Most of the cryptosystems currently used are based on number theoretic problems. We focus on cryptosystems based on finite automata (FA) which are lightweight in nature and have relatively small key sizes. The security of these systems relies on the difficulties in inverting non-linear finite automata and factoring matrix polynomials. In symmetric or single key encryption, the secret key consists of two finite automata and their inverses. By applying the inverses of the automata to the cipher text, the plain text can be effectively calculated. In case of asymmetric or public key encryption, the public key consists of another automaton, which is the combination of the two finite automata while the private key consists of the inverse of the two individual automata. It is hard to invert the combined automaton without the knowledge of the private key automata. We propose a third variant which is based on a 128-bit key and uses a DES-based key generation algorithm. We implement and test all three cryptosystems - the standard single key and public key cryptosystems as well as our novel DES-based FA cryptosystem. We also extensively test the finite automata cryptosystems on a standard desktop machine as well as the Nokia N900 smartphone. All statistical tests carried out on the ciphertext are satisfactory. / Graduate

La sécurité de l'information repose étroitement sur les circuits intégrés (CI). Malheureusement, les CIs sont soumis à de nombreuses menaces telles que les attaques par canaux auxiliaires ou par injection de fautes. Ce travail se concentre sur les petites vulnérabilités et les contremesures liées à l’algorithme ECDSA. La motivation est qu’une source de vulnérabilité peut être utilisée dans différent scénario d’attaque. En corrigeant la vulnérabilité, les attaques existantes sont évitées mais également les attaques non découvertes ou non publiées utilisant la vulnérabilité en question. De plus, bien que le scalaire sur courbe elliptique soit au cœur de la sécurité de tous les schémas cryptographiques à base de courbe elliptique, l’ensemble du système a besoin d’être sécurisé. Une vulnérabilité concernant simplement quelques bits de secret peut suffire à récupérer la clef privée et donc doit être évité.L’ECDSA peut être implémenté de différentes façons, en logiciel ou via du matériel dédié ou un mix des deux. De nombreuses architectures différentes sont donc possibles pour implémenter un système à base d’ECDSA. Pour cette raison, ces travaux se concentrent principalement sur les contremesures algorithmiques. / Information security heavily relies on integrated circuits (ICs). Unfortunately, ICs face a lot of threats such as side channel or fault attacks. This work focuses on small vulnerabilities and countermeasures for the Elliptic Curve Digital Signature Algorithm (ECDSA). The motivation is that leakage sources may be used in different attack scenarios. By fixing the leakage, existing attacks are prevented but also undiscovered or non-disclosed attacks based on the leakage. Moreover, while the elliptic curve scalar algorithm is at the heart of the security of all elliptic curve related cryptographic schemes, all the ECDSA system needs security. A small leakage of few secret bits may conduct to fully disclose the private key and thus should be avoided.The ECDSA can be implemented in different flavors such as in a software that runs on a microcontroller or as a hardware self-contained block or also as a mix between software and hardware accelerator. Thus, a wide range of architectures is possible to implement an ECDSA system. For this reason, this work mainly focuses on algorithmic countermeasures as they allow being compliant with different kinds of implementations.

Iris recognition constitutes one of the most powerful method for the iden- tification and authentication of people today. This thesis aims to describe the algorithms used in a sophisticated and mathematically correct way, while re- maining comprehensible. The description of these algorithms is not the only objective of this thesis; the reason they were chosen and potential improvements or substitutions are also discussed. The background of iris recognition, its use in cryptosystems, and the application of error-correcting codes are investigated as well.

Iris recognition constitutes one of the most powerful method for the iden- tification and authentication of people today. This thesis aims to describe the algorithms used by a mathematical apparatus. The description of these algo- rithms is not the only objective of this thesis; the reason they were chosen and potential improvements or substitutions are also discussed. The background of iris recognition, its use in cryptosystems, and the application of error-correcting codes are investigated as well. The second version of the thesis eliminates errata and a quantum of inaccu- racies discovered in the first version, especially in the ROI Definition, the Hough Transform and the Feature Extraction sections. Besides that, it also contains se- veral new propositions. Last, but not least, it shows a potential implementation of the algorithms described by appending pseudocodes to the relevant sections. 1

