Linear feedback shift register
A linear feedback shift register is a shift register whose input is the exclusive-or of some of its outputs. The outputs that influence the input are called taps. A maximal LFSR produces an n-sequence, unless it contains all zeros. The tap sequence of an LFSR can be represented as a polynomial mod 2 - called the feedback polynomial. For example, if the taps are at positions 17 and 15 (as below), the polynomial is
. If this polynomial is primitive, then the LFSR is maximal.
LFSR's can be implemented in hardware, and this makes them useful in applications that require very fast generation of a pseudo-random sequence, such as direct-sequence spread spectrum radio.
LFSRs have long been used as a pseudo-random number generator for use in stream ciphers (especially in military cryptography), due to the ease of construction from simple electromechanical or electronic circuits, long periodss, and very uniformly distributed outputs. However the outputs of LFSRs are completely linear, leading to fairly easy cryptanalysis. Three general methods are employed to reduce this problem in LFSR based stream ciphers:
- Non-linear combination of several bits from the LFSR state;
- Non-linear combination of the outputs of two or more LFSRs; or
- Irregular clocking of the LFSR.
