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From: Stephen Wolfram, A New Kind of Science
Notes for Chapter 10: Processes of Perception and Analysis
Section: Cryptography and Cryptanalysis
Page 1085

History [of cryptography]. Cryptography has been in use since antiquity, and has been a decisive factor in a remarkably large number of military and other campaigns. Typical of early systems was the substitution cipher of Julius Caesar, in which every letter was cyclically shifted in the alphabet by three positions, with A being replaced by D, B by E, and so on. Systems based on more arbitrary substitutions were in use by the 1300s. And while methods for their cryptanalysis were developed in the 1400s, such systems continued to see occasional serious use until the early 1900s. Ciphers of the type shown on page 599 were introduced in the 1500s, notably by Blaise de Vigenère; systematic methods for their cryptanalysis were developed in the mid-1800s and early 1900s. By the mid-1800s, however, codes based on books of translations for whole phrases were much more common than ciphers, probably because more sophisticated algorithms for ciphers were difficult to implement by hand. But in the 1920s electromechanical technology led to the development of rotor machines, in which an encrypting sequence with an extremely long period was generated by rotating a sequence of noncommensurate rotors. A notable achievement of cryptanalysis was the 1940 breaking of the German Enigma rotor machine using a mixture of statistical analysis and automatic enumeration of keys. Starting in the 1950s, electronic devices were the primary ones used for cryptography. Linear feedback shift registers and perhaps nonlinear ones seem to have been common, though little is publicly known about military cryptographic systems after World War II. In 1977 the U.S. government introduced the DES data encryption standard, and in the 1980s this became the dominant force in the growing field of commercial cryptography. DES takes 64-bit blocks of data and a 56-bit key, and applies 16 rounds of substitutions and permutations. The S-box that implements each substitution works much like a single step of a cellular automaton. No fast method of cryptanalysis for DES is publicly known, although by now for a single DES system an exhaustive search of keys has become feasible. Two major changes occurred in cryptography in the 1980s. First, cryptographic systems routinely began to be implemented in software rather than in special-purpose hardware, and thus became much more widely available. And second, following the introduction of public-key cryptography in 1975, the idea emerged of basing cryptography not on systems with complicated and seemingly arbitrary construction, but instead on systems derived from well-known mathematical problems. Initially several different problems were considered, but after a while the only ones to survive were those such as the RSA system discussed below based essentially on the problem of factoring integers. Present-day publicly available cryptographic systems are almost all based on variants of either DES (such as the IDEA system of PGP), linear feedback shift registers or RSA. My cellular automaton cryptographic system is one of the very few fundamentally different systems to have been introduced in recent years.

Stephen Wolfram, A New Kind of Science (Wolfram Media, 2002), page 1085.
© 2002, Stephen Wolfram, LLC