Analysis and Design Security Primitives Based on Chaotic Systems for eCommerce

Security is considered the most important requirement for the success of electronic commerce, which is built based on the security of hash functions, encryption algorithms and pseudorandom number generators. Chaotic systems and security algorithms have similar properties including sensitivity to any change or changes in the initial parameters, unpredictability, deterministic nature and random-like behaviour. Several security algorithms based on chaotic systems have been proposed; unfortunately some of them were found to be insecure and/or slow. In view of this, designing new secure and fast security algorithms based on chaotic systems which guarantee integrity, authentication and confidentiality is essential for electronic commerce development. In this thesis, we comprehensively explore the analysis and design of security primitives based on chaotic systems for electronic commerce: hash functions, encryption algorithms and pseudorandom number generators. Novel hash functions, encryption algorithms and pseudorandom number generators based on chaotic systems for electronic commerce are proposed. The securities of the proposed algorithms are analyzed based on some well-know statistical tests in this filed. In addition, a new one-dimensional triangle-chaotic map (TCM) with perfect chaotic behaviour is presented. We have compared the proposed chaos-based hash functions, block cipher and pseudorandom number generator with well-know algorithms. The comparison results show that the proposed algorithms are better than some other existing algorithms. Several analyses and computer simulations are performed on the proposed algorithms to verify their characteristics, confirming that these proposed algorithms satisfy the characteristics and conditions of security algorithms. The proposed algorithms in this thesis are high-potential for adoption in e-commerce applications and protocols

Mind the Gap - A Closer Look at the Security of Block Ciphers against Differential Cryptanalysis

Resistance against differential cryptanalysis is an important design criteria for any modern block cipher and most designs rely on finding some upper bound on probability of single differential characteristics. However, already at EUROCRYPT'91, Lai et al. comprehended that differential cryptanalysis rather uses differentials instead of single characteristics. In this paper, we consider exactly the gap between these two approaches and investigate this gap in the context of recent lightweight cryptographic primitives. This shows that for many recent designs like Midori, Skinny or Sparx one has to be careful as bounds from counting the number of active S-boxes only give an inaccurate evaluation of the best differential distinguishers. For several designs we found new differential distinguishers and show how this gap evolves. We found an 8-round differential distinguisher for Skinny-64 with a probability of 2−56.932−56.93, while the best single characteristic only suggests a probability of 2−722−72. Our approach is integrated into publicly available tools and can easily be used when developing new cryptographic primitives. Moreover, as differential cryptanalysis is critically dependent on the distribution over the keys for the probability of differentials, we provide experiments for some of these new differentials found, in order to confirm that our estimates for the probability are correct. While for Skinny-64 the distribution over the keys follows a Poisson distribution, as one would expect, we noticed that Speck-64 follows a bimodal distribution, and the distribution of Midori-64 suggests a large class of weak keys

Design and Cryptanalysis of Symmetric-Key Algorithms in Black and White-box Models

Cryptography studies secure communications. In symmetric-key cryptography, the communicating parties have a shared secret key which allows both to encrypt and decrypt messages. The encryption schemes used are very efficient but have no rigorous security proof. In order to design a symmetric-key primitive, one has to ensure that the primitive is secure at least against known attacks. During 4 years of my doctoral studies at the University of Luxembourg under the supervision of Prof. Alex Biryukov, I studied symmetric-key cryptography and contributed to several of its topics. Part I is about the structural and decomposition cryptanalysis. This type of cryptanalysis aims to exploit properties of the algorithmic structure of a cryptographic function. The first goal is to distinguish a function with a particular structure from random, structure-less functions. The second goal is to recover components of the structure in order to obtain a decomposition of the function. Decomposition attacks are also used to uncover secret structures of S-Boxes, cryptographic functions over small domains. In this part, I describe structural and decomposition cryptanalysis of the Feistel Network structure, decompositions of the S-Box used in the recent Russian cryptographic standard, and a decomposition of the only known APN permutation in even dimension. Part II is about the invariant-based cryptanalysis. This method became recently an active research topic. It happened mainly due to recent extreme cryptographic designs, which turned out to be vulnerable to this cryptanalysis method. In this part, I describe an invariant-based analysis of NORX, an authenticated cipher. Further, I show a theoretical study of linear layers that preserve low-degree invariants of a particular form used in the recent attacks on block ciphers. Part III is about the white-box cryptography. In the white-box model, an adversary has full access to the cryptographic implementation, which in particular may contain a secret key. The possibility of creating implementations of symmetric-key primitives secure in this model is a long-standing open question. Such implementations have many applications in industry; in particular, in mobile payment systems. In this part, I study the possibility of applying masking, a side-channel countermeasure, to protect white-box implementations. I describe several attacks on direct application of masking and provide a provably-secure countermeasure against a strong class of the attacks. Part IV is about the design of symmetric-key primitives. I contributed to design of the block cipher family SPARX and to the design of a suite of cryptographic algorithms, which includes the cryptographic permutation family SPARKLE, the cryptographic hash function family ESCH, and the authenticated encryption family SCHWAEMM. In this part, I describe the security analysis that I made for these designs

