Algebraic normal form for rapid prototyping of elementary hybrid cellular automata in FPGA

Abstract

This paper introduces a methodology based on algebraic normal form representations and software tools to rapidly generate the VHDL code description of elementary hybrid cellular automata with arbitrary parameters. Such parameters include the CA local rule, the number of cells and the mask, which is specific for hybrid CA. This tool allows rapid synthesis of various CA types, as they are required by various applications. Synthesis, post-place and route and functional simulation are given for a specific case of a random number generator to prove the functionality of our software tools. IndexTerms-cellular automata, Boolean functions, algebraic normal form, Reed-Muller codes, VHDL, FPGA.

Efficient and cryptographically secure pseudorandom number generators based on chains of hybrid cellular automata maps

“…As shown previously [12] in FPGA implementations, one HCA cell is allocated to only one basic logical element.…”

“…As shown in [10,12] an algebraic normal form representation can be associated with each particular ID, the algebraic normal form having several advantages such as: i) it provides a simple and efficient way for hardware description; ii) clearly shows whether a cell is linear or not -a linear cell has only 1'st degree terms.…”

Survey on hardware implementation of random number generators on FPGA: Theory and experimental analyses

“…The FPGA implementation of each CA is done with a logic combinational circuit (LCC) to define the rules. Then it uses LCG to control the loading operation of the CA and stores the data into a D flip-flop.Authors of[59], for their part, create an automatic software tool to generate the RTL code of any HCA configuration. Finally, in[60], authors increase the ratio of frequency/area and the security of their previous PRNG[59] by using a chain of HCAs instead of a single one.…”