Irreducible compositions of degree two polynomials over finite fields have regular structure

Let $q$ be an odd prime power and $D$ be the set of monic irreducible polynomials in $\mathbb F_q[x]$ which can be written as a composition of monic degree two polynomials. In this paper we prove that $D$ has a natural regular structure by showing that there exists a finite automaton having $D$ as accepted language. Our method is constructive.Comment: To appear in The Quarterly Journal of Mathematic

Group key management based on semigroup actions

In this work we provide a suite of protocols for group key management based on general semigroup actions. Construction of the key is made in a distributed and collaborative way. Examples are provided that may in some cases enhance the security level and communication overheads of previous existing protocols. Security against passive attacks is considered and depends on the hardness of the semigroup action problem in any particular scenario.Comment: accepted for publication in Journal of algebra and its application

An Active Attack on a Multiparty Key Exchange Protocol

The multiparty key exchange introduced in Steiner et al.\@ and presented in more general form by the authors is known to be secure against passive attacks. In this paper, an active attack is presented assuming malicious control of the communications of the last two users for the duration of only the key exchange

An active attack on a distributed Group Key Exchange system

In this work, we introduce an active attack on a Group Key Exchange protocol by Burmester and Desmedt. The attacker obtains a copy of the shared key, which is created in a collaborative manner with the legal users in a communication group

On the Density of Coprime m-tuples over Holomorphy Rings

Let $\mathbb F_q$ be a finite field, $F/\mathbb F_q$ be a function field of genus $g$ having full constant field $\mathbb F_q$, $\mathcal S$ a set of places of $F$ and $H$ the holomorphy ring of $\mathcal S$. In this paper we compute the density of coprime $m$-tuples of elements of $H$. As a side result, we obtain that whenever the complement of $\mathcal S$ is finite, the computation of the density can be reduced to the computation of the $L$-polynomial of the function field. In the rational function field case, classical results for the density of coprime $m$-tuples of polynomials are obtained as corollaries.Comment: To appear in International Journal of Number Theor

Shifted Eisenstein polynomials, irreducible compositions of polynomials and group key exchanges

In my dissertation, I have covered multiple different topics. First, we consider the concept of natural density over the integers, and extend it to holomorphy rings over function fields. This allows us to give a function field analogue of Cesàro’s theorem, which gives the “probability” that an m-tuple of random elements of the holomorphy ring is oprime. We also generalize this and consider the density of k × m matrices over holomorphy rings which can be extended to unimodular m × m matrices. In the second part, we determine the natural density of shifted Eisenstein polynomials. This means that we compute the density of integer polynomials f(x) of a fixed degree n for which some shift f(x + i) for an integer i satisfies Eisenstein’s irreducibility criterion. We then also compute the density of affine Eisenstein polynomials. Thirdly, we consider an arbitrary set of monic quadratic polynomials over a finite field and ask ourselves which compositions of copies of them are irreducible. We first give a criterion to decide whether all such compositions are irreducible, and then show that in general, the irreducible compositions have the structure of a regular language. In the final chapter, we study cryptographic protocols for key exchange in ad-hoc groups. We first translate some protocols from the literature to the more general setting of semigroup actions, and then propose our own variants of these protocols, which aim to have improved security or efficiency. Then, we demonstrate a couple of active attacks on certain such protocols which are in some ways more powerful than man-in-the-middle attacks

Design choices for next-generation IIoT-connected MES/MOM:An empirical study on smart factories

