Matrix Approach of an Encryption System Based on Cellular Automata and Its Numerical Implementation

Abstract

The main components of an encryption system based on rule 90 cellular automata, i.e., two indexed families of permutations and a pseudo-random bit generator are implemented in a very flexible way through a convenient matrix approach.

Design and Implementation of a Configurable Encryption System for Power-Constrained Devices

“…The word m is obtained iterating forward in time employing as inputs x and c, and corresponds to the indexed family Φ t . On the other hand, word t is generated iteratively backward in time using x and y, and correspond to the function t = h(x, y) [25], [27]. A simpler version to implement a BUC is the one-time algorithm, in which these words are calculated using the XOR sum of only the required elements.…”

“…In addition, a substitution box (S-box) based on the cellular automata rule-90 [30], was added to confer greater security to the system. In [27], an ESCA system matrix approach was proposed to have a simple implementation when larger block sizes are required, and is the notation used in this work. The encryption procedure starts with the pre-processing stage, where the plain-text is transformed to an unintelligible form; afterwards, the S-box applies a non-linear transformation; finally, the data are encrypted with permutation Ψ, and the key is generated to be employed in the permutation.…”

“…The key t of N elements and plain-text m of J elements, are multiplied by the matrices P N and Q N respectively, and then added to complete the transformation. Matrix P N has dimensions of J × N and is generated by applying a zero-fill right shift of one position to the previous row, from the first row whose components in position j = (2 n + 1) − 2 i+1 for i = 0, 1, 2, ..., (n − 1) are equal to 1 and the rest are equal to 0 [27]. The matrix Q N has dimensions of J × J and is generated as if it were a grid of CA by applying the 90 rule, with zeros as boundary conditions and taking the first row as q = [q 1 , 0, ..., 0], where q 1 = 1 [27].…”

“…In this paper, we propose a configurable ASIC implementation of the ESCA system. The fundamental transformations are built around additive CA rules [26], [27], which makes them suitable for hardware implementations. The implemented system allows a trade-off between power consumption and security level, depending on the needs, by disabling selected modules and reusing hardware.…”

A highly nonlinear S-box based on a fractional linear transformation

“…In the last few years many efficient algorithm have been presented by the researchers regarding secure image encryption schemes (Bao and Zhou 2015 ; Gao and Chen 2008 ; Murguia et al. 2012 ; Ramirez-Torres et al. 2014 ; Vargas-Olmos et al.…”