Knapsack sets for cryptography

The basic goal of this study is to extend old and propose new ways to generate knapsack sets suitable for use in public key cryptography. The knapsack problem and its cryptographic use are reviewed in the introductory chapter. Terminology is based on common cryptographic vocabulary. For example, solving the knapsack problem (which is here a subset sum problem) is termed decipherment. Chapter 1 also reviews the most famous knapsack cryptosystem, the Merkle Hellman system. It is based on a superincreasing knapsack and uses modular multiplication as a trapdoor transformation. The insecurity caused by these two properties exemplifies the two general categories of attacks against knapsack systems. These categories provide the motivation for Chapters 2 and 4. Chapter 2 discusses the density of a knapsack and the dangers of having a low density. Chapter 3 interrupts for a while the more abstract treatment by showing examples of small injective knapsacks and extrapolating conjectures on some characteristics of knapsacks of larger size, especially their density and number. The most common trapdoor technique, modular multiplication, is likely to cause insecurity, but as argued in Chapter 4, it is difficult to find any other simple trapdoor techniques. This discussion also provides a basis for the introduction of various categories of non injectivity in Chapter 5. Besides general ideas of non injectivity of knapsack systems, Chapter 5 introduces and evaluates several ways to construct such systems, most notably the "exceptional blocks" in superincreasing knapsacks and the usage of "too small" a modulus in the modular multiplication as a trapdoor technique. The author believes that non injectivity is the most promising direction for development of knapsack cryptosystema. Chapter 6 modifies two well known knapsack schemes, the Merkle Hellman multiplicative trapdoor knapsack and the Graham Shamir knapsack. The main interest is in aspects other than non injectivity, although that is also exploited. In the end of the chapter, constructions proposed by Desmedt et. al. are presented to serve as a comparison for the developments of the subsequent three chapters. Chapter 7 provides a general framework for the iterative construction of injective knapsacks from smaller knapsacks, together with a simple example, the "three elements" system. In Chapters 8 and 9 the general framework is put into practice in two different ways. Modularly injective small knapsacks are used in Chapter 9 to construct a large knapsack, which is called the congruential knapsack. The addends of a subset sum can be found by decrementing the sum iteratively by using each of the small knapsacks and their moduli in turn. The construction is also generalized to the non injective case, which can lead to especially good results in the density, without complicating the deciphering process too much. Chapter 9 presents three related ways to realize the general framework of Chapter 7. The main idea is to join iteratively small knapsacks, each element of which would satisfy the superincreasing condition. As a whole, none of these systems need become superincreasing, though the development of density is not better than that. The new knapsack systems are injective but they can be deciphered with the same searching method as the non injective knapsacks with the "exceptional blocks" in Chapter 5. The final Chapter 10 first reviews the Chor Rivest knapsack system, which has withstood all cryptanalytic attacks. A couple of modifications to the use of this system are presented in order to further increase the security or make the construction easier. The latter goal is attempted by reducing the size of the Chor Rivest knapsack embedded in the modified system. '

Anàlisi de les claus criptogràfiques utilitzades en bitcoin

El present projecte realitza una anàlisi de les claus criptogràfiques utilitzades en bitcoin. El projecte introdueix les nocions bàsiques necessàries de les corbes el·líptiques, la criptografia de corbes el·líptiques i els bitcoins per a realitzar l’anàlisi. Aquesta anàlisi consisteix en explorar el codi de diferents wallets bitcoin i realitzar un estudi empíric de l’aleatorietat de les claus. Per últim, el projecte introdueix el concepte de wallet determinista, el seu funcionament i alguns dels problemes que presenta.

Internet Turvallisuus ja GOST Algoritmit

Tämä tutkimus keskittyy Venäjän kryptografian standardeihin ja niiden toteutukseen sertifioiduissa tuotteissa. Tässä työssä myös pohditaan menetelmiä, jotka parantavat suorituskykyä. Tutkimus jatkuu turvallisuuspalveluiden toimittajien vertailulla niitten saadun sertifikaattimäärän perusteella. Tämä auttaa arvioimaan Venäjän nykyistä markkinatilannetta. Sen lisäksi työssä kuvataan venäläisten algoritmien integraatiota TLS-, PKI- ja IKEv1-protokolleihin. Tavoitteena on protokollien yhteensopivuus erilaisiin tuotteisiin. Diplomityötä jatketaan tutkimalla IKEv2-protokolan integroinnin vaatimuksia. Lopuksi diplomityössä todetaan, että venäläiset algoritmit ovat turvallisia ja standardisointi auttaa ulkomaisia yrityksiä saamaan tarvittavat sertifikaatit.

