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.
A Galois LFSR, or a LFSR in Galois configuration is a variation on typical LFSR design. In Galois configuration, the output is individually xor'ed with each tap, before becoming the new input. Galois LFSRs do not concatenate every tap to produce the new input, thus it is possible for each tap to be computed in parallel, increasing the speed of execution.
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: