Filter Generator

Related Concepts

Boolean Functions; Combination Generator; Linear Feedback Shift Register; Stream Cipher

Definition

A filter generator is a running-key generator for stream cipher applications. It consists of a single linear feedback shift register (LFSR) which is filtered by a nonlinear function. More precisely, the output sequence of a filter generator corresponds to the output of a nonlinear function whose inputs are taken from some stages of the LFSR. If ${({u}_{t})}_{t\geq 0}$ denotes the sequence generated by the LFSR, the output sequence ${({s}_{t})}_{t\geq 0}$ of the filter generator is given by

$${s}_{t} = f({u}_{t+{\gamma }_{1}},{u}_{t+{\gamma }_{2}},\ldots, {u}_{t+{\gamma }_{n}}),\qquad \forall t \geq 0$$

where $f$ is a function of $n$ variables, $n$ is less than or equal to the LFSR length, and ${({\gamma }_{i})}_{1\leq i\leq n}$ is a decreasing sequence of nonnegative integers called the tapping sequence.

Theory

In order to obtain a keystream sequence having...