Dynamics of coherent vortices in mixing layers using direct numerical and large-eddy simulations

Coherent vortices in turbulent mixing layers are investigated by means of Direct Numerical Simulation (DNS) and Large-Eddy Simulation (LES). Subgrid-scale models defined in spectral and physical spaces are reviewed. The new "spectral-dynamic viscosity model", that allows to account for non-developed turbulence in the subgrid-scales, is discussed. Pseudo-spectral methods, combined with sixth-order compact finite differences schemes (when periodic boundary conditions cannot be established), are used to solve the Navier- Stokes equations. Simulations in temporal and spatial mixing layers show two types of pairing of primary Kelvin-Helmholtz (KH) vortices depending on initial conditions (or upstream conditions): quasi-2D and helical pairings. In both cases, secondary streamwise vortices are stretched in between the KH vortices at an angle of 45° with the horizontal plane. These streamwise vortices are not only identified in the early transitional stage of the mixing layer but also in self-similar turbulence conditions. The Re dependence of the "diameter" of these vortices is analyzed. Results obtained in spatial growing mixing layers show some evidences of pairing of secondary vortices; after a pairing of the primary Kelvin-Helmholtz (KH) vortices, the streamwise vortices are less numerous and their diameter has increased than before the pairing of KH vortices.

Effect of the establishment of dominance relationships on cortisol and other metabolic parameters in Nile tilapia (Oreochromis niloticus)

The objective of the present study was to investigate the influence of the establishment of dominance relationships and social stress on plasma cortisol and metabolite levels in Nile tilapia (Oreochromis niloticus). During the 30-day experiment, the fish weighing 236 ± 29 g were kept in individual aquaria, except for two pairings lasting 6 h each. Blood samples were taken from the animals before and after pairing. Display, approach, attack, rebuff, chase flight, and coloration were carried out on days 16 and 30. Activities and behaviors characteristic of the establishment of dominance relationships were described. It was possible to classify all experimental fish (N = 30) as dominant or subordinate. No differences were detected between dominant (N = 15) and subordinate (N = 15) fish during isolation or after pairing in cortisol (isolated: 5.76 ± 0.98 vs 5.42 ± 0.63; paired: 10.94 ± 1.62 vs 11.21 ± 2.45 µg/dl), glucose (isolated: 60.02 ± 4.9 vs 67.85 ± 16.16; paired: 110.44 ± 15.72 vs 136.26 ± 22.46 mg/dl), triglyceride (isolated: 167.87 ± 5.06 vs 185.68 ± 7.24; paired: 210.85 ± 13.40 vs 221.82 ± 12.70 mg/dl) or total protein levels (isolated: 7.01 ± 0.42 vs 6.69 ± 0.59; paired: 9.21 ± 0.62 vs 9.51 ± 0.66 g/dl). However, when isolated (N = 30) and paired (N = 30) tilapia were compared, there were significant differences in cortisol and metabolite levels. The similar response presented by dominant and subordinate tilapia indicates that establishment of dominance relationships was a stressor for both groups.

Novel word learning ability in chronic post-stroke aphasia : variability and modality effects

Novel word learning has been rarely studied in people with aphasia (PWA), although it can provide a relatively pure measure of their learning potential, and thereby contribute to the development of effective aphasia treatment methods. The main aim of the present thesis was to explore the capacity of PWA for associative learning of word–referent pairings and cognitive-linguistic factors related to it. More specifically, the thesis examined learning and long-term maintenance of the learned pairings, the role of lexical-semantic abilities in learning as well as acquisition of phonological versus semantic information in associative novel word learning. Furthermore, the effect of modality on associative novel word learning and the neural underpinnings of successful learning were explored. The learning experiments utilized the Ancient Farming Equipment (AFE) paradigm that employs drawings of unfamiliar referents and their unfamiliar names. Case studies of Finnishand English-speaking people with chronic aphasia (n = 6) were conducted in the investigation. The learning results of PWA were compared to those of healthy control participants, and active production of the novel words and their semantic definitions was used as learning outcome measures. PWA learned novel word–novel referent pairings, but the variation between individuals was very wide, from more modest outcomes (Studies I–II) up to levels on a par with healthy individuals (Studies III–IV). In incidental learning of semantic definitions, none of the PWA reached the performance level of the healthy control participants. Some PWA maintained part of the learning outcomes up to months post-training, and one individual showed full maintenance of the novel words at six months post-training (Study IV). Intact lexical-semantic processing skills promoted learning in PWA (Studies I–II) but poor phonological short-term memory capacities did not rule out novel word learning. In two PWA with successful learning and long-term maintenance of novel word–novel referent pairings, learning relied on orthographic input while auditory input led to significantly inferior learning outcomes (Studies III–IV). In one of these individuals, this previously undetected modalityspecific learning ability was successfully translated into training with familiar but inaccessible everyday words (Study IV). Functional magnetic resonance imaging revealed that this individual had a disconnected dorsal speech processing pathway in the left hemisphere, but a right-hemispheric neural network mediated successful novel word learning via reading. Finally, the results of Study III suggested that the cognitive-linguistic profile may not always predict the optimal learning channel for an individual with aphasia. Small-scale learning probes seem therefore useful in revealing functional learning channels in post-stroke aphasia.

