II. Diante disto, propomos a utilização de temas que tragam significado à aprendizagem e cativem o aluno. A criptografia pode ser abordada em vários conteúdos do Ensino Fundamental e Médio, como funções e matrizes, assuntos abordados no presente trabalho. Pretendemos, com a utilização da Criptografia no ensino dos conteúdos matemáticos, proporcionar sentido prático ao conteúdo estudado de forma que a aprendizagem se torne significativa para o aluno. Apresentaremos alguns modelos de atividades que abordam o tema criptografia e poderão ser aplicados no Ensino Fundamental e no Ensino Médio. / Encryption has the basic purpose of transmitting a message to a recipient without anyone else being able to know its contents, so that this occurs using the mathematical resources as a tool. The concern with privacy and security is very old, over time many codes have been used and used mainly to protect military secrets. With the advent of electronic communication, many essential activities depend on secrecy in the exchange of messages, especially those involving financial transactions and safe use of the internet. The present work treats Cryptography as a teaching tool in Mathematics classes, considering that the teaching of mathematics is increasingly compromised, mainly due to the lack of interest of the students and the large gap with which they arrive in Elementary School II. In view of this, we propose the use of themes that bring meaning to learning and captivate the student. The cryptography can be approached in several contents of Elementary and Middle School, like functions and matrices, subjects approached in the present work. We intend, with the use of Cryptography in the teaching of mathematical contents, to provide meaning practice to the content studied so that learning becomes meaningful for the student.We will present some models of activities that approach the subject of encryption and database is not Elementary and High School.

L'annonce de l'essor du chiffrement des données se heurte à celle de l'avènement du "big data". Il n'est maintenant plus suffisant d'envoyer et de recevoir des données, il faut pouvoir les analyser, les exploiter ou encore les partager à grande échelle. Or, les données à protéger sont de plus en plus nombreuses, notamment avec la prise de conscience de l'impact qu'ont les nouvelles technologies (smartphones, internet of things, cloud,...) sur la vie privée des utilisateurs. En rendant ces données inaccessibles, le chiffrement bloque a priori les fonctionnalités auxquelles les utilisateurs et les fournisseurs de service sont habitués. Pour rétablir ces fonctionnalités, il est nécessaire de savoir calculer des fonctions de données chiffrées, et cette thèse explore plusieurs pistes dans ce sens. Dans une première partie, nous nous intéressons au chiffrement totalement homomorphe qui permet de réaliser des calculs arbitraires sur les données chiffrées. Ce type de chiffrement est cependant particulièrement coûteux, notamment à cause de l'appel souvent nécessaire à une procédure très coûteuse : le réamorçage. Nous prouvons ici que minimiser le nombre de réamorçages est un problème NP-complet et donnons une méthode pratique pour approximer ce minimum. Dans une seconde partie, nous étudions des schémas dédiés à une fonctionnalité donnée. Le premier cas d'usage considéré est celui de la déduplication vérifiable de données chiffrées. Il s'agit pour un serveur de stockage externe d'être assuré qu'il ne conserve qu'un seul exemplaire de chaque fichier, même si ceux-ci sont chiffrés, ce qui lui permet d'optimiser l'usage de ses ressources mémoires. Ensuite, nous proposons un schéma de chiffrement cherchable permettant de détecter des intrusions dans un réseau de télécommunications chiffrés. En effet, le travail d'inspection du réseau par des moteurs d'analyse est actuellement entravé par la croissance du trafic chiffré. Les résultats obtenus permettent ainsi d'assurer la confidentialité des échanges tout en garantissant l'absence d'intrusions malveillantes dans le trafic / Nowadays, encryption and services issued of ``big data" are at odds. Indeed, encryption is about protecting users privacy, while big data is about analyzing users data. Being increasingly concerned about security, users tend to encrypt their sensitive data that are subject to be accessed by other parties, including service providers. This hinders the execution of services requiring some kind of computation on users data, which makes users under obligation to choose between these services or their private life. We address this challenge in this thesis by following two directions.In the first part of this thesis, we study fully homomorphic encryption that makes possible to perform arbitrary computation on encrypted data. However, this kind of encryption is still inefficient, and this is due in part to the frequent execution of a costly procedure throughout evaluation, namely the bootstrapping. Thus, efficiency is inversely proportional to the number of bootstrappings needed to evaluate functions on encrypted data. In this thesis, we prove that finding such a minimum is NP-complete. In addition, we design a new method that efficiently finds a good approximation of it. In the second part, we design schemes that allow a precise functionality. The first one is verifiable deduplication on encrypted data, which allows a server to be sure that it keeps only one copy of each file uploaded, even if the files are encrypted, resulting in an optimization of the storage resources. The second one is intrusion detection over encrypted traffic. Current encryption techniques blinds intrusion detection services, putting the final user at risks. Our results permit to reconcile users' right to privacy and their need of keeping their network clear of all intrusion

O papel das eleições tem crescido de importância na sociedade moderna. Se, por um lado, é necessário garantir a universalização do voto, por outro lado é fundamental garantir a qualidade e a lisura do processo eleitoral. Neste sentido, muitos trabalhos têm sido apresentados com o objetivo de usar recursos computacionais no processo eleitoral. Computadores podem facilitar o acesso dos eleitores aos sistemas e processos de votação, como também aceleram a apuração dos resultados. Entretanto, redes de computadores são alvos de ataques sistemáticos. Esses ataques podem afetar a disponibilidade do processo e, além disso, interferir nos resultados da eleição ou afetar seus fundamentos. Garantir que os princípios exigidos para uma eleição segura sejam respeitados é a finalidade dos sistemas baseados em protocolos criptográficos. Muitas propostas de sistemas têm sido feitas. Algumas utilizam certo grau de obscuridade de funcionamento como garantia contra ataques; outras utilizam técnicas amplamente conhecidas, embora com grau elevado de complexidade. O presente trabalho apresenta a proposta de um sistema completo para execução de uma votação digital segura. O sistema é baseado em um protocolo simples, porém completo, que utiliza técnicas criptográficas amplamente conhecidas. O protocolo é descrito gradativamente, e é provada a sua eficiência contra os ataques possíveis. O texto ainda apresenta alguns outros protocolos criados para esse mesmo propósito. Finalmente, é apresentado o protótipo de um sistema de software que emprega o protocolo considerado. / The role of the elections has grown of importance in the modern society. If it is necessary to guarantee the universalization of the vote, on the other hand it is basic to guarantee the quality and the correctness of the electoral process. In this direction, many works have been presented with the objective to use computational resources in the electoral process. Computers can facilitate to the access of the voters to the voting systems and processes, as also they speed up the verification of the results. However, computer networks are target of systematic attacks. These attacks can affect the availability of the process and, moreover, intervene with the results of the election or affect its fundamentals. To guarantee that the principles demanded for a safe election are respected is the purpose of the systems based on cryptographic protocols. Many proposals of systems have been made. Some use certain degree of functional obscurity as warranty against attacks; others use widely known techniques, even so with high degree of complexity. The present work presents the proposal of a complete system for execution of a secure digital voting. The system is based on a simple protocol, however complete, that uses widely known cryptographic techniques. The protocol is gradually described, and its efficiency against the possible attacksis proven. The text still presents some other protocols created for this same purpose. Finally, the prototype of a software system that uses the considered protocol is presented .