The role of enterprise information systems is becoming increasingly crucial for improving customer responsiveness in the manufacturing industry. However, manufacturers engaged in mass customization are currently facing challenges related to implementing Industrial Internet of Things (IIoT) concepts of Industry 4.0 in order to increase responsiveness. In this article, we apply the findings from a two-year design science study to establish the role of manufacturing execution systems/manufacturing operations management (MES/MOM) in an IIoT-enabled brownfield manufacturing enterprise. We also present design recommendations for developing next-generation MES/MOM as a strong core to make factories smart and responsive. First, we analyze the architectural design challenges of MES/MOM in IIoT through a selective literature review. We then present an exploratory case study in which we implement our homegrown MES/MOM data model design based on ISA 95 in Aalborg University's Smart Production Lab, which is a reconfigurable cyber-physical production system. This was achieved through the use of a custom module for the open-source Odoo ERP platform (mainly version 14). Finally, we enrich our case study with three industrial design demonstrators and combine the findings with a quality function deployment (QFD) method to determine design requirements for next-generation IIoT-connected MES/MOM. The results from our QFD analysis indicate that interoperability is the most important characteristic when designing a responsive smart factory, with the highest relative importance of 31% of the eight characteristics we studied

Efficient Description of some Classes of Codes using Group Algebras

Circulant matrices are an important tool widely used in coding theory and cryptography. A circulant matrix is a square matrix whose rows are the cyclic shifts of the first row. Such a matrix can be efficiently stored in memory because it is fully specified by its first row. The ring of n x n circulant matrices can be identified with the quotient ring F[x]/(x(n) - 1). In consequence, the strong algebraic structure of the ring F[x]/(x(n) - 1) can be used to study properties of the collection of all n x n circulant matrices. The ring F[x]/(x(n) - 1) is a special case of a group algebra and elements of any finite dimensional group algebra can be represented with square matrices which are specified by a single column. In this paper we study this representation and prove that it is an injective Hamming weight preserving homomorphism of F-algebras and classify it in the case where the underlying group is abelian

Securing IT/OT Links for Low Power IIoT Devices:Design considerations for industry 4.0

Manufacturing is facing a host of new security challenges due to the convergence of information technology (IT) and operational technology (OT) in the industry. This article addresses the challenges that arise due to the use of low power Industrial Internet of Things (IIoT) devices in modular manufacturing systems of Industry 4.0. First, we analyze security challenges concerning the manufacturing execution system (MES) and programmable logic controllers (PLC) in IIoT through a selective literature review. Second, we present an exploratory case study to determine a protocol for cryptographic key management and key exchange suitable for the Smart Production Lab of Aalborg University (a learning cyber-physical factory). Finally, we combine the findings of the case study with a quality function deployment (QFD) method to determine design requirements for Industry 4.0. We identify specific requirements from both the high-level domain of factory capabilities and the low-level domain of cryptography and translate requirements between these domains using a QFD analysis. The recommendations for designing a secure smart factory focus on how security can be implemented for low power and low-cost IIoT devices. Even though there have been a few studies on securing IT to OT data exchange, we conclude that the field is not yet in a state where it can be applied in practice with confidence

Detection of liver metastases under 2cm: comparison of different acquisition protocols in four row multidetector-CT (MDCT)

This study compared different acquisition protocols performance to detect small liver metastases (<2cm). Thirty consecutive patients with histologically proven hepatic metastases were explored by MDCT at the liver equilibrium phase by four successive acquisitions. We compared the following protocols (1-4): 5/30/1.5 (section thickness/table speed/pitch); 5/15/0.75; 5/11.25/0.75; and 2.5/15/1.5 with the same X-ray dose. The gold standard was based on patient radiological follow-up. Evolutive lesions were considered as true positive (TP). The described lesions, not found on the follow-up exams despite tumoral progression, were considered as false positive (FP). Stable lesions could not be considered as metastasis and were eliminated. One hundred and seventy-six lesions were detected: 61 TP and 91 FP. Twenty-four lesions were eliminated. The mean kappa values for protocols 1, 2, 3 and 4 were, respectively, 0.43, 0.68, 0.73 and 0.51 (0.61-0.80: substantial agreement) and the mean areas under the ROC curve were, respectively, 0.76, 0.87, 0.86 and 0.80. The results of protocols 2 and 3 were significantly superior to those of protocols 1 and 4. MDCT protocols using thin sections or an increased table speed are less efficient in detecting small metastase