Redes de sensores sem fio (RSSF) tipicamente consistem de nós sensores com limitação de energia, processamento, comunicação e memória. A segurança em RSSF está se tornando fundamental com o surgimento de aplicações que necessitam de mecanismos que permitam autenticidade, integridade e confidencialidade. Devido a limitações de recursos em RSSF, adequar criptossistemas de chaves públicas (PKC) para estas redes é um problema de pesquisa em aberto. Meados de 2008, Danilo Gligoroski et al. propuseram um novo PKC baseado em quase-grupos multivariados quadráticos (MQQ). Experimentos feitos por Gligoroski na plataforma FPGA mostram que MQQ executou em tempo menor que principais PKC (DH, RSA e ECC) existentes, tanto que alguns artigos afirmam que MQQ possui velocidade de uma típica cifra de bloco simétrica. Além disto, o MQQ exibiu o mesmo nível de segurança que outros PKC (DH, RSA e ECC) necessitando chaves menores. Outra propriedade que chama atenção no MQQ é o uso das operações básicas XOR, AND e deslocamento de bits nos processos de encriptação e decriptação, fato importante considerando que uma RSSF possui processamento limitado. Estas características tornam o MQQ promissor a levar um novo caminho na difícil tarefa de dotar redes de sensores sem fio de criptossistemas de chaves públicas. Neste contexto se insere este trabalho que analisa a viabilidade de implementar o algoritmo MQQ em uma plataforma de RSSF. Sendo importante considerar que este trabalho inova na proposta de levar para RSSF este novo PKC baseado quase-grupos multivariados quadráticos, além de contribuir com um método para reduzir o tamanho da chave pública utilizada pelo MQQ. Foram feitos testes com MQQ nas plataformas TelosB e MICAz, sendo que o MQQexibiu os tempos de 825; 1 ms para encriptar e 116; 6 ms para decriptar no TelosB e 445 ms para encriptar no MICAz. / Wireless sensor networks (WSN) typically consist of sensor nodes with limited energy, processing, communication and memory. Security in WSN is becoming critical with the emergence of applications that require mechanisms for authenticity, integrity and confidentiality. Due to resource constraints in sensor networks, public key cryptosystems suit (PKC) for these networks is an open research problem. In 2008 Danilo Gligoroski et al. proposed a new PKC based on quasi-groups multivariate quadratic (MQQ). Experiments by Gligoroski on FPGA platform show that MQQ performed in less time than most popular PKC (DH, RSA and ECC), so that some papers say MQQ has a typical speed of symmetric block cipher. Moreover, the MQQ exhibited same level of security that other PKC (DH, RSA and ECC) requiring keys minors. Another property that draws attention in MQQ is the use of basic operations XOR, AND, and bit shifting in the processes of encryption and decryption, important fact considering that a WSN has limited processing. These features make the MQQ promising to take a new path in the difficult task of providing wireless sensor networks in public key cryptosystems. Appears in this context that this study examines the feasibility of implementing MQQ a platform for WSN. Is important to consider this innovative work in the proposal to bring this new PKC for WSN based multivariate quadratic quasigroups, and contribute a method to reduce the size public key used by MQQ. Tests with MQQ on platforms TelosB and MICAz, the MQQ exhibited 825ms to encrypt and 116ms to decrypt on TelosB and 445 ms to encrypt on MICAz.

