Abstract
Nonlinear feedback shift registers (NFSRs) are used in many stream ciphers as their main building blocks. One security criterion for the design of stream ciphers is to assure the output sequences of their used NFSRs have long periods. The periodicity of those sequences are guaranteed by the NFSRs’ nonsingularity. The nonsingularity is well solved for Fibonacci NFSRs, whereas it is not for Galois ones. This paper considers the nonsingularity of Galois NFSRs. Some necessary conditions are presented, first for general Galois NFSRs, and then for submaximum and maximum length Galois NFSRs. Moreover, both particular Galois NFSRs are enumerated. All these extend the known results for Fibonacci NFSRs into Galois ones.
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