Abstract
Nonlinear feedback shift registers (NFSRs) are used in many stream ciphers as their main building blocks. In particular, Galois NFSRs with terminal bits are used in typical stream ciphers Grain and Trivium. Seven types of Galois NFSRs have been found equivalent to Fibonacci ones, among which three types are particular cases of another type of lower triangular Galois NFSRs. This paper continues the research of equivalence between Galois NFSRs and Fibonacci ones. It first enumerates the Galois NFSRs with terminal bits that are equivalent to a Fibonacci NFSR. It then discloses n-stage (n−2)-terminal-bit Galois NFSRs equivalent to Fibonacci ones, must be lower triangular Galois NFSRs. Finally, it presents two new types of Galois NFSRs that are equivalent to Fibonacci NFSRs. Some examples show that, compared to a Fibonacci NFSR, its equivalent Galois NFSR from our new types may decrease the area and increase the throughput of the circuits implementing feedback functions.
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