A reversible system based on hybrid toggle radius-4 cellular automata and its application as a block cipher

The dynamical system described herein uses a hybrid cellular automata (CA) mechanism to attain reversibility, and this approach is adapted to create a novel block cipher algorithm called HCA. CA are widely used for modeling complex systems and employ an inherently parallel model. Therefore, applications derived from CA have a tendency to fit very well in the current computational paradigm where scalability and multi-threading potential are quite desirable characteristics. HCA model has recently received a patent by the Brazilian agency INPI. Several evaluations and analyses performed on the model are presented here, such as theoretical discussions related to its reversibility and an analysis based on graph theory, which reduces HCA security to the well-known Hamiltonian cycle problem that belongs to the NP-complete class. Finally, the cryptographic robustness of HCA is empirically evaluated through several tests, including avalanche property compliance and the NIST randomness suite.Comment: 34 pages, 12 figure

Applications of Artificial Intelligence to Cryptography

This paper considers some recent advances in the field of Cryptography using Artificial Intelligence (AI). It specifically considers the applications of Machine Learning (ML) and Evolutionary Computing (EC) to analyze and encrypt data. A short overview is given on Artificial Neural Networks (ANNs) and the principles of Deep Learning using Deep ANNs. In this context, the paper considers: (i) the implementation of EC and ANNs for generating unique and unclonable ciphers; (ii) ML strategies for detecting the genuine randomness (or otherwise) of finite binary strings for applications in Cryptanalysis. The aim of the paper is to provide an overview on how AI can be applied for encrypting data and undertaking cryptanalysis of such data and other data types in order to assess the cryptographic strength of an encryption algorithm, e.g. to detect patterns of intercepted data streams that are signatures of encrypted data. This includes some of the authors’ prior contributions to the field which is referenced throughout. Applications are presented which include the authentication of high-value documents such as bank notes with a smartphone. This involves using the antenna of a smartphone to read (in the near field) a flexible radio frequency tag that couples to an integrated circuit with a non-programmable coprocessor. The coprocessor retains ultra-strong encrypted information generated using EC that can be decrypted on-line, thereby validating the authenticity of the document through the Internet of Things with a smartphone. The application of optical authentication methods using a smartphone and optical ciphers is also briefly explored

Contributions to Confidentiality and Integrity Algorithms for 5G

The confidentiality and integrity algorithms in cellular networks protect the transmission of user and signaling data over the air between users and the network, e.g., the base stations. There are three standardised cryptographic suites for confidentiality and integrity protection in 4G, which are based on the AES, SNOW 3G, and ZUC primitives, respectively. These primitives are used for providing a 128-bit security level and are usually implemented in hardware, e.g., using IP (intellectual property) cores, thus can be quite efficient. When we come to 5G, the innovative network architecture and high-performance demands pose new challenges to security. For the confidentiality and integrity protection, there are some new requirements on the underlying cryptographic algorithms. Specifically, these algorithms should: 1) provide 256 bits of security to protect against attackers equipped with quantum computing capabilities; and 2) provide at least 20 Gbps (Gigabits per second) speed in pure software environments, which is the downlink peak data rate in 5G. The reason for considering software environments is that the encryption in 5G will likely be moved to the cloud and implemented in software. Therefore, it is crucial to investigate existing algorithms in 4G, checking if they can satisfy the 5G requirements in terms of security and speed, and possibly propose new dedicated algorithms targeting these goals. This is the motivation of this thesis, which focuses on the confidentiality and integrity algorithms for 5G. The results can be summarised as follows.1. We investigate the security of SNOW 3G under 256-bit keys and propose two linear attacks against it with complexities 2172 and 2177, respectively. These cryptanalysis results indicate that SNOW 3G cannot provide the full 256-bit security level. 2. We design some spectral tools for linear cryptanalysis and apply these tools to investigate the security of ZUC-256, the 256-bit version of ZUC. We propose a distinguishing attack against ZUC-256 with complexity 2236, which is 220 faster than exhaustive key search. 3. We design a new stream cipher called SNOW-V in response to the new requirements for 5G confidentiality and integrity protection, in terms of security and speed. SNOW-V can provide a 256-bit security level and achieve a speed as high as 58 Gbps in software based on our extensive evaluation. The cipher is currently under evaluation in ETSI SAGE (Security Algorithms Group of Experts) as a promising candidate for 5G confidentiality and integrity algorithms. 4. We perform deeper cryptanalysis of SNOW-V to ensure that two common cryptanalysis techniques, guess-and-determine attacks and linear cryptanalysis, do not apply to SNOW-V faster than exhaustive key search. 5. We introduce two minor modifications in SNOW-V and propose an extreme performance variant, called SNOW-Vi, in response to the feedback about SNOW-V that some use cases are not fully covered. SNOW-Vi covers more use cases, especially some platforms with less capabilities. The speeds in software are increased by 50% in average over SNOW-V and can be up to 92 Gbps.Besides these works on 5G confidentiality and integrity algorithms, the thesis is also devoted to local pseudorandom generators (PRGs). 6. We investigate the security of local PRGs and propose two attacks against some constructions instantiated on the P5 predicate. The attacks improve existing results with a large gap and narrow down the secure parameter regime. We also extend the attacks to other local PRGs instantiated on general XOR-AND and XOR-MAJ predicates and provide some insight in the choice of safe parameters