A Study of Privacy Preserving Queries with Bloom Filters

This thesis focuses on the private membership test (PMT) problem and presents three single server protocols to resolve this problem. In the presented solutions, a client can perform an inclusion test for some record x in a server's database, without revealing his record. Moreover after executing the protocols, the contents of server's database remain secret. In each of these solutions, a different cryptographic protocol is utilized to construct a privacy preserving variant of Bloom filter. The three suggested solutions are slightly different from each other, from privacy perspective and also from complexity point of view. Therefore, their use cases are different and it is impossible to choose one that is clearly the best between all three. We present the software developments of the three protocols by utilizing various pseudocodes. The performance of our implementation is measured based on a real case scenario. This thesis is a spin-off from the Academy of Finland research project "Cloud Security Services".

Web2.0, knowledge sharing and privacy in E-learning

Quand le E-learning a émergé il ya 20 ans, cela consistait simplement en un texte affiché sur un écran d'ordinateur, comme un livre. Avec les changements et les progrès dans la technologie, le E-learning a parcouru un long chemin, maintenant offrant un matériel éducatif personnalisé, interactif et riche en contenu. Aujourd'hui, le E-learning se transforme de nouveau. En effet, avec la prolifération des systèmes d'apprentissage électronique et des outils d'édition de contenu éducatif, ainsi que les normes établies, c’est devenu plus facile de partager et de réutiliser le contenu d'apprentissage. En outre, avec le passage à des méthodes d'enseignement centrées sur l'apprenant, en plus de l'effet des techniques et technologies Web2.0, les apprenants ne sont plus seulement les récipiendaires du contenu d'apprentissage, mais peuvent jouer un rôle plus actif dans l'enrichissement de ce contenu. Par ailleurs, avec la quantité d'informations que les systèmes E-learning peuvent accumuler sur les apprenants, et l'impact que cela peut avoir sur leur vie privée, des préoccupations sont soulevées afin de protéger la vie privée des apprenants. Au meilleur de nos connaissances, il n'existe pas de solutions existantes qui prennent en charge les différents problèmes soulevés par ces changements. Dans ce travail, nous abordons ces questions en présentant Cadmus, SHAREK, et le E-learning préservant la vie privée. Plus précisément, Cadmus est une plateforme web, conforme au standard IMS QTI, offrant un cadre et des outils adéquats pour permettre à des tuteurs de créer et partager des questions de tests et des examens. Plus précisément, Cadmus fournit des modules telles que EQRS (Exam Question Recommender System) pour aider les tuteurs à localiser des questions appropriées pour leur examens, ICE (Identification of Conflits in Exams) pour aider à résoudre les conflits entre les questions contenu dans un même examen, et le Topic Tree, conçu pour aider les tuteurs à mieux organiser leurs questions d'examen et à assurer facilement la couverture des différent sujets contenus dans les examens. D'autre part, SHAREK (Sharing REsources and Knowledge) fournit un cadre pour pouvoir profiter du meilleur des deux mondes : la solidité des systèmes E-learning et la flexibilité de PLE (Personal Learning Environment) tout en permettant aux apprenants d'enrichir le contenu d'apprentissage, et les aider à localiser nouvelles ressources d'apprentissage. Plus précisément, SHAREK combine un système recommandation multicritères, ainsi que des techniques et des technologies Web2.0, tels que le RSS et le web social, pour promouvoir de nouvelles ressources d'apprentissage et aider les apprenants à localiser du contenu adapté. Finalement, afin de répondre aux divers besoins de la vie privée dans le E-learning, nous proposons un cadre avec quatre niveaux de vie privée, ainsi que quatre niveaux de traçabilité. De plus, nous présentons ACES (Anonymous Credentials for E-learning Systems), un ensemble de protocoles, basés sur des techniques cryptographiques bien établies, afin d'aider les apprenants à atteindre leur niveau de vie privée désiré.

