Rule 30 cryptography
Rule 30 is known to have many of the properties desirable for practical cryptography. It does not repeat with any short period or show any obvious structure for almost all keys. Small changes in keys typically leads to large changes in the encrypting sequence. The Boolean expressions which determine the encrypting sequence from the key rapidly become highly complex (see page 618). And furthermore the system can be implemented very efficiently, particularly in parallel hardware.
I originally studied rule 30 in the context of basic science, but I soon realized that it could serve as the basis for practical random sequence generation and cryptography, and I analyzed this extensively in 1985. (Most but not all of the results from my original paper are included in this book, together with various new results.) In 1985 and soon thereafter a number of people (notably Richard and Carl Feynman) tried to cryptanalyze rule 30, but without success. From the beginning, computations of spacetime entropies for rule 30 (see page 960) gave indications that for strong cryptography one should not sample all cells in a column, and in 1991 Willi Meier and Othmar Staffelbach described essentially the explicit cryptanalysis approach shown on page 601. Rule 30 has been widely used for random sequence generation, but for a variety of reasons I have not in the past much emphasized its applications in cryptography.