Selected Topics in Cryptanalysis of Symmetric Ciphers

It is well established that a symmetric cipher may be described as a system of Boolean polynomials, and that the security of the cipher cannot be better than the difficulty of solving said system. Compressed Right-Hand Side (CRHS) Equations is but one way of describing a symmetric cipher in terms of Boolean polynomials. The first paper of this thesis provides a comprehensive treatment firstly of the relationship between Boolean functions in algebraic normal form, Binary Decision Diagrams and CRHS equations. Secondly, of how CRHS equations may be used to describe certain kinds of symmetric ciphers and how this model may be used to attempt a key-recovery attack. This technique is not left as a theoretical exercise, as the process have been implemented as an open-source project named CryptaPath. To ensure accessibility for researchers unfamiliar with algebraic cryptanalysis, CryptaPath can convert a reference implementation of the target cipher, as specified by a Rust trait, into the CRHS equations model automatically. CRHS equations are not limited to key-recovery attacks, and Paper II explores one such avenue of CRHS equations flexibility. Linear and differential cryptanalysis have long since established their position as two of the most important cryptanalytical attacks, and every new design since must show resistance to both. For some ciphers, like the AES, this resistance can be mathematically proven, but many others are left to heuristic arguments and computer aided proofs. This work is tedious, and most of the tools require good background knowledge of a tool/technique to transform a design to the right input format, with a notable exception in CryptaGraph. CryptaGraph is written in Rust and transforms a reference implementation into CryptaGraphs underlying data structure automatically. Paper II introduces a new way to use CRHS equations to model a symmetric cipher, this time in such a way that linear and differential trail searches are possible. In addition, a new set of operations allowing us to count the number of active S-boxes in a path is presented. Due to CRHS equations effective initial data compression, all possible trails are captured in the initial system description. As is the case with CRHS equations, the crux is the memory consumption. However, this approach also enables the graph of a CRHS equation to be pruned, allowing the memory consumption to be kept at manageable levels. Unfortunately, pruning nodes also means that we will lose valid, incomplete paths, meaning that the hulls found are probably incomplete. On the flip side, all paths, and their corresponding probabilities, found by the tool are guaranteed to be valid trails for the cipher. This theory is also implemented in an extension of CryptaPath, and the name is PathFinder. PathFinder is also able to automatically turn a reference implementation of a cipher into its CRHS equations-based model. As an additional bonus, PathFinder supports the reference implementation specifications specified by CryptaGraph, meaning that the same reference implementation can be used for both CryptaGraph and PathFinder. Paper III shifts focus onto symmetric ciphers designed to be used in conjunction with FHE schemes. Symmetric ciphers designed for this purpose are relatively new and have naturally had a strong focus on reducing the number of multiplications performed. A multiplication is considered expensive on the noise budget of the FHE scheme, while linear operations are viewed as cheap. These ciphers are all assuming that it is possible to find parameters in the various FHE schemes which allow these ciphers to work well in symbiosis with the FHE scheme. Unfortunately, this is not always possible, with the consequence that the decryption process becomes more costly than necessary. Paper III therefore proposes Fasta, a stream cipher which has its parameters and linear layer especially chosen to allow efficient implementation over the BGV scheme, particularly as implemented in the HElib library. The linear layers are drawn from a family of rotation-based linear transformations, as cyclic rotations are cheap to do in FHE schemes that allow packing of multiple plaintext elements in one FHE ciphertext. Fasta follows the same design philosophy as Rasta, and will never use the same linear layer twice under the same key. The result is a stream cipher tailor-made for fast evaluation in HElib. Fasta shows an improvement in throughput of a factor more than 7 when compared to the most efficient implementation of Rasta.Doktorgradsavhandlin

Multi-algorithmic Cryptography using Deterministic Chaos with Applications to Mobile Communications

In this extended paper, we present an overview of the principal issues associated with cryptography, providing historically significant examples for illustrative purposes as part of a short tutorial for readers that are not familiar with the subject matter. This is used to introduce the role that nonlinear dynamics and chaos play in the design of encryption engines which utilize different types of Iteration Function Systems (IFS). The design of such encryption engines requires that they conform to the principles associated with diffusion and confusion for generating ciphers that are of a maximum entropy type. For this reason, the role of confusion and diffusion in cryptography is discussed giving a design guide to the construction of ciphers that are based on the use of IFS. We then present the background and operating framework associated with a new product - CrypsticTM - which is based on the application of multi-algorithmic IFS to design encryption engines mounted on a USB memory stick using both disinformation and obfuscation to ‘hide’ a forensically inert application. The protocols and procedures associated with the use of this product are also briefly discussed