While 5G energy harvesting makes 5G smart dust possible, stretching computation across power cycles affects cryptographic algorithms. This effect may lead to new security issues that make the system vulnerable to adversary attacks. Therefore, security measures are needed to protect data at rest and in transit across the network. In this paper, we identify the security requirements of existing 5G networks and the best-of-breed cryptographic algorithms for ultra-low SWaP devices in an energy harvesting context. To do this, we quantify the performance vs. energy tradespace, investigate the device features that impact the tradespace the most, and assess the security impact when the attacker has access to intermediate results. Our open-source energy-harvesting-tolerant versions of the cryptographic algorithms provide algorithm and device recommendations and ultra-low SWaP energy-harvesting-device-optimized versions of the cryptographic algorithms. / Master of Science / Smart dust is a network of tiny and energy-efficient devices that can gather data from the environment using various sensors, such as temperature, pressure, and humidity sensors. These devices are extremely small, often as small as a grain of sand or smaller, and have numerous applications, including environmental monitoring, structural health monitoring, and military surveillance. One of the main challenges of smart dust is its small size and limited energy resources, making it challenging to power and process the collected data. However, advancements in energy harvesting and low-power computing are being developed to overcome these challenges. In the case of 5G, energy harvesting technologies can be used to power small sensors and devices that are part of the 5G network, such as the Internet of Things (IoT) devices. Examples of IoT devices are wearable fitness trackers, smart thermostats, security cameras, home automation systems, and industrial sensors. Since 5G energy harvesting impacts the daily lives of people using the relevant devices, our research seeks to find out what kind of measures are necessary to guarantee their security.

Denna bok riktar sig till gymnasieelever som vill fördjupa sig i ämnet RSA-kryptografi . RSA-kryptografi är en avancerad metod för att kommunicera med hemliga meddelanden och används flitigt inom t.ex. bankvärlden. När du handlar med ditt kort eller använder din e-legitimation används RSA-kryptogra fi för att allt du gör ska vara skyddat och säkert. Vid stora transaktioner mellan olika banker används också RSA-kryptogra fi för att både den som betalar och den som får betalt ska vara säkra att allt går rätt till.Boken är uppdelad i fyra kapitel. Kapitel 3 och 4 är betydligt mer avancerade än kapitel 1 och 2. Kapitel 1 består mestadels av exempel och övningar som behandlar matematiken som krävs för att kunna utföra RSA-kryptogra fi med små tal. Kapitel 2 använder matematiken i kapitel 1 för att genom exempel och övingar metodiskt lära ut hur RSA-kryptogra fi med små tal går till. Kapitel 3 visar matematiken som ligger till grund för att RSA-kryptografi fungerar. Detta visas med hjälp av exempel, satser, förtydligade bevis samt några enstaka övningar. Kapitel 4 förklarar varför RSA-kryptografi är säkert och enkelt att använda. Primtalstester utgör det viktigaste ämnet i detta sista kapitel.

Cette thèse analyse les tensions vécues et les négociations menées, au quotidien, par des jeunes diplômés, en prenant en compte leurs parcours de formation et le recours au RSA. Partant d’entretiens et de récits, la recherche porte sur les processus socio-biographiques, avec leurs nombreuses transformations identitaires et relationnelles. Une typologie des modes de vie a d’abord été construite pour décrire les multiples usages du RSA pratiqués au quotidien. Une analyse des parcours dans le dispositif a permis ensuite de saisir les manières dont ces jeunes renégociaient les usages du RSA avec leur entourage proche et avec les professionnels chargés de l'accompagnement des allocataires. Enfin cette thèse montre que le recours au RSA représente une expérience sociale marquante pour des jeunes diplômés, sortis de l'enseignement supérieur et confrontés à la précarité professionnelle, notamment dans la manière dont ils vivent leurs transitions sociales vers la vie adulte. / This thesis analyzes the lived tensions and negotiations conducted on a daily basis by young graduates, taking into account their training program and the use of RSA. Starting with interviews and stories, research focuses on socio-biographical process, with their many identities and relational transformations. A typology of lifestyles was first constructed to describe the multiple uses of RSA practiced daily. An analysis of the course in the device was then used to grasp the ways in which these young renegotiating uses RSA with their entourage and the professionals responsible for the accompaniment of the beneficiaries. Finally, this thesis shows that the use of RSA represents a significant social experience for young graduates, out of higher education and faced with job insecurity, particularly in the way they live their social transitions to adulthood.

