On the Relationship between Resilient Boolean Functions and Linear Branch Number of S-boxes

Differential branch number and linear branch number are critical for the security of symmetric ciphers. The recent trend in the designs like PRESENT block cipher, ASCON authenticated encryption shows that applying S-boxes that have nontrivial differential and linear branch number can significantly reduce the number of rounds. As we see in the literature that the class of 4 x 4 S-boxes have been well-analysed, however, a little is known about the n x n S-boxes for n >= 5. For instance, the complete classification of 5 x 5 affine equivalent S-boxes is still unknown. Therefore, it is challenging to obtain “the best” S-boxes with dimension >= 5 that can be used in symmetric cipher designs. In this article, we present a novel approach to construct S-boxes that identifies classes of n x n S-boxes (n = 5, 6) with differential branch number 3 and linear branch number 3, and ensures other cryptographic properties. To the best of our knowledge, we are the first to report 6 x 6 S-boxes with linear branch number 3, differential branch number 3, and with other good cryptographic properties such as nonlinearity 24 and differential uniformity 4

Large substitution boxes with efficient combinational implementations

At a fundamental level, the security of symmetric key cryptosystems ties back to Claude Shannon\u27s properties of confusion and diffusion. Confusion can be defined as the complexity of the relationship between the secret key and ciphertext, and diffusion can be defined as the degree to which the influence of a single input plaintext bit is spread throughout the resulting ciphertext. In constructions of symmetric key cryptographic primitives, confusion and diffusion are commonly realized with the application of nonlinear and linear operations, respectively. The Substitution-Permutation Network design is one such popular construction adopted by the Advanced Encryption Standard, among other block ciphers, which employs substitution boxes, or S-boxes, for nonlinear behavior. As a result, much research has been devoted to improving the cryptographic strength and implementation efficiency of S-boxes so as to prohibit cryptanalysis attacks that exploit weak constructions and enable fast and area-efficient hardware implementations on a variety of platforms. To date, most published and standardized S-boxes are bijective functions on elements of 4 or 8 bits. In this work, we explore the cryptographic properties and implementations of 8 and 16 bit S-boxes. We study the strength of these S-boxes in the context of Boolean functions and investigate area-optimized combinational hardware implementations. We then present a variety of new 8 and 16 bit S-boxes that have ideal cryptographic properties and enable low-area combinational implementations

Bounds on Differential and Linear Branch Number of Permutations

Nonlinear permutations (S-boxes) are key components in block ciphers. The differential branch number measures the diffusion power of a permutation, whereas the linear branch number measures resistance against linear cryptanalysis. There has not been much analysis done on the differential branch number of nonlinear permutations of $\mathbb{F}_2^n$, although it has been well studied in case of linear permutations. Similarly upper bounds for the linear branch number have also not been studied in general. In this paper we obtain bounds for both the differential and the linear branch number of permutations (both linear and nonlinear) of $\mathbb{F}_2^n$. We also prove that in the case of $\mathbb{F}_2^4$, the maximum differential branch number can be achieved only by affine permutations

Implementing Symmetric Cryptography Using Sequence of Semi-Bent Functions

Symmetric cryptography is a cornerstone of everyday digital security, where two parties must share a common key to communicate. The most common primitives in symmetric cryptography are stream ciphers and block ciphers that guarantee confidentiality of communications and hash functions for integrity. Thus, for securing our everyday life communication, it is necessary to be convinced by the security level provided by all the symmetric-key cryptographic primitives. The most important part of a stream cipher is the key stream generator, which provides the overall security for stream ciphers. Nonlinear Boolean functions were preferred for a long time to construct the key stream generator. In order to resist several known attacks, many requirements have been proposed on the Boolean functions. Attacks against the cryptosystems have forced deep research on Boolean function to allow us a more secure encryption. In this work we describe all main requirements for constructing of cryptographically significant Boolean functions. Moreover, we provide a construction of Boolean functions (semi-bent Boolean functions) which can be used in the construction of orthogonal variable spreading factor codes used in code division multiple access (CDMA) systems as well as in certain cryptographic applications

On applications of simulated annealing to cryptology

Boolean functions are critical building blocks of symmetric-key ciphers. In most cases, the security of a cipher against a particular kind of attacks can be explained by the existence of certain properties of its underpinning Boolean functions. Therefore, the design of appropriate functions has received significant attention from researchers for several decades. Heuristic methods have become very powerful tools for designing such functions. In this thesis, we apply simulated annealing methods to construct Boolean functions with particular properties. Our results meet or exceed the best results of available theoretical constructions and/or heuristic searches in the literature, including a 10-variable balanced Boolean function with resiliency degree 2, algebraic degree 7, and nonlinearity 488 for the first time. This construction affirmatively answers the open problem about the existence of such functions. This thesis also includes results of cryptanalysis for symmetric ciphers, such as Geffe cipher and TREYFER cipher

