Computing Aggregate Properties of Preimages for 2D Cellular Automata

Computing properties of the set of precursors of a given configuration is a common problem underlying many important questions about cellular automata. Unfortunately, such computations quickly become intractable in dimension greater than one. This paper presents an algorithm --- incremental aggregation --- that can compute aggregate properties of the set of precursors exponentially faster than na{\"i}ve approaches. The incremental aggregation algorithm is demonstrated on two problems from the two-dimensional binary Game of Life cellular automaton: precursor count distributions and higher-order mean field theory coefficients. In both cases, incremental aggregation allows us to obtain new results that were previously beyond reach

An optimized 128-bit cellular automata-based hash function for authentication of data at rest and in transit

The cryptographic hash functions are the most fundamental cryptographic concept. These functions are used as basic building blocks for digital signatures and message authentication. Boolean functions are the core of hash functions. These functions are expected to provide pseudo-randomness as well as input sensitivity. Cellular automata are a form of Boolean function that exhibits strong cryptography properties as well as chaotic behavior. This paper proposes a hash function, designed on the principle of cellular automata. The proposed algorithm is secure and meets the requirements for a successful hashing scheme. The hash function has strong statistical and cryptographic characteristics, according to the findings of the avalanche test and the National Institute of Standards and Technology (NIST) Statistical Test Suite. The modularity of different operations of this algorithm makes it suitable for a high-capacity processing environment to produce efficient performance

Fast, parallel and secure cryptography algorithm using Lorenz's attractor

A novel cryptography method based on the Lorenz's attractor chaotic system is presented. The proposed algorithm is secure and fast, making it practical for general use. We introduce the chaotic operation mode, which provides an interaction among the password, message and a chaotic system. It ensures that the algorithm yields a secure codification, even if the nature of the chaotic system is known. The algorithm has been implemented in two versions: one sequential and slow and the other, parallel and fast. Our algorithm assures the integrity of the ciphertext (we know if it has been altered, which is not assured by traditional algorithms) and consequently its authenticity. Numerical experiments are presented, discussed and show the behavior of the method in terms of security and performance. The fast version of the algorithm has a performance comparable to AES, a popular cryptography program used commercially nowadays, but it is more secure, which makes it immediately suitable for general purpose cryptography applications. An internet page has been set up, which enables the readers to test the algorithm and also to try to break into the cipher in

Programs as Polypeptides

We describe a visual programming language for defining behaviors manifested by reified actors in a 2D virtual world that can be compiled into programs comprised of sequences of combinators that are themselves reified as actors. This makes it possible to build programs that build programs from components of a few fixed types delivered by diffusion using processes that resemble chemistry as much as computation.Comment: in European Conference on Artificial Life (ECAL '15), York, UK, 201

Building Secure and Fast Cryptographic Hash Functions Using Programmable Cellular Automata

Cryptographic hash functions have recently brought an exceptional research interest. With the increasing number of attacks against the widely used functions as MD5, SHA-1 and RIPEMD, the need to consider new hash functions design and conception strategies becomes crucial. In this paper, we propose a fast and efficient hash function using programmable cellular automata that are very suitable for cryptographic applications due to their chaotic and complex behavior derived from simple rules interaction. The proposed function is evaluated using several statistical tests, while obtained results demonstrate very admissible cryptographic properties such as confusion/diffusion capability and high sensitivity to input changes. Furthermore, the hashing scheme can be easily implemented through software or hardware, so it provides very competitive running performances

Investigations of cellular automata-based stream ciphers

In this thesis paper, we survey the literature arising from Stephan Wolfram\u27s original paper, “Cryptography with Cellular Automata” [WOL86] that first suggested stream ciphers could be constructed with cellular automata. All published research directly and indirectly quoting this paper are summarized up until the present. We also present a novel stream cipher design called Sum4 that is shown to have good randomness properties and resistance to approximation using linear finite shift registers. Sum4 is further studied to determine its effective strength with respect to key size given that an attack with a SAT solver is more efficient than a bruteforce attack. Lastly, we give ideas for further research into improving the Sum4 cipher

OPRACOWANIE I BADANIA KRYPTOGRAFICZNYCH FUNKCJI SKRÓTU (HASH) NA PODSTAWIE DWUWYMIAROWYCH AUTOMATÓW KOMÓRKOWYCH

Software solution for cryptographic hash functions based on sponge construction with inner state implemented as two-dimensional cellular automata (CA) has been developed. To perform pseudorandom permutation in round transformation function several combinations of CA rules 30, 54, 86, 150 and 158 have been proposed. The developed hashing mechanism provides effective parallel processing, ensures good statistical and scattering properties, enables one to obtain hash of a varying length and reveals strong avalanche effect.Za pomocą oprogramowania zostały opracowane kryptograficzne funkcje skrótu (hash) na podstawie gąbki kryptograficznej, której stan wewnętrzny został zrealizowany w postaci dwuwymiarowych automatów komórkowych (KA). W celu implementacji permutacji pseudolosowych zaproponowano kombinację zasad obróbki CA 30, 54, 86, 150 i 158 w celu realizacji funkcji transformacji rundy. Opracowany mechanizm haszowania pozwala na skuteczne przetwarzanie równoległe, zapewnia jakościowe charakterystyki statystyczne i rozproszenia, pozwala na otrzymanie skrótu o zmiennej długości i ujawnia stabilny efekt lawinowy

Revisiting LFSMs

Linear Finite State Machines (LFSMs) are particular primitives widely used in information theory, coding theory and cryptography. Among those linear automata, a particular case of study is Linear Feedback Shift Registers (LFSRs) used in many cryptographic applications such as design of stream ciphers or pseudo-random generation. LFSRs could be seen as particular LFSMs without inputs. In this paper, we first recall the description of LFSMs using traditional matrices representation. Then, we introduce a new matrices representation with polynomial fractional coefficients. This new representation leads to sparse representations and implementations. As direct applications, we focus our work on the Windmill LFSRs case, used for example in the E0 stream cipher and on other general applications that use this new representation. In a second part, a new design criterion called diffusion delay for LFSRs is introduced and well compared with existing related notions. This criterion represents the diffusion capacity of an LFSR. Thus, using the matrices representation, we present a new algorithm to randomly pick LFSRs with good properties (including the new one) and sparse descriptions dedicated to hardware and software designs. We present some examples of LFSRs generated using our algorithm to show the relevance of our approach.Comment: Submitted to IEEE-I