Rule 30

Abstract: Visual cryptography depends on two shares. The initial configuration, extra security bits and the number of the rule for the CA along with the number of computed steps serve as a password for a visually encrypted image. The second share could contain a predefined pattern; the developed algorithm uses a snapshot of a CA after a certain number of steps to generate the predefined share. Only one of these shares has to be random. The developed encryption system is a hybrid between visual and classical cryptographic approaches. It requires less storage space compared to a standalone visual encryption system and relies on Rule 30’s tested statistically significant randomness.

Abstract: At row 2n in the cellular automaton rule 30, a region of the initial condition reappears on the right side, which causes the automaton to “begin again” locally. As a result, local nested structure is produced. This phenomenon is ultimately due to the property that rule 30 is reversible in time under the condition that the right half of each row is white. The main result of the paper establishes the presence of local nested structure in k-color rules with this bijectivity property, and we explore a class of integer sequences characterizing the nested structure. We also prove an observation of Wolfram regarding the period length doubling of diagonals on the left side of rule 30.

Abstract: This article mainly describes a way of designing an efficient pseudo-random number generator. Combining that the cellular automaton has many characteristics, such as simple rules of the component units, the local connectivity of units, the high degree of parallelism in information processing, and the complicated global characteristics, we use the rule 30 of one-dimensional cellular automaton to drive the state change. Finally, the pseudo-random numbers produced from the generator are tested the performance. And the results show that this design can be better applied to cryptography to ensure information technology and network security[1].

Abstract: The goal of this thesis is the investigation of Cellular Automata (CA) from the perspective of Boolean functions and combinatorial designs. Beside its theoretical interest, this research finds its motivation in cryptography, since Boolean functions and combinatorial designs are used to construct Pseudorandom Number Generators (PRNG) and Secret Sharing Schemes (SSS). The results presented in the thesis are developed along three research lines, organized as follows. The first line considers the use of heuristic optimization algorithms to search for Boolean functions with good cryptographic properties, to be used as local rules in CA-based PRNG. The main motivation is to improve Wolfram's generator based on rule 30, which has been shown to be vulnerable against two cryptanalytic attacks. The second line deals with vectorial Boolean functions induced by CA global rules. The first contribution considers the period of preimages of spatially periodic configurations in surjective CA, and analyze the cryptographic properties of CA global rules. The third line focuses on the combinatorial designs generated by CA, specifically considering Orthogonal Latin Squares (OLS), which are equivalent to SSS. In particular, an algebraic characterization of OLS generated by linear CA is given, and heuristic algorithms are used to build OLS based on nonlinear CA.