Horst Meets Fluid-SPN: Griffin for Zero-Knowledge Applications

Zero-knowledge (ZK) applications form a large group of use cases in modern cryptography, and recently gained in popularity due to novel proof systems. For many of these applications, cryptographic hash functions are used as the main building blocks, and they often dominate the overall performance and cost of these approaches. Therefore, in the last years several new hash functions were built in order to reduce the cost in these scenarios, including Poseidon and Rescue among others. These hash functions often look very different from more classical designs such as AES or SHA-2. For example, they work natively over prime fields rather than binary ones. At the same time, for example Poseidon and Rescue share some common features, such as being SPN schemes and instantiating the nonlinear layer with invertible power maps. While this allows the designers to provide simple and strong arguments for establishing their security, it also introduces crucial limitations in the design, which may affect the performance in the target applications. In this paper, we propose the Horst construction, in which the addition in a Feistel scheme (x, y) -> (y + F(x), x) is extended via a multiplication, i.e., (x, y) -> (y * G(x) + F(x), x). By carefully analyzing the performance metrics in SNARK and STARK protocols, we show how to combine an expanding Horst scheme with a Rescue-like SPN scheme in order to provide security and better efficiency in the target applications. We provide an extensive security analysis for our new design Griffin and a comparison with all current competitors

Arion: Arithmetization-Oriented Permutation and Hashing from Generalized Triangular Dynamical Systems

In this paper we propose the (keyed) permutation Arion and the hash function ArionHash over $\mathbb{F}_p$ for odd and particularly large primes. The design of Arion is based on the newly introduced Generalized Triangular Dynamical System (GTDS), which provides a new algebraic framework for constructing (keyed) permutation using polynomials over a finite field. At round level Arion is the first design which is instantiated using the new GTDS. We provide extensive security analysis of our construction including algebraic cryptanalysis (e.g. interpolation and Groebner basis attacks) that are particularly decisive in assessing the security of permutations and hash functions over $\mathbb{F}_p$. From a application perspective, ArionHash is aimed for efficient implementation in zkSNARK protocols and Zero-Knowledge proof systems. For this purpose, we exploit that CCZ-equivalence of graphs can lead to a more efficient implementation of Arithmetization-Oriented primitives. We compare the efficiency of ArionHash in R1CS and Plonk settings with other hash functions such as Poseidon, Anemoi and Griffin. For demonstrating the practical efficiency of ArionHash we implemented it with the zkSNARK libraries libsnark and Dusk Network Plonk. Our result shows that ArionHash is significantly faster than Poseidon - a hash function designed for zero-knowledge proof systems. We also found that an aggressive version of ArionHash is considerably faster than Anemoi and Griffin in a practical zkSNARK setting

Cryptographic key management for the vehicles of tomorrow

The automotive industry is undergoing a major transformation process in which nearly every part of the vehicle is becoming digital and connected. Modern vehicles are often connected to the internet, feature several wireless interfaces and will soon communicate directly with surrounding vehicles and roadside infrastructure using V2X technology. However, this transformation has not yet been paralleled by the development of techniques or standards which address the cyber security challenges posed by these systems. The automotive industry has historically failed to use secure cryptography or appropriate key management techniques and there is no sign that things have improved. In this thesis, we present several new cryptographic and key management flaws in an existing automotive immobiliser system and we develop two new V2X architectures for improving the safety and privacy of tomorrow’s connected and autonomous vehicles. Specifically, we study the AUT64 automotive block cipher and its associated authentication protocol in a real-world immobiliser system. Despite having a 120~bit key, we find a number of flaws in the system which we combine to present several practical key-recovery attacks. Our first new V2X architecture, IFAL, provides a practical and secure improvement to the leading European standard for V2X. IFAL introduces a new certificate issuance mechanism that eliminates the trade-off between pseudonym duration and bandwidth. Our second architecture, VDAA, addresses the need for efficient techniques that preserve vehicle privacy despite dishonest or colluding certificate authorities