Linear Feedback Shift Registers (LFSRs) are the basic components of many running-key generators for stream cipher applications, because they are appropriate to hardware implementation and they produce sequences with good statistical properties. LFSR refers to a feedback shift register with a linear feedback function (see Nonlinear FeedbackShift Register).
An LFSR of length L over F q (see finite field) is a finite state automaton which produces a semi-infinite sequence of elements of F q, \( {\bf s} =(s_t)_{t \geq 0} = s_0 s_1{\ldots} \) , satisfying a linear recurrence relation of degree L over F q
The L coefficients \( c_1,{\ldots}\,,c_L \) are elements of F q. They are called the feedback coefficients of the LFSR.
An LFSR of length L over F q has the following form:
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References
Golomb, S.W. (1982). Shift Register Sequences. Aegean Park Press, revised edition.
Lidl, R. and H. Niederreiter (1983). Finite Fields. Cambridge University Press, Cambridge.
Rueppel, R.A. (1986). Analysis and Design of, Stream Ciphers. Springer-Verlag, Berlin.
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Canteaut, A. (2005). Linear Feedback Shift Register. In: van Tilborg, H.C.A. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA . https://doi.org/10.1007/0-387-23483-7_235
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