Esta pesquisa foi realizada com a intenção de motivar o estudo da criptografia, mostrando que a matemática e a comunicação estão presentes em diversos momentos, tanto no passado quanto no presente. Este trabalho mostra a origem da criptoanálise e toda a sua evolução dando ênfase nos mecanismos de codificação e decodificação através de exemplos práticos. Além disso, alguns métodos criptográficos são destacados como a cifra de substituição monoalfabética, a cifra de Vigenère, a criptografia RSA que é o método mais conhecido de criptografia de chave pública, as cifras de Hill, o método das transformações lineares e o método de Rabin, devido a sua grande importância para a evolução de sistemas computacionais e assinaturas digitais entre outros. Por fim, mostra-se a importância e a necessidade dos recursos criptográficos nos dias de hoje, na tentativa de impedir que hackers e pessoas que fazem mau uso do conhecimento matemático possam causar danos a sociedade, seja por uma simples mensagem ou até mesmo através de situações mais imprudentes como as transações bancárias indevidas / This research was conducted with the intention of motivating the study of cryptography, showing that mathematics and the communication are present at various times, both past and present. This work shows the origin of cryptanalysis and all its evolution giving emphasis on coding and decoding mechanisms through practical examples. In addition, some methods cryptographic are highlighted as the monoalphabetic substitution cipher, the Vigenere cipher, RSA encryption that is the best known method of public key cryptography , ciphers Hill, the method of linear transformations and the Rabin method, due to its great importance for the evolution of computer systems and signatures digital among others. Finally, we show the importance and the need for cryptographic resources these days, in an attempt to prevent hackers and people who make bad use of mathematical knowledge can cause damage to society, whether by a simple message or through more situations reckless as improper banking transactions

Esta pesquisa foi realizada com a intenção de motivar o estudo da criptografia, mostrando que a matemática e a comunicação estão presentes em diversos momentos, tanto no passado quanto no presente. Este trabalho mostra a origem da criptoanálise e toda a sua evolução dando ênfase nos mecanismos de codificação e decodificação através de exemplos práticos. Além disso, alguns métodos criptográficos são destacados como a cifra de substituição monoalfabética, a cifra de Vigenère, a criptografia RSA que é o método mais conhecido de criptografia de chave pública, as cifras de Hill, o método das transformações lineares e o método de Rabin, devido a sua grande importância para a evolução de sistemas computacionais e assinaturas digitais entre outros. Por fim, mostra-se a importância e a necessidade dos recursos criptográficos nos dias de hoje, na tentativa de impedir que hackers e pessoas que fazem mau uso do conhecimento matemático possam causar danos a sociedade, seja por uma simples mensagem ou até mesmo através de situações mais imprudentes como as transações bancárias indevidas / This research was conducted with the intention of motivating the study of cryptography, showing that mathematics and the communication are present at various times, both past and present. This work shows the origin of cryptanalysis and all its evolution giving emphasis on coding and decoding mechanisms through practical examples. In addition, some methods cryptographic are highlighted as the monoalphabetic substitution cipher, the Vigenere cipher, RSA encryption that is the best known method of public key cryptography , ciphers Hill, the method of linear transformations and the Rabin method, due to its great importance for the evolution of computer systems and signatures digital among others. Finally, we show the importance and the need for cryptographic resources these days, in an attempt to prevent hackers and people who make bad use of mathematical knowledge can cause damage to society, whether by a simple message or through more situations reckless as improper banking transactions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Given the evolution of the data communication field, and the resulting increase of the information flow in data, networks security became a major concern. Modern cryptographic methods are mathematically reliable. However their implementation in hardware leaks confidential information through side-channels like power consumption and electromagnetic