The thesis is focused on the theory of special lattices that are important in cryptography, namely ideal, cyclic and NTRU lattices. Specifically, we expand and generalise the work of Ding and Lindner on Identifying Ideal Lattices. The algorithm for identifying ideal lattices is included, along with illustrative examples and more detailed proofs of propositions on which the algorithm is based. In the section about Lattice Isomorphism there is also included a generalised theorem from the paper. We extend the result of identifying the NTRU lattices and supplement it with several examples. The thesis also contains Chapter Applications in Cryptography where we describe a cryptographic hash function based on ideal lattices. And finally, we provide a brief overview of the cryptographic algorithms using NTRU lattices.

NTRU is a fast public-key cryptosystem that is constructed using polynomial rings with integer coefficients. We present ETRU, an NTRU-like cryptosystem based on the Eisenstein integers. We discuss parameter selection and develop a model for the probabilty of decryption failure. We also provide an implementation of ETRU. We use theoretical and experimental data to compare the security and efficiency of ETRU to NTRU with comparable parameter sets and show that ETRU is an improvement over NTRU in terms of security.

NTRU is a fast public-key cryptosystem that is constructed using polynomial rings with integer coefficients. We present ETRU, an NTRU-like cryptosystem based on the Eisenstein integers. We discuss parameter selection and develop a model for the probabilty of decryption failure. We also provide an implementation of ETRU. We use theoretical and experimental data to compare the security and efficiency of ETRU to NTRU with comparable parameter sets and show that ETRU is an improvement over NTRU in terms of security.

NTRU is a fast public-key cryptosystem that is constructed using polynomial rings with integer coefficients. We present ETRU, an NTRU-like cryptosystem based on the Eisenstein integers. We discuss parameter selection and develop a model for the probabilty of decryption failure. We also provide an implementation of ETRU. We use theoretical and experimental data to compare the security and efficiency of ETRU to NTRU with comparable parameter sets and show that ETRU is an improvement over NTRU in terms of security.

NTRU is a fast public-key cryptosystem that is constructed using polynomial rings with integer coefficients. We present ETRU, an NTRU-like cryptosystem based on the Eisenstein integers. We discuss parameter selection and develop a model for the probabilty of decryption failure. We also provide an implementation of ETRU. We use theoretical and experimental data to compare the security and efficiency of ETRU to NTRU with comparable parameter sets and show that ETRU is an improvement over NTRU in terms of security.

Secure and reliable communication have always been critical part of todays infrastructure. Various asymmetric encryption schemes, such as RSA, have been used to achieve this goal. However, with advancements in quantum computing, current encryption schemes are becoming more vulnerable since they are weak to certain quantum attacks, such as Shor’s Algorithm. Therefore demand for post-quantum cryptography (PQC), which is not vulnerable to quantum attacks, is apparent. This work’s goal is to evaluate and compare PQC algorithms.

Asymmetric cryptography uses two keys for encryption public key and for decryption private key. The asymmetric cryptosystems include RSA, ElGamal, Elliptic Curves and others. Generally, asymmetric cryptography is mainly used for secure short messages and transmission encryption key for symmetric cryptography. The thesis deals with these systems and implements selected systems (RSA, ElGamal, McEliece, elliptic curves and NTRU) into the application. The application can test the features of chosen cryptosystems. These systems and their performance are compared and evaluated with the measured values. These results can predict the future usage of these systems in modern informatics systems.

Cette thèse se concentre sur les problèmes liés à l’authentification dans la technologie RFID. Cette technologie est l’une des technologies les plus prometteuses dans le domaine de l’informatique ubiquitaire, elle est souvent désignée comme la prochaine révolution après Internet. Cependant, à cause des ressources très limitées en termes de calcul, mémoire et énergie sur les étiquettes RFID, les algorithmes classiques de sécurité ne peuvent pas être implémentés sur les étiquettes à bas coût rendant ainsi la sécurité et la vie privée un important sujet de recherche aujourd’hui. Dans un premier temps, nous étudions le passage à l’échelle dans les systèmes RFID à bas coût en développant un module pour ns-3 qui simule le standard EPC Class 1 Generation 2 pour établir un cadre stricte pour l’identification sécurisée des RFID à bas coût, ce qui nous conduit à l’utilisation de la cryptographie à clés publiques. Ensuite, nous proposons un protocole d’authentification basé sur une adaptation que nous avons introduit sur le célèbre cryptosystème NTRU. Ce protocole est spécialement conçu pour les RFID à bas coût comme les étiquettes n’implémentent que des opérations simples (xor, décalages, addition) et il garantit le passage à l’échelle. Enfin, nous considérons l’identification à divulgation nulle de connaissance, ce type d’approches est très utile dans de nombreuses applications RFID. Nous proposons deux protocoles à divulgation nulle de connaissance basés sur cryptoGPS et cryptoGPS randomisé. Ces approches consistent à stocker sur le serveur des coupons pré-calculés, ainsi la sécurité et la vie privée sont mieux supportées que dans les autres approches de ce type / This thesis focuses on issues related to authentication in low-cost radio frequency identification technology, more commonly referred to as RFID. This technology it is often referred to as the next technological revolution after the Internet. However, due to the very limited resources in terms of computation, memory and energy on RFID tags, conventional security algorithms cannot be implemented on low-cost RFID tags making security and privacy an important research subject today. First of all, we investigate the scalability in low-cost RFID systems by developing a ns-3 module to simulate the universal low-cost RFID standard EPC Class-1 Generation-2 in order to establish a strict framework for secure identification in low-cost RFID systems. We show that, the symmetrical key cryptography is excluded from being used in any scalable low-cost RFID standard. Then, we propose a scalable authentification protocol based on our adaptation of the famous public key cryptosystem NTRU. This protocol is specially designed for low-cost RFID systems, it can be efficiently implemented into low-cost tags. Finally, we consider the zero-knowledge identification i.e. when the no secret sharing between the tag and the reader is needed. Such identification approaches are very helpful in many RFID applications when the tag changes constantly the field of administration. We propose two lightweight zero-knowledge identification approaches based on GPS and randomized GPS schemes. The proposed approaches consist in storing in the back-end precomputed values in the form of coupons. So, the GPS-based variant can be private and the number of coupons can be much higher than in other approaches thus leading to higher resistance to denial of service attacks for cheaper tags

In this thesis, we review basic properties of linear codes and lattices with a certain focus on their interplay. In particular, we focus on the analogous con- structions of cyclic codes and cyclic lattices. We start out with a brief overview of the basic theory and properties of linear codes. We then demonstrate the construction of cyclic codes and emphasize their importance in error-correcting coding theory. Next we survey properties of lattices, focusing on algorithmic lattice problems, exhibit the construction of cyclic lattices and discuss their applications in cryptography. We emphasize the similarity and common prop- erties of the two cyclic constructions.

The theses firstly introduces the basics of lattice problems. Then it focuses on various aspects of the cryptosystem NTRU which is based on the mentioned problems. The system is then compared with the most common encryption methods used nowadays. Its supposed quantum resistence is mentioned briefly. Subsequently the author tries to minimize the system's disadvantages by various cryptosystem modifications. Powered by TCPDF (www.tcpdf.org)