Redes de sensores sem fio (RSSF) tipicamente consistem de nós sensores com limitação de energia, processamento, comunicação e memória. A segurança em RSSF está se tornando fundamental com o surgimento de aplicações que necessitam de mecanismos que permitam autenticidade, integridade e confidencialidade. Devido a limitações de recursos em RSSF, adequar criptossistemas de chaves públicas (PKC) para estas redes é um problema de pesquisa em aberto. Meados de 2008, Danilo Gligoroski et al. propuseram um novo PKC baseado em quase-grupos multivariados quadráticos (MQQ). Experimentos feitos por Gligoroski na plataforma FPGA mostram que MQQ executou em tempo menor que principais PKC (DH, RSA e ECC) existentes, tanto que alguns artigos afirmam que MQQ possui velocidade de uma típica cifra de bloco simétrica. Além disto, o MQQ exibiu o mesmo nível de segurança que outros PKC (DH, RSA e ECC) necessitando chaves menores. Outra propriedade que chama atenção no MQQ é o uso das operações básicas XOR, AND e deslocamento de bits nos processos de encriptação e decriptação, fato importante considerando que uma RSSF possui processamento limitado. Estas características tornam o MQQ promissor a levar um novo caminho na difícil tarefa de dotar redes de sensores sem fio de criptossistemas de chaves públicas. Neste contexto se insere este trabalho que analisa a viabilidade de implementar o algoritmo MQQ em uma plataforma de RSSF. Sendo importante considerar que este trabalho inova na proposta de levar para RSSF este novo PKC baseado quase-grupos multivariados quadráticos, além de contribuir com um método para reduzir o tamanho da chave pública utilizada pelo MQQ. Foram feitos testes com MQQ nas plataformas TelosB e MICAz, sendo que o MQQexibiu os tempos de 825; 1 ms para encriptar e 116; 6 ms para decriptar no TelosB e 445 ms para encriptar no MICAz. / Wireless sensor networks (WSN) typically consist of sensor nodes with limited energy, processing, communication and memory. Security in WSN is becoming critical with the emergence of applications that require mechanisms for authenticity, integrity and confidentiality. Due to resource constraints in sensor networks, public key cryptosystems suit (PKC) for these networks is an open research problem. In 2008 Danilo Gligoroski et al. proposed a new PKC based on quasi-groups multivariate quadratic (MQQ). Experiments by Gligoroski on FPGA platform show that MQQ performed in less time than most popular PKC (DH, RSA and ECC), so that some papers say MQQ has a typical speed of symmetric block cipher. Moreover, the MQQ exhibited same level of security that other PKC (DH, RSA and ECC) requiring keys minors. Another property that draws attention in MQQ is the use of basic operations XOR, AND, and bit shifting in the processes of encryption and decryption, important fact considering that a WSN has limited processing. These features make the MQQ promising to take a new path in the difficult task of providing wireless sensor networks in public key cryptosystems. Appears in this context that this study examines the feasibility of implementing MQQ a platform for WSN. Is important to consider this innovative work in the proposal to bring this new PKC for WSN based multivariate quadratic quasigroups, and contribute a method to reduce the size public key used by MQQ. Tests with MQQ on platforms TelosB and MICAz, the MQQ exhibited 825ms to encrypt and 116ms to decrypt on TelosB and 445 ms to encrypt on MICAz.

The purpose of this thesis is to design a secure and optimized cryptographic stream cipher for passive type Radio Frequency Identification (RFID) tags. RFID technology is a wireless automatic tracking and identification device. It has become an integral part of our daily life and it is used in many applications such as electronic passports, contactless payment systems, supply chain management and so on. But the information carried on RFID tags are vulnerable to unauthorized access (or various threats) which raises the security and privacy concern over RFID devices. One of the possible solutions to protect the confidentiality, integrity and to provide authentication is, to use a cryptographic stream cipher which encrypts the original information with a pseudo-random bit sequence. Besides that RFID tags require a resource constrained environment such as efficient area, power and high performance cryptographic systems with large security margins. Therefore, the architecture of stream cipher provides the best trade-off between the cryptographic security and the hardware efficiency. In this thesis, we first described the RFID technology and explain the design requirements for passive type RFID tags. The hardware design for passive tags is more challenging due to its stringent requirements like power consumption and the silicon area. We presented different design measures and some of the optimization techniques required to achieve low-resource cryptographic hardware implementation for passive tags. Secondly, we propose and implement a lightweight WG-5 stream cipher, which has good proven cryptographic mathematical properties. Based on these properties we measured the security analysis of WG-5 and showed that the WG-5 is immune to different types of attacks such as algebraic attack, correlation attack, cube attack, differential attack, Discrete Fourier Transform attack (DFT), Time-Memory-Data trade-off attack. The implementation of WG-5 was carried out using 65 nm and 130 nm CMOS technologies. We achieved promising results of WG-5 implementation in terms of area, power, speed and optimality. Our results outperforms most of the other stream ciphers which are selected in eSTREAM project. Finally, we proposed RFID mutual authentication protocol based on WG-5. The security and privacy analysis of the proposed protocol showed that it is resistant to various RFID attacks such as replay attacks, Denial-of-service (DoS) attack, ensures forward privacy and impersonation attack.