emissions. Although performance issues are crucial for a hardware design, aspects of robustness against attacks based on side-channel informations have gained much attention in recent years. This work focuses on hardware architectures based on the RSA public-key algorithm, originally proposed in 1977 by Rivest, Shamir and Adleman. This algorithm has the modular exponentiation as its main operation and it is performed through successive modular multiplications. Because the RSA involves integers of 1024 bits or more, the inherent division of modular multiplications became the main concern. The Montgomery algorithm, proposed in 1985, is a largely used method for hardware designs of modular multiplications, because it avoids divisions and all operations are performed in a multiple-precision context with all terms represented in a numerical base, generally, a power of two. This dissertation proposes a systolic architecture able to perform the Montgomery modular multiplication with multiple-precision arithmetic. Following, an improvement to the systolic architecture is presented, through an architecture that computes the Montgomery multiplication by multiplexing the multi-precision arithmetic processes. The multiplexed architecture is employed in the left-to-right square-and-multiply and square-and-multiply always modular exponentiation methods and is subjected to SPA (Simple Power Analysis) and SEMA (Simple Electromagnetic Analysis) side-channel attacks and robustness aspects are analysed. Different word sizes (numerical bases) are applied as well as different input operands. As an improvement to SPA and SEMA attacks, the power consumption and electromagnetic traces are demodulated in amplitude to eliminate the clock harmonics influence in the acquired traces. Finally, interpretations, conclusions and countermeasure propositions to the multiplexed architecture against the implemented side-channel attacks are presented. / Com a expansão da área de comunicação de dados e o consequente aumento do fluxo de informações, a segurança tem se tornado uma grande preocupação. Apesar dos métodos criptográficos modernos serem matematicamente seguros, sua implementação em hardware tende a apresentar fugas de informações confidenciais por canais laterais, tais como consumo de potência e emissões eletromagnéticas. Embora questões de desempenho sejam cruciais para um projeto de hardware, aspectos de robustez contra ataques baseados em fugas de informações por canais laterais tem ganhado maior atenção nos últimos anos. Neste trabalho, explora-se arquiteturas em hardware voltadas para o algoritmo de chave pública RSA, originalmente proposto em 1977 por Rivest, Shamir e Adleman. Este algoritmo possui como principal operação a exponenciação modular, e esta é calculada através de sucessivas multiplicações modulares. Sendo que o RSA envolve números inteiros da ordem de 1024 bits ou mais, a operação de divisão inerente em multiplicações modulares torna-se o principal problema. O algoritmo de Montgomery, proposto em 1985, é um método bastante utilizado na implementação da multiplicação modular em hardware, pois além de evitar divisões, trabalha em um contexto de precisão múltipla com termos representados por bases numéricas, geralmente, potências de dois. Dentro deste contexto, propõe-se inicialmente uma arquitetura sistólica, baseada nas propriedades de aritmética de precisão múltipla do Algoritmo de Montgomery. Em seguida, apresenta-se uma melhoria para a arquitetura sistólica, através de uma arquitetura que realiza a multiplicação modular de Montgomery voltada à multiplexação dos processos aritméticos. A arquitetura multiplexada é empregada nos métodos de exponenciação modular left-to-right square-and-multiply e square-and-multiply always e é submetida a ataques por canais laterais SPA (Simple Power Analysis) e SEMA (Simple Electromagnetic Analysis) e aspectos de robustez da arquitetura multiplexada são analisados para diversos tamanhos de palavras (base numérica do algoritmo de Montgomery). Como proposta de melhoria aos ataques por canais laterais simples, os traços de consumo de potência e emissão eletromagnética são demodulados em amplitude de modo a eliminar a influência das harmônicas do sinal de clock sobre os traços coletados. Por fim, interpretações e conclusões dos resultados são apresentados, assim como propostas de contra-medidas para a arquitetura multiplexada com relação aos ataques por canais laterais realizados.