On the Design and Analysis of Stream Ciphers

This thesis presents new cryptanalysis results for several different stream cipher constructions. In addition, it also presents two new stream ciphers, both based on the same design principle. The first attack is a general attack targeting a nonlinear combiner. A new class of weak feedback polynomials for linear feedback shift registers is identified. By taking samples corresponding to the linear recurrence relation, it is shown that if the feedback polynomial has taps close together an adversary to take advantage of this by considering the samples in a vector form. Next, the self-shrinking generator and the bit-search generator are analyzed. Both designs are based on irregular decimation. For the self-shrinking generator, it is shown how to recover the internal state knowing only a few keystream bits. The complexity of the attack is similar to the previously best known but uses a negligible amount of memory. An attack requiring a large keystream segment is also presented. It is shown to be asymptotically better than all previously known attacks. For the bit-search generator, an algorithm that recovers the internal state is given as well as a distinguishing attack that can be very efficient if the feedback polynomial is not carefully chosen. Following this, two recently proposed stream cipher designs, Pomaranch and Achterbahn, are analyzed. Both stream ciphers are designed with small hardware complexity in mind. For Pomaranch Version 2, based on an improvement of previous analysis of the design idea, a key recovery attack is given. Also, for all three versions of Pomaranch, a distinguishing attack is given. For Achterbahn, it is shown how to recover the key of the latest version, known as Achterbahn-128/80. The last part of the thesis introduces two new stream cipher designs, namely Grain and Grain-128. The ciphers are designed to be very small in hardware. They also have the distinguishing feature of allowing users to increase the speed of the ciphers by adding extra hardware

Engineering Self-Adaptive Collective Processes for Cyber-Physical Ecosystems

The pervasiveness of computing and networking is creating significant opportunities for building valuable socio-technical systems. However, the scale, density, heterogeneity, interdependence, and QoS constraints of many target systems pose severe operational and engineering challenges. Beyond individual smart devices, cyber-physical collectives can provide services or solve complex problems by leveraging a “system effect” while coordinating and adapting to context or environment change. Understanding and building systems exhibiting collective intelligence and autonomic capabilities represent a prominent research goal, partly covered, e.g., by the field of collective adaptive systems. Therefore, drawing inspiration from and building on the long-time research activity on coordination, multi-agent systems, autonomic/self-* systems, spatial computing, and especially on the recent aggregate computing paradigm, this thesis investigates concepts, methods, and tools for the engineering of possibly large-scale, heterogeneous ensembles of situated components that should be able to operate, adapt and self-organise in a decentralised fashion. The primary contribution of this thesis consists of four main parts. First, we define and implement an aggregate programming language (ScaFi), internal to the mainstream Scala programming language, for describing collective adaptive behaviour, based on field calculi. Second, we conceive of a “dynamic collective computation” abstraction, also called aggregate process, formalised by an extension to the field calculus, and implemented in ScaFi. Third, we characterise and provide a proof-of-concept implementation of a middleware for aggregate computing that enables the development of aggregate systems according to multiple architectural styles. Fourth, we apply and evaluate aggregate computing techniques to edge computing scenarios, and characterise a design pattern, called Self-organising Coordination Regions (SCR), that supports adjustable, decentralised decision-making and activity in dynamic environments.Con lo sviluppo di informatica e intelligenza artificiale, la diffusione pervasiva di device computazionali e la crescente interconnessione tra elementi fisici e digitali, emergono innumerevoli opportunità per la costruzione di sistemi socio-tecnici di nuova generazione. Tuttavia, l'ingegneria di tali sistemi presenta notevoli sfide, data la loro complessità—si pensi ai livelli, scale, eterogeneità, e interdipendenze coinvolti. Oltre a dispositivi smart individuali, collettivi cyber-fisici possono fornire servizi o risolvere problemi complessi con un “effetto sistema” che emerge dalla coordinazione e l'adattamento di componenti fra loro, l'ambiente e il contesto. Comprendere e costruire sistemi in grado di esibire intelligenza collettiva e capacità autonomiche è un importante problema di ricerca studiato, ad esempio, nel campo dei sistemi collettivi adattativi. Perciò, traendo ispirazione e partendo dall'attività di ricerca su coordinazione, sistemi multiagente e self-*, modelli di computazione spazio-temporali e, specialmente, sul recente paradigma di programmazione aggregata, questa tesi tratta concetti, metodi, e strumenti per l'ingegneria di ensemble di elementi situati eterogenei che devono essere in grado di lavorare, adattarsi, e auto-organizzarsi in modo decentralizzato. Il contributo di questa tesi consiste in quattro parti principali. In primo luogo, viene definito e implementato un linguaggio di programmazione aggregata (ScaFi), interno al linguaggio Scala, per descrivere comportamenti collettivi e adattativi secondo l'approccio dei campi computazionali. In secondo luogo, si propone e caratterizza l'astrazione di processo aggregato per rappresentare computazioni collettive dinamiche concorrenti, formalizzata come estensione al field calculus e implementata in ScaFi. Inoltre, si analizza e implementa un prototipo di middleware per sistemi aggregati, in grado di supportare più stili architetturali. Infine, si applicano e valutano tecniche di programmazione aggregata in scenari di edge computing, e si propone un pattern, Self-Organising Coordination Regions, per supportare, in modo decentralizzato, attività decisionali e di regolazione in ambienti dinamici