Sécurité polynomiale en cryptographie

Dans ce mémoire, nous proposons des protocoles cryptographiques d'échange de clef, de mise en gage, et de transfert équivoque. Un premier protocole de transfert équivoque, primitive cryptographique universelle pour le calcul multi-parties, s'inspire du protocole d'échange de clef par puzzle de Merkle, et améliore les résultats existants. Puis, nous montrons qu'il est possible de construire ces mêmes primitives cryptographiques sans l'hypothèse des fonctions à sens unique, mais avec le problème 3SUM. Ce problème simple ---dans une liste de n entiers, en trouver trois dont la somme a une certaine valeur--- a une borne inférieure conjecturée de Omega(n^2).

Key Agreement Against Quantum Adversaries

Key agreement is a cryptographic scenario between two legitimate parties, who need to establish a common secret key over a public authenticated channel, and an eavesdropper who intercepts all their messages in order to learn the secret. We consider query complexity in which we count only the number of evaluations (queries) of a given black-box function, and classical communication channels. Ralph Merkle provided the first unclassified scheme for secure communications over insecure channels. When legitimate parties are willing to ask O(N) queries for some parameter N, any classical eavesdropper needs Omega(N^2) queries before being able to learn their secret, which is is optimal. However, a quantum eavesdropper can break this scheme in O(N) queries. Furthermore, it was conjectured that any scheme, in which legitimate parties are classical, could be broken in O(N) quantum queries. In this thesis, we introduce protocols à la Merkle that fall into two categories. When legitimate parties are restricted to use classical computers, we offer the first secure classical scheme. It requires Omega(N^{13/12}) queries of a quantum eavesdropper to learn the secret. We give another protocol having security of Omega(N^{7/6}) queries. Furthermore, for any k>= 2, we introduce a classical protocol in which legitimate parties establish a secret in O(N) queries while the optimal quantum eavesdropping strategy requires Theta(N^{1/2+k/{k+1}}) queries, approaching Theta(N^{3/2}) when k increases. When legitimate parties are provided with quantum computers, we present two quantum protocols improving on the best known scheme before this work. Furthermore, for any k>= 2, we give a quantum protocol in which legitimate parties establish a secret in O(N) queries while the optimal quantum eavesdropping strategy requires Theta(N^{1+{k}/{k+1}})} queries, approaching Theta(N^{2}) when k increases.

Complexité de la communication sur un canal avec délai

Nous introduisons un nouveau modèle de la communication à deux parties dans lequel nous nous intéressons au temps que prennent deux participants à effectuer une tâche à travers un canal avec délai d. Nous établissons quelques bornes supérieures et inférieures et comparons ce nouveau modèle aux modèles de communication classiques et quantiques étudiés dans la littérature. Nous montrons que la complexité de la communication d’une fonction sur un canal avec délai est bornée supérieurement par sa complexité de la communication modulo un facteur multiplicatif d/ lg d. Nous présentons ensuite quelques exemples de fonctions pour lesquelles une stratégie astucieuse se servant du temps mort confère un avantage sur une implémentation naïve d’un protocole de communication optimal en terme de complexité de la communication. Finalement, nous montrons qu’un canal avec délai permet de réaliser un échange de bit cryptographique, mais que, par lui-même, est insuffisant pour réaliser la primitive cryptographique de transfert équivoque.

From Classical to Quantum Secret Sharing

Dans ce mémoire, nous nous pencherons tout particulièrement sur une primitive cryptographique connue sous le nom de partage de secret. Nous explorerons autant le domaine classique que le domaine quantique de ces primitives, couronnant notre étude par la présentation d’un nouveau protocole de partage de secret quantique nécessitant un nombre minimal de parts quantiques c.-à-d. une seule part quantique par participant. L’ouverture de notre étude se fera par la présentation dans le chapitre préliminaire d’un survol des notions mathématiques sous-jacentes à la théorie de l’information quantique ayant pour but primaire d’établir la notation utilisée dans ce manuscrit, ainsi que la présentation d’un précis des propriétés mathématique de l’état de Greenberger-Horne-Zeilinger (GHZ) fréquemment utilisé dans les domaines quantiques de la cryptographie et des jeux de la communication. Mais, comme nous l’avons mentionné plus haut, c’est le domaine cryptographique qui restera le point focal de cette étude. Dans le second chapitre, nous nous intéresserons à la théorie des codes correcteurs d’erreurs classiques et quantiques qui seront à leur tour d’extrême importances lors de l’introduction de la théorie quantique du partage de secret dans le chapitre suivant. Dans la première partie du troisième chapitre, nous nous concentrerons sur le domaine classique du partage de secret en présentant un cadre théorique général portant sur la construction de ces primitives illustrant tout au long les concepts introduits par des exemples présentés pour leurs intérêts autant historiques que pédagogiques. Ceci préparera le chemin pour notre exposé sur la théorie quantique du partage de secret qui sera le focus de la seconde partie de ce même chapitre. Nous présenterons alors les théorèmes et définitions les plus généraux connus à date portant sur la construction de ces primitives en portant un intérêt particulier au partage quantique à seuil. Nous montrerons le lien étroit entre la théorie quantique des codes correcteurs d’erreurs et celle du partage de secret. Ce lien est si étroit que l’on considère les codes correcteurs d’erreurs quantiques étaient de plus proches analogues aux partages de secrets quantiques que ne leur étaient les codes de partage de secrets classiques. Finalement, nous présenterons un de nos trois résultats parus dans A. Broadbent, P.-R. Chouha, A. Tapp (2009); un protocole sécuritaire et minimal de partage de secret quantique a seuil (les deux autres résultats dont nous traiterons pas ici portent sur la complexité de la communication et sur la simulation classique de l’état de GHZ).

Use of Novel Algorithms MAJE4 and MACJER-320 for Achieving Confidentiality and Message Authentication in SSL & TLS

Extensive use of the Internet coupled with the marvelous growth in e-commerce and m-commerce has created a huge demand for information security. The Secure Socket Layer (SSL) protocol is the most widely used security protocol in the Internet which meets this demand. It provides protection against eaves droppings, tampering and forgery. The cryptographic algorithms RC4 and HMAC have been in use for achieving security services like confidentiality and authentication in the SSL. But recent attacks against RC4 and HMAC have raised questions in the confidence on these algorithms. Hence two novel cryptographic algorithms MAJE4 and MACJER-320 have been proposed as substitutes for them. The focus of this work is to demonstrate the performance of these new algorithms and suggest them as dependable alternatives to satisfy the need of security services in SSL. The performance evaluation has been done by using practical implementation method.

Algebraic Geometric Codes and their relation to Cryptography using Elliptic Curves

Communication is the process of transmitting data across channel. Whenever data is transmitted across a channel, errors are likely to occur. Coding theory is a stream of science that deals with finding efficient ways to encode and decode data, so that any likely errors can be detected and corrected. There are many methods to achieve coding and decoding. One among them is Algebraic Geometric Codes that can be constructed from curves. Cryptography is the science ol‘ security of transmitting messages from a sender to a receiver. The objective is to encrypt message in such a way that an eavesdropper would not be able to read it. A eryptosystem is a set of algorithms for encrypting and decrypting for the purpose of the process of encryption and decryption. Public key eryptosystem such as RSA and DSS are traditionally being prel‘en‘ec| for the purpose of secure communication through the channel. llowever Elliptic Curve eryptosystem have become a viable altemative since they provide greater security and also because of their usage of key of smaller length compared to other existing crypto systems. Elliptic curve cryptography is based on group of points on an elliptic curve over a finite field. This thesis deals with Algebraic Geometric codes and their relation to Cryptography using elliptic curves. Here Goppa codes are used and the curves used are elliptic curve over a finite field. We are relating Algebraic Geometric code to Cryptography by developing a cryptographic algorithm, which includes the process of encryption and decryption of messages. We are making use of fundamental properties of Elliptic curve cryptography for generating the algorithm and is used here to relate both.

A new fast stream cipher: MAJE4

A new fast stream cipher, MAJE4 is designed and developed with a variable key size of 128-bit or 256-bit. The randomness property of the stream cipher is analysed by using the statistical tests. The performance evaluation of the stream cipher is done in comparison with another fast stream cipher called JEROBOAM. The focus is to generate a long unpredictable key stream with better performance, which can be used for cryptographic applications.