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The expansion of the data communication, due to the large ow of information that pass through these systems has meant that the security becomes an item of constant concern. Even when considering the efficient encryption systems that exists today, which present relevant mathematical protection, some implementations in hardware of these systems will favor the leak of confidential information through side channels attacks, such as power consumption and electromagnetic radiation. Performance issues have fundamental importance in the design of a physical system, however aspects which make the system robust against side channel attacks has gotten more attention nowadays.This work focuses on hardware architectures based on the RSA public key algorithm, proposed by Rivest, Shamir and Adleman in 1977, which presents the modular exponentiation operation, calculated from several modular multiplications, as main operation. The RSA algorithm involves integers in order of 1024 or 2048 bits, so the division inherent in modular multiplications can become a major problem. In order to avoid these divisions, the Montgomery algorithm, proposed in 1985, appears as an efficient alternative. On this context, this dissertation presents a multiplexed architecture based on the properties of the Montgomery's algorithm. Forwarding, an improvement to this architecture is presented, implemented with the randomization of internal memories accesses, in order to increase system robustness against specialized side-channel attacks. Thus, the implemented architecture is exposed to side channels SPA (Simple Power Analysis) and SEMA (Simple Electromagnetig Analysis) and the aspects of security and robustness of the implemented system are evaluated and presented. / A constante expansão dos sistemas de comunicação de dados devido ao grande fluxo de informações que trafegam por estes sistemas tem feito com que a segurança se torne um item de constante preocupação. Mesmo ao considerar-se os eficientes sistemas de criptografia atuais, os quais apresentam relevante proteção matemática, a implementação em hardware destes sistemas tende a propiciar a fuga de informações confidenciais através de ataques por canais laterais, como consumo de potência e emissão eletromagnética. Mesmo sabendo-se que questões de desempenho tem fundamental importância no projeto de um sistema físico, aspectos que tornem o sistema robusto frente a ataques por canais laterais tem obtido maior atenção nos últimos anos. Neste trabalho apresentam-se arquiteturas implementadas em hardware para o cálculo do algoritmo de chave pública RSA, proposto por Rivest, Shamir e Adleman em 1977, o qual tem como principal operarção a exponenciação modular, calculada a partir de várias multiplicações modulares. Sabendo-se que o algoritmo RSA envolve números inteiros da ordem de 1024 ou 2048 bits, a divisão inerente em multiplicações modulares pode tornar-se o grande problema. A fim de que se evite estas divisões, o algoritmo de Montgomery, proposto em 1985, aparece como uma boa alternativa por também trabalhar em um contexto de precisão múltipla e com números na base numérica de potência de dois. Neste contexto apresenta-se inicialmente uma arquitetura multiplexada, baseada nas propriedades de execução do algoritmo de Montgomery. A seguir apresenta-se uma melhoria a esta arquitetura com a implementação da randomização dos acessos as memórias internas, com o objetivo de aumentar a robustez do sistema frente a ataques por canais laterais especializados. Sendo assim, a arquitetura implementada é submetida a ataques por canais laterais SPA (Simple Power Analysis) e SEMA (Simple Electromagnetig Analysis) e os aspectos de segurança e robustez do sistema implementado são analisados e apresentados.

This paper follows up the factorization of integers. Factorization is the most popular and used method for RSA cryptoanalysis. The SIQS was chosen as a factorization method that will be used in this paper. Although SIQS is the fastest method (up to 100 digits), it can't be effectively computed at polynomial time, so it's needed to look up for options, how to speed up the method as much as possible. One of the possible ways is paralelization. In this case OpenMP was used. Other possible way is optimalization. The goal of this paper is also to show, how easily is possible to use paralelizion and thanks to detailed analyzation the source codes one can reach relatively large speed up. Used method of iterative optimalization showed itself as a very effective tool. Using this method the implementation of SIQS achieved almost 100 multiplied speed up and at some parts of the code even more.

