This thesis describes the theory behind elliptic-curve Diffie-Hellman key exchanges. All the way from the definition of a group until how the operator over an elliptic curve forms an abelian group. This is illustrated with clear examples. After that a smaller study is made to determine if there is a connection betweenthe size of the underlying field, the amount of points on the curve and the order of the points to determine how hard it is to find out the secret key in elliptic-curve Diffie-Hellman key exchanges. No clear connection is found. Since elliptic curves over extension fields have more computational heavy operations, it is concluded that these curves serve no practical use in elliptic-curve Diffie-Hellman key exchange. / Denna rapport går igenom teorin bakom Diffie-Hellmans nyckelutbyte över elliptiska kurvor. Från definitionen av en grupp hela vägen till hur operatorn över en elliptisk kurva utgör en abelsk grupp gås igenom och görs tydligt med konstruktiva exempel. Sedan görs en mindre undersökning av sambandet mellan storleken av den underliggande kroppen, antal punkter på kurvan och ordning av punkterna på kurvan, det vill säga svårigheten att hitta den hemliga nyckeln framtagen med Diffie-Hellmans nyckelutbyte för elliptiska kurvor. Ingen tydlig koppling hittas. Då elliptiska kurvor över utvidgade kroppar har mer beräkningstunga operationer dras slutsatsen att dessa kurvor inte är praktiska inom Diffie-Hellman nyckelutbyte över elliptiska kurvor.

Les réseaux de capteurs sans fil (RCSF) sont devenus un thème porteur aussi bien pour la recherche académique que pour les activités des services de R&D en raison de leur simplicité de déploiement et de leur potentiel applicatif dans des domaines très variés (militaire, environnemental, industriel). Un RCSF est composé d'un ensemble de noeuds devant être opérationnels et autonomes énergétiquement pour de longues périodes. De ce fait ils sont limités en capacité mémoire et de calcul, et contraint à exploiter une faible puissance de transmission, ce qui en limite leur portée et rend leur débit modeste. Le besoin de sécuriser les communications dans un RCSF dépend de la criticité des données échangées pour l'application supportée. La solution doit reposer sur des échanges sûrs, confidentiels et fiables. Pour assurer la sécurisation des échanges, des techniques de cryptographie existent dans la littérature. Conçues à l'origine pour des réseaux informatiques majoritairement câblés, elles se basent généralement sur des algorithmes complexes et gourmands en ressource. Dans le cadre de cette thèse, nous avons proposé, implémenté et évalué une architecture sécurisée et dynamique adaptée aux communications des RCSF. Elle permet de garantir et de maintenir la sécurité des communications durant toute la durée de vie d'un réseau multi-saut. Nous avons utilisé et adapté des algorithmes standards de cryptographie, tels que AES-CTR et la suite d'algorithmes basée sur ECC, qui permettent à notre architecture de résister à la majorité d'attaques. Nous avons quantifié le surcoût en temps de calcul et en occupation mémoire de notre solution. Les résultats d’implémentation de notre proposition sont issus de mesures réelles faites sur une maquette réalisée à partir de cartes TelosB. / Wireless sensor networks (WSNs) have become an attractive topic for both academic research and the activity of R&D services due to their simple deployment and their potential of application in varied fields (military, environmental, industrial). A WSN is composed of a set of nodes that are supposed to operate and to be energetically autonomous for long durations. Thus, they are limited in memory and computing capacities, and constrained to function in a low-power transmission mode which limit their communication range and leave them with low data rates.The need to secure communications in a WSN depends on the criticality of the exchanged data for the supported application. The solution must be based on safe, confidential and reliable exchanges. To ensure the security of exchanges, cryptographic techniques exist in the literature. Originally designed for mostly wired computer networks, they are usually based on complex and resource-consuming algorithms. In this thesis, we have proposed, implemented and evaluated a secure and dynamic architecture suitable for WSNs communications. It ensures and maintains secured communications throughout the lifetime of a multi-hop network. We have used and adapted standard cryptographic algorithms, such as AES-CTR and algorithms based on ECC cipher suites, which allow our architecture to resist against most attacks. We have quantified the overhead of our solution in terms of computation time and memory occupancy. The results of implementation of our proposal are obtained through real measurements on testbeds using TelosB motes.

