Nonlinear n-stage feedback shift-register sequences over the finite field F_g of period q~n — 1 are investigated under linear operations on sequences. We prove that all members of an easily described class of linear combinations of shifted versions of these sequences possess useful properties for cryptographic applications: large periods, large linear complexities and good distribution properties. They typically also have good maximum order complexity values as has been observed experimentally. A running key generator is introduced based on certain nonlinear feedback shift registers with modifiable linear feedforward output functions.
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