The rise of the Internet of Things (IoT) and autonomous robots/vehicles comes with a lot of embedded electronic systems. Small printed circuit boards with microcomputers will be embedded almost everywhere. Therefore, the security and data protection of those systems will be a significant challenge to take into consideration for the future development of IoT devices. Cryptographic algorithms can be used to provide confidentiality and integrity for data transmitted between those embedded devices. It is important to know what kind of algorithm is the most suitable for the specified task and the selected embedded device.  In this thesis, several commonly used cryptographic algorithms are evaluated and an EPS32 based IoT device is chosen as the evaluation platform. ESP32 is a series of low cost and low power System-on-Chip microcontrollers with integrated Wi-Fi and dual-mode Bluetooth. Additionally, ESP32 has the hardware acceleration feature for commonly used cryptographic algorithms. The goal of this thesis is to evaluate the performances of different cryptographic algorithms on the ESP32 with and without using the hardware acceleration feature. The execution times of different cryptographic algorithms processing data with varying sizes are collected, and the performance of each cryptographic algorithm is then evaluated.  A data logging scenario is evaluated as a case study where the ESP32 periodically sends data to a remote database. Under different configurations of the ESP32, the transmission time of encrypted and non-encrypted communications via Hypertext Transfer Protocol Secure (HTTPS) and Hypertext Transfer Protocol (HTTP) will be compared.  The results can be used to simplify the calculation of performance/protection trade-offs for specific algorithms. It also shows that the built-in hardware acceleration has a significant impact on increasing those algorithms’ performances. For Advanced Encryption Standard (AES), the throughput for encryption increased by 257.8%, and for decryption 222.7%. For Secure Hash Algorithm (SHA-2), the throughput increased by 165.2%. For Rivest-Shamir-Adleman (RSA), the encryption throughput has a decrease of 40.7%, and decryption has an increase of 184%. Furthermore, the results can also aid the design and development of a secure IoT system incorporating devices built with ESP32. / Uppkomsten av Internet of Things (IoT) och autonoma robotar / fordon kommer med många inbyggda elektroniska system. Små kretskort med mikrodatorer kommer att vara inbäddade nästan överallt. Därför kommer säkerheten och dataskyddet för dessa system att vara en betydande utmaning att ta hänsyn till för den framtida utvecklingen av IoT-enheter. Kryptografiska algoritmer kan användas för att ge sekretess och integritet för data som överförs mellan de inbäddade enheterna. Det är viktigt att veta vilken typ av algoritm som är bäst lämpad för den angivna uppgiften och den valda inbäddade enheten.  I denna avhandling utvärderas flera vanliga kryptografiska algoritmer och en EPS32-baserad IoT-enhet väljs som utvärderingsplattform. ESP32 är en serie av låga och lågeffektiva system-on-chip-mikrokontroller med integrerat Wi-Fi och dual-mode Bluetooth. Dessutom har ESP32 hårdvaruaccelereringsfunktionen för vanliga kryptografiska algoritmer. Målet med denna avhandling är att utvärdera prestanda för olika kryptografiska algoritmer på ESP32 med och utan att använda hårdvaruaccelereringsfunktionen. Exekveringstiderna för olika kryptografiska algoritmer som behandlar data med olika storlekar samlas in och prestanda för varje kryptografisk algoritm utvärderas sedan.  Ett dataloggningsscenario utvärderas som en fallstudie där ESP32 regelbundet skickar data till en fjärrdatabas. Under olika konfigurationer av ESP32 jämförs överföringstiden för krypterad och icke-krypterad kommunikation via Hypertext Transfer Protocol Secure (HTTPS) och Hypertext Transfer Protocol (HTTP).  Resultaten kan användas för att förenkla beräkningen av prestanda / skydda avvägningar för specifika algoritmer. Det visar också att den inbyggda hårdvaruaccelerationen har en betydande inverkan på att öka dessa algoritmers prestanda. För Advanced Encryption Standard (AES) ökade genomströmningen för kryptering med 257,8% och för dekryptering 222,7%. För Secure Hash Algorithm (SHA-2) ökade kapaciteten med 165,2%. För Rivest-Shamir-Adleman (RSA) har krypteringsflödet minskat med 40,7% och dekryptering har ökat med 184%. Dessutom kan resultaten också hjälpa till att utforma och utveckla ett säkert IoT-system som innehåller enheter byggda med ESP32.

Cryptography fascinates people of all generations and is increasingly presented as an example for the relevance and application of the mathematical sciences. Indeed, many principles of modern cryptography can be described at a secondary school level. In this context, the mathematical background is often only sparingly shown. In the worst case, giving mathematics this character of a tool reduces the application of mathematical insights to the message ”cryptography contains math”. This paper examines the question as to what else cryptography can offer to mathematics education. Using the RSA cryptosystem and related content, specific mathematical competencies are highlighted that complement standard teaching, can be taught with cryptography as an example, and extend and deepen key mathematical concepts.