Chapter 10: Processes of Perception and Analysis

Section 10: Cryptography and Cryptanalysis

Linear feedback shift registers

See notes on pages 974 and 1084. LFSR sequences are widely used in radio technology, particularly in the context of spread spectrum applications. Their purpose is usually to provide a way to distinguish or synchronize signals, and sometimes to provide a level of cryptographic security. In CDMA technology for cellular telephones, for example, data is overlaid on LFSR sequences, and sequences other than the one intended for a particular receiver seem like noise which can be ignored. As another example, the Global Positioning System (GPS) works by having 24 satellites each transmit maximal length sequences from different length 10 LFSRs. Position is deduced from the arrival times of signals, as determined by the relative phases of the LFSR sequences received. (GPS P-code apparently uses much longer LFSR sequences and repeats only every 267 days. Before May 2000 it was used to add unpredictable timing errors to ordinary GPS signals.)

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From Stephen Wolfram: A New Kind of Science [citation]