Elliptic curve cryptography (ECC) has played a significant role on secure devices since it was introduced by Koblitz and Miller more than three decades ago. The great demand for ECC is created by its shorter key length while it provides an equivalent security level in comparison to previously introduced public-key cryptosystems (e.g.RSA). From an implementation point of view a shorter key length means a higher processing speed, smaller power consumption, and silicon area requirement. Scalar multiplication is the main operation in Elliptic Curve Diffie-Hellman (ECDH), which is a key-agreement protocol using ECC. As shown in the prior literature, this operation is both vulnerable to Power Analysis attack and requires a large amount of time. Therefore, a lot of research has focused on enhancing the performance and security of scalar multiplication. In this work, we describe three schemes to counter power analysis cryptographic attacks. The first scheme provides improved security at the expense of a very small cost of additional hardware overhead; its basic idea is to randomize independent field operations in order to have multiple power consumption traces for each point operation. In the second scheme, we introduce an atomic block that consists of addition, multiplication and addition [A-M-A]. This technique provides a very good scalar multiplication protection but with increased computation cost. The third scheme provides both security and speed by adopting the second tech- nique and enhancing the instruction-level parallelism at the atomic level. As a result, the last scheme also provides a reduction in computing time. With these schemes the users can optimize the trade-off between speed, cost, and security level according to their needs and resources. / Graduate / 0544 / 0984 / z.mohaimeed@gmail.com

No description available.

Les réseaux de capteurs sans fil (RCSF) sont devenus un thème porteur aussi bien pour la recherche académique que pour les activités des services de R&D en raison de leur simplicité de déploiement et de leur potentiel applicatif dans des domaines très variés (militaire, environnemental, industriel). Un RCSF est composé d'un ensemble de noeuds devant être opérationnels et autonomes énergétiquement pour de longues périodes. De ce fait ils sont limités en capacité mémoire et de calcul, et contraint à exploiter une faible puissance de transmission, ce qui en limite leur portée et rend leur débit modeste. Le besoin de sécuriser les communications dans un RCSF dépend de la criticité des données échangées pour l'application supportée. La solution doit reposer sur des échanges sûrs, confidentiels et fiables. Pour assurer la sécurisation des échanges, des techniques de cryptographie existent dans la littérature. Conçues à l'origine pour des réseaux informatiques majoritairement câblés, elles se basent généralement sur des algorithmes complexes et gourmands en ressource. Dans le cadre de cette thèse, nous avons proposé, implémenté et évalué une architecture sécurisée et dynamique adaptée aux communications des RCSF. Elle permet de garantir et de maintenir la sécurité des communications durant toute la durée de vie d'un réseau multi-saut. Nous avons utilisé et adapté des algorithmes standards de cryptographie, tels que AES-CTR et la suite d'algorithmes basée sur ECC, qui permettent à notre architecture de résister à la majorité d'attaques. Nous avons quantifié le surcoût en temps de calcul et en occupation mémoire de notre solution. Les résultats d'implémentation de notre proposition sont issus de mesures réelles faites sur une maquette réalisée à partir de cartes TelosB.

Data security will play a central role in the design of future IT systems. The PC has been a major driver of the digital economy. Recently, there has been a shift towards IT applications realized as embedded systems, because they have proved to be good solutions for many applications, especially those which require data processing in real time. Examples include security for wireless phones, wireless computing, pay-TV, and copy protection schemes for audio/video consumer products and digital cinemas. Most of these embedded applications will be wireless, which makes the communication channel vulnerable. The implementation of cryptographic systems presents several requirements and challenges. For example, the performance of algorithms is often crucial, and guaranteeing security is a formidable challenge. One needs encryption algorithms to run at the transmission rates of the communication links at speeds that are achieved through custom hardware devices. Public-key cryptosystems such as RSA, DSA and DSS have traditionally been used to accomplish secure communication via insecure channels. Elliptic curves are the basis for a relatively new class of public-key schemes. It is predicted that elliptic curve cryptosystems (ECCs) will replace many existing schemes in the near future. The main reason for the attractiveness of ECC is the fact that significantly smaller parameters can be used in ECC than in other competitive system, but with equivalent levels of security. The benefits of having smaller key size include faster computations, and reduction in processing power, storage space and bandwidth. This makes ECC ideal for constrained environments where resources such as power, processing time and memory are limited. The implementation of ECC requires several choices, such as the type of the underlying finite field, algorithms for implementing the finite field arithmetic, the type of the elliptic curve, algorithms for implementing the elliptic curve group operation, and elliptic curve protocols. Many of these selections may have a major impact on overall performance. In this dissertation a finite field from a special class called the Optimal Extension Field (OEF) is chosen as the underlying finite field of implementing ECC. OEFs utilize the fast integer arithmetic available on modern microcontrollers to produce very efficient results without resorting to multiprecision operations or arithmetic using polynomials of large degree. This dissertation discusses the theoretical and implementation issues associated with the development of this finite field in a low end embedded system. It also presents various improvement techniques for OEF arithmetic. The main objectives of this dissertation are to --Implement the functions required to perform the finite field arithmetic operations. -- Implement the functions required to generate an elliptic curve and to embed data on that elliptic curve. -- Implement the functions required to perform the elliptic curve group operation. All of these functions constitute a library that could be used to implement any elliptic curve cryptosystem. In this dissertation this library is implemented in an 8-bit AVR Atmel microcontroller. / Dissertation (MEng (Computer Engineering))--University of Pretoria, 2006. / Electrical, Electronic and Computer Engineering / unrestricted