Recursive Diffusion Layers for Block Ciphers and Hash Functions

Many modern block ciphers use maximum distance separable (MDS) matrices as the main part of their diffusion layers. In this paper, we propose a new class of diffusion layers constructed from several rounds of Feistel-like structures whose round functions are linear. We investigate the requirements of the underlying linear functions to achieve the maximal branch number for the proposed 4*4 words diffusion layer. The proposed diffusion layers only require word-level XORs, rotations, and they have simple inverses. They can be replaced in the diffusion layer of the block ciphers MMB and Hierocrypt to increase their security and performance, respectively. Finally, we try to extend our results for up to 8*8 words diffusion layers

Direct Construction of Lightweight Rotational-XOR MDS Diffusion Layers

As a core component of Substitution-Permutation Networks, diffusion layer is mainly introduced by matrices from maximum distance separable (MDS) codes. Surprisingly, up to now, most constructions of MDS matrices require to perform an equivalent or even exhaustive search. Especially, not many MDS proposals are known that obtain an excellent hardware efficiency and simultaneously guarantee a remarkable software implementation. In this paper, we study the cyclic structure of rotational-XOR diffusion layer, one of the commonly used linear layers over ${(\mathbb{F}_{\rm{2}}^b)^n}$, which consists of only rotation and XOR operations. First, we provide novel properties on this class of matrices, and prove the a lower bound on the number of rotations for $n \ge 4$ and show the tightness of the bound for $n=4$. Next, by precisely characterizing the relation among sub-matrices for each possible form, we can eliminate all the other non-optimal cases. Finally, we present a direct construction of such MDS matrices, which allows to generate $4 \times 4$ perfect instances for arbitrary $b \ge 4$. Every example contains the fewest possible rotations, so under this construction strategy, our proposal costs the minimum gate equivalents (resp. cyclic shift instructions) in the hardware (resp. software) implementation. To the best of our knowledge, it is the first time that rotational-XOR MDS diffusion layers have been constructed without any auxiliary search

A Salad of Block Ciphers

This book is a survey on the state of the art in block cipher design and analysis. It is work in progress, and it has been for the good part of the last three years -- sadly, for various reasons no significant change has been made during the last twelve months. However, it is also in a self-contained, useable, and relatively polished state, and for this reason I have decided to release this \textit{snapshot} onto the public as a service to the cryptographic community, both in order to obtain feedback, and also as a means to give something back to the community from which I have learned much. At some point I will produce a final version -- whatever being a ``final version\u27\u27 means in the constantly evolving field of block cipher design -- and I will publish it. In the meantime I hope the material contained here will be useful to other people

Analyse et Conception d'Algorithmes de Chiffrement Légers

The work presented in this thesis has been completed as part of the FUI Paclido project, whose aim is to provide new security protocols and algorithms for the Internet of Things, and more specifically wireless sensor networks. As a result, this thesis investigates so-called lightweight authenticated encryption algorithms, which are designed to fit into the limited resources of constrained environments. The first main contribution focuses on the design of a lightweight cipher called Lilliput-AE, which is based on the extended generalized Feistel network (EGFN) structure and was submitted to the Lightweight Cryptography (LWC) standardization project initiated by NIST (National Institute of Standards and Technology). Another part of the work concerns theoretical attacks against existing solutions, including some candidates of the nist lwc standardization process. Therefore, some specific analyses of the Skinny and Spook algorithms are presented, along with a more general study of boomerang attacks against ciphers following a Feistel construction.Les travaux présentés dans cette thèse s’inscrivent dans le cadre du projet FUI Paclido, qui a pour but de définir de nouveaux protocoles et algorithmes de sécurité pour l’Internet des Objets, et plus particulièrement les réseaux de capteurs sans fil. Cette thèse s’intéresse donc aux algorithmes de chiffrements authentifiés dits à bas coût ou également, légers, pouvant être implémentés sur des systèmes très limités en ressources. Une première partie des contributions porte sur la conception de l’algorithme léger Lilliput-AE, basé sur un schéma de Feistel généralisé étendu (EGFN) et soumis au projet de standardisation international Lightweight Cryptography (LWC) organisé par le NIST (National Institute of Standards and Technology). Une autre partie des travaux se concentre sur des attaques théoriques menées contre des solutions déjà existantes, notamment un certain nombre de candidats à la compétition LWC du NIST. Elle présente donc des analyses spécifiques des algorithmes Skinny et Spook ainsi qu’une étude plus générale des attaques de type boomerang contre les schémas de Feistel

Design of Efficient Symmetric-Key Cryptographic Algorithms

兵庫県立大学大学院202

Proceedings of AUTOMATA 2011 : 17th International Workshop on Cellular Automata and Discrete Complex Systems

International audienceThe proceedings contain full (reviewed) papers and short (non reviewed) papers that were presented at the workshop

Modelling the role of polarity and geometry in cell-fate dynamics of mammary organoids

Mammary organoids are three-dimensional structures that are derived from mammary gland cells and can recapitulate the complex architecture and functionality of the mammary gland in vitro. Mammary organoids hold great promise for advancing our understanding of mammary gland biology, breast cancer, and precision medicine. However, phenotypic and genetic instabilities observed in long-term expansion limit their applications to prolonged experiments and large-scale production. A proposed factor driving this organoid-wise heterogeneity is plasticity within mammary epithelial cells, the phenotypic switching of cells. Therefore, we examine the dynamics of key intracellular pathways that govern cell-fate commitment in mammary organoids. Specifically, we explore the influence of local tissue geometry and polarity in cell-cell signalling in stabilising cell-fate determinants using a combination of analytic and numerical multiscale modelling approaches. We introduce interconnected dynamical systems, graph-coupled dynamical systems with input-output representations to describe intercellular signal flow between cells. Exploiting structural properties of the bilayer graphs describing mammary tissue architecture, we derive low-dimensional forms of these models enabling the analytic examination of the interplay of structure and polarity on cell-fate patterning, extending existing methods to include pathway crosstalk and providing rigorous links between low-dimensional and their associated large-scale representations. Supporting the analytic investigations of static spatial domains with cellbased modelling, we provide evidence that sufficiently strong cell-cell signal polarity has the capacity to generate and sustain bilayer laminar patterns of Notch1, a critical cell-fate determinant and inducer of plasticity in mammary epithelial cells. Furthermore, we demonstrate how local tissue curvature can relax the constraints of polarity supporting healthy tissue growth and supporting branching morphologies. Fundamentally, this study highlights the significance of cell signalling polarity as a control mechanism of cell-fate commitment. Thus, the establishment and maintenance of epithelial polarity should be considered in long-term mammary organoid expansion protocol development

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal