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<p><font face="CMR12"> <p align="left">Cryptology is the study of systems that typically originate from a consideration of the ideal circumstances under which secure information exchange is to take place. It involves the study of cryptographic and other processes that might be introduced for breaking the output of such systems - cryptanalysis. This includes the introduction of formal mathematical methods for the design of a cryptosystem and for estimating its theoretical level of security</p> </font></p>

<p><font face="CMR12"> <p align="left">Cryptology is the study of systems that typically originate from a consideration of the ideal circumstances under which secure information exchange is to take place. It involves the study of cryptographic and other processes that might be introduced for breaking the output of such systems - cryptanalysis. This includes the introduction of formal mathematical methods for the design of a cryptosystem and for estimating its theoretical level of security</p> </font></p>

Philosophiae Doctor - PhD / Cryptology is the study of systems that typically originate from a consideration of the ideal circumstances under which secure information exchange is to take place. It involves the study of cryptographic and other processes that might be introduced for breaking the output of such systems - cryptanalysis. This includes the introduction of formal mathematical methods for the design of a cryptosystem and for estimating its theoretical level of security

<p>This study in an extension of a Master's study, entitled Realistic Mathematics Education and the strategies grade 8 learners develop for the solution of two simultaneous linear equations. the current study investigates how new content could be introduced into a school mathematical curriculum. The new topic under discussion for this study is the topis of Cryptology. Two research cycles were carried out. For the first design research cycle there were three teaching experiments with teachers, grade 10 learners and students as participants. Seven activities weere developed from the second design research cycle which was worked through with gade 10 learners. All sessions for the second design research cycle were video taped. Important to the development of instrutional materials was the development of a hypothetical learning trajetory about the learning and teaching of each activity. the results of the study indicated that the way learners understood the content and the different ways in which they presented solutions augers well for the introduction of a specific new content strand, cryptology, into a new school mathematical curriculum. It is also important for developers of instructional material to have a strong mathematical content knowledge for the design of instructional materials</p>

<p>This study in an extension of a Master's study, entitled Realistic Mathematics Education and the strategies grade 8 learners develop for the solution of two simultaneous linear equations. the current study investigates how new content could be introduced into a school mathematical curriculum. The new topic under discussion for this study is the topis of Cryptology. Two research cycles were carried out. For the first design research cycle there were three teaching experiments with teachers, grade 10 learners and students as participants. Seven activities weere developed from the second design research cycle which was worked through with gade 10 learners. All sessions for the second design research cycle were video taped. Important to the development of instrutional materials was the development of a hypothetical learning trajetory about the learning and teaching of each activity. the results of the study indicated that the way learners understood the content and the different ways in which they presented solutions augers well for the introduction of a specific new content strand, cryptology, into a new school mathematical curriculum. It is also important for developers of instructional material to have a strong mathematical content knowledge for the design of instructional materials</p>

Philosophiae Doctor - PhD / This study in an extension of a Master's study, entitled Realistic Mathematics Education and the strategies grade 8 learners develop for the solution of two simultaneous linear equations. the current study investigates how new content could be introduced into a school mathematical curriculum. The new topic under discussion for this study is the topis of Cryptology. Two research cycles were carried out. For the first design research cycle there were three teaching experiments with teachers, grade 10 learners and students as participants. Seven activities weere developed from the second design research cycle which was worked through with gade 10 learners. All sessions for the second design research cycle were video taped. Important to the development of instrutional materials was the development of a hypothetical learning trajetory about the learning and teaching of each activity. the results of the study indicated that the way learners understood the content and the different ways in which they presented solutions augers well for the introduction of a specific new content strand, cryptology, into a new school mathematical curriculum. It is also important for developers of instructional material to have a strong mathematical content knowledge for the design of instructional materials / South Africa

Biological cryptology, a new branch of cryptology combines computer science and chemistry together. It uses biological molecules, such as DNA, RNA, PNA or proteins, or it is inspired by biological principles happening in living cells. Biological cryptology is still in the development stage, so the goal of my Master thesis is to describe existing biological cryptologic methods and to draw interest in this new field. Thus the first chapter states advantages of biological cryptology. Then three big chapters follow afterwards, describing chemical background, DNA computing and the most importantly a field of DNA cryptology. In the last chapter I summarized drawbacks which turned up while I was studying those methods and which need to be handled before biological cryptology moves from labs into our normal lives.

Herein I cover the basics of cryptology and the mathematical techniques used in the field. Aside from an overview of cryptology the text provides an in-depth look at block cipher algorithms and the techniques of cryptanalysis applied to block ciphers. The text also includes details of knapsack cryptosystems and pseudo-random number generators.

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). / 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).