The purpose of this thesis is to design a secure and optimized cryptographic stream cipher for passive type Radio Frequency Identification (RFID) tags. RFID technology is a wireless automatic tracking and identification device. It has become an integral part of our daily life and it is used in many applications such as electronic passports, contactless payment systems, supply chain management and so on. But the information carried on RFID tags are vulnerable to unauthorized access (or various threats) which raises the security and privacy concern over RFID devices. One of the possible solutions to protect the confidentiality, integrity and to provide authentication is, to use a cryptographic stream cipher which encrypts the original information with a pseudo-random bit sequence. Besides that RFID tags require a resource constrained environment such as efficient area, power and high performance cryptographic systems with large security margins. Therefore, the architecture of stream cipher provides the best trade-off between the cryptographic security and the hardware efficiency. In this thesis, we first described the RFID technology and explain the design requirements for passive type RFID tags. The hardware design for passive tags is more challenging due to its stringent requirements like power consumption and the silicon area. We presented different design measures and some of the optimization techniques required to achieve low-resource cryptographic hardware implementation for passive tags. Secondly, we propose and implement a lightweight WG-5 stream cipher, which has good proven cryptographic mathematical properties. Based on these properties we measured the security analysis of WG-5 and showed that the WG-5 is immune to different types of attacks such as algebraic attack, correlation attack, cube attack, differential attack, Discrete Fourier Transform attack (DFT), Time-Memory-Data trade-off attack. The implementation of WG-5 was carried out using 65 nm and 130 nm CMOS technologies. We achieved promising results of WG-5 implementation in terms of area, power, speed and optimality. Our results outperforms most of the other stream ciphers which are selected in eSTREAM project. Finally, we proposed RFID mutual authentication protocol based on WG-5. The security and privacy analysis of the proposed protocol showed that it is resistant to various RFID attacks such as replay attacks, Denial-of-service (DoS) attack, ensures forward privacy and impersonation attack.

Le résultat principal dans le travail présenté est le calcul explicite de la série génératrice des opérateurs de Hecke dans l'algèbre de Hecke locale pour les groupes symplectiques de genre 3 et 4. L'algorithme est basé sur l'isomorphisme de Satake, qui permet de réaliser toutes les opérations dans l'algèbre des polynômes à plusieurs variables. C'est la première fois que cette expression est calculée pour le genre 4. Pour obtenir le résultat principal, une méthode de calcul symbolique a été développée. Cette approche algorithmique s'applique à d'autres types de séries de Hecke. En particulier, nous formulons et prouvons un analogue du Lemme de Rankin pour le genre 2. Nous avons aussi calculé les séries génératrices des carrés symétriques et des cubes symétriques.<br /><br />Se basant sur nos résultats nous formulons une conjecture de modularité pour les convolutions des fonctions L spineurs associées aux formes modulaires de Siegel. Nous considérons d'autres conjectures importantes liées aux formes modulaires de Siegel et à leurs fonctions L. Nous utilisons ces constructions pour calculer les facteurs algébriques rationnels aux valeurs critiques de la fonction L spineur attachée à F12 de Miyawaki. A notre connaissance c'est le premier exemple d'une fonction L-spineur de forme parabolique de Siegel de degré 3, dont certaines valeurs spéciales peuvent être calculées explicitement.<br /><br />Finalement, nous appliquons la théorie des algèbres de Hecke pour construire des cryptosystèmes algébriques sur ensembles finis de classes à gauches dans l'algèbre de Hecke. Nous utilisons une relation entre les classes à gauches et les points sur certains variétés algébriques projectives.

The aim of this dissertation is to improve computational efficiency of modular exponentiation-based public-key cryptosystems. The operational speed of these public-key cryptosystems is largely determined by the modular exponentiation operation of the form A = ge mod m where g is the base, e is the exponent and m is the modulus. The required modular exponentiation is computed by a series of modular multiplications. Optimized algorithms are required for various platforms, especially for lower-end platforms. These require the algorithms to be efficient and consume as little resources as possible. In these dissertation algorithms for integer multiplication, modular reduction and modular exponentiation, was developed and implemented in software, as required for public-key cryptography. A detailed analysis of these algorithms is given, as well as exact measurement of the computational speed achieved by each algorithm. This research shows that a total speed improvement of 13% can be achieved on existing modular exponentiation based public-key cryptosystems, in particular for the RSA cryptosystem. Three novel approaches are also presented for improving the decryption speed efficiency of the RSA algorithm. These methods focus on the selection of the decryption exponent by careful consideration of the difference between the two primes p and q. The resulting reduction of the decryption exponent improves the decryption speed by approximately 45%. / Dissertation (MEng (Electronics))--University of Pretoria, 2006. / Electrical, Electronic and Computer Engineering / unrestricted