Miroslaw Szaban

Cryptographically Strong S-Boxes Based on Cellular Automata

Substitution boxes (S-boxes) are the main elements of block ciphers, wide used in modern cryptography. In this paper we propose a new method to create S-boxes, which is based on application of Cellular Automata (CA). We present results of testing CA-based S-boxes, which confirm that CA are able to realize efficiently Boolean functions corresponding to classical S-boxes. Proposed CA-based S-boxes offer cryptographic properties comparable or better than classical S-box tables.

Collective Behavior of Rules for Cellular Automata-based Stream Ciphers

The problem of generation by cellular automata of high quality pseudorandom sequences useful in cryptography is considered in the paper. For this purpose one dimensional nonuniform cellular automata is considered. The quality of pseudorandom sequences generated by cellular automata depends on collective behavior of rules assigned to cellular automata cells. Genetic algorithm is used to find suitable rules from predefined earlier set of rules. It has been shown that genetic algorithm eliminates bad subsets of rules and founds subsets of rules, which provide high quality pseudorandom sequences. These sequences are suitable for symmetric key cryptography and can be used in different cryptographic modules.

Dynamic cellular automata-based s-boxes

The most important elements of many block ciphers are nonlinear functions known as substitution boxes (S-boxes). Classical S-boxes are usually represented by numerical tables, which are used today in current cryptographic standards, such as Data Encryption Standard (DES) or Advanced Encryption Standard (AES), but in the result of developing methods of cryptanalysis they do not ensure enough safety of ciphers. Therefore, the open research issue now is to design new more sophisticated classes of S-boxes, in particular dynamic ones. In this paper we propose a methodology to design dynamic cellular automata (CA)-based S-boxes, which can be considered as a generator of CA-based S-boxes. We provide an exhaustive experimental analysis of the proposed CA-based S-boxes in terms of non-linearity, autocorrelation, balance and strict avalanche criterion. We show that the proposed S-boxes have high quality cryptographic properties (high non-linearity and balance, also low autocorrelation and distance to fulfill strict avalanche criterion). The interesting feature of the proposed S-boxes is a dynamic flexible structure, fully functionally realized by CA, while the classical S-boxes are represented by predefined unchangeable table structures.

Cellular Automata-Based S-Boxes vs. DES S-Boxes

In the paper we use recently proposed cellular automata (CA) - based methodology [9] to design 6x4 S-boxes functionally equivalent to S-boxes used in current cryptographic standard known as DES. We provide an exhaustive experimental analysis of the proposed CA-based S-box in terms of non-linearity, autocorrelation, balance and strict avalanche criterion, and compare it with DES S-boxes. We show that the proposed CA-based S-box has cryptographic properties comparable or better than classical S-box tables. The interesting feature of the proposed S-box is a dynamic flexible structure fully functionally realized by CA, while the classical DES S-box is represented by predefined unchangeable table structure.

Learning cellular automata rules for binary classification problem

This paper proposes a cellular automata-based solution of a binary classification problem. The proposed method is based on a two-dimensional, three-state cellular automaton (CA) with the von Neumann neighborhood. Since the number of possible CA rules (potential CA-based classifiers) is huge, searching efficient rules is conducted with use of a genetic algorithm (GA). Experiments show an excellent performance of discovered rules in solving the classification problem. The best found rules perform better than the heuristic CA rule designed by a human and also better than one of the most widely used statistical method: the k-nearest neighbors algorithm (k-NN). Experiments show that CAs rules can be successfully reused in the process of searching new rules.

Application of cellular automata to create S-box functions

Substitution boxes (S-boxes) play very important role in cryptography. In this paper we propose a new method based on applying Cellular Automata (CA) to create S-boxes. We present preliminary results suggesting that CA are able to realize a function of classical S-boxes. It was shown that proposed CA fulfills a number of creation conditions necessary to play a role of S-box table. Proposed CA offer a solution which produces result comparable with classical S-boxes.

Evolving collective behavior of cellular automata for cryptography

We consider 1D cellular automata (CA) and apply genetic algorithm (GA) to discover subsets of rules controlling CA cells, which collective behavior results in a high quality of pseudorandom number sequences (PNSs) suitable for symmetric key cryptography. The search of subsets of rules is performed in a set of predefined rules. We discover new subsets of CA rules providing very high quality of PNSs, which can be used in cryptographic modules

CA-based generator of S-boxes for cryptography use

Substitution boxes (S-boxes) are important elements of many block ciphers, which serve as tools of nonlinear transformation of information in the cipher process. Classical S-boxes are usually represented by specially designed tables, which are used today in current cryptographic standards, such as Data Encryption Standard (DES) or Advanced Encryption Standard (AES), but in the result of developing methods of cryptanalysis they do not ensure enough safety of ciphers. Therefore, the open research issue now is to design new more sophisticated classes of S-boxes, in particular dynamic ones. In this paper we propose a methodology to design dynamic cellular automata (CA)-based S-boxes, which can be considered as generator od CA-based S-boxes. We provide an exhaustive experimental analysis of the proposed CA-based S-boxes in terms of non-linearity, autocorrelation, balance and strict avalanche criterion. We show that the proposed S-boxes have high quality cryptographic properties (high non-linearity and balance, also low autocorrelation and distance to fulfill strict avalanche criterion). The interesting feature of the proposed S-boxes is a dynamic flexible structure, fully functionally realized by CA, while the classical S-boxes are represented by predefined unchangeable table structures.

Application of Cellular Automata in Symmetric Key Cryptography

The main concern of this paper is cryptosystems with a symmetric key, in particular block ciphers. The most important components of block ciphers are substitution boxes (S-boxes). Developing methods of cryptanalysis make ciphers worked on classical S-boxes not safe enough. Therefore, we propose a methodology of generation cellular automata (CA)-based S-boxes with enhanced quality. We provide an exhaustive experimental analysis of the proposed CA-based S-boxes in terms of non-linearity, autocorrelation, balance and strict avalanche criterion. We show that proposed S-boxes have high cryptographic quality. The interesting feature of the proposed S-boxes is a dynamic flexible structure, fully functionally realized by CA, while the classical S-boxes are represented by fixed table structures.

Probabilistic Binary Classification with Use of 2D Cellular Automata

In this paper are presented wide known classification methods modified from almost deterministic into probabilistic forms. The rule for the classification problem designed by Fawcett, known as \(n4\_V1\_nonstable\) is modified into two proposed forms partially (\(n4\_V1\_nonstable\_PP\)) and fully probabilistic (\(n4\_V1\_nonstable\_FP\)). The effectiveness of classifications of these three methods is analysed and compared. The classification methods are used as the rules in the two-dimensional three-state cellular automaton with the von Neumann and Moore neighbourhood. Preliminary experiments show that probabilistic modification of Fawcett’s method can give better results in the process of reconstruction (classification) than the original algorithm.