Representation of Symmetric Shift Registers
Provides a new theoretical foundation for analyzing symmetric shift registers, which is relevant to cryptography and coding theory, but the results are theoretical without concrete performance numbers.
The paper establishes a mathematical framework for symmetric shift registers over GF(2) by representing them as systems of nonlinear difference equations, using arithmetical progressions to clarify structures and simplify determination of minimal periods.
The objective of this work is to establish a mathematical framework for the study of symmetric shift registers over the field GF(2). The present paper gives a new approach where the symmetric shift registers are represented by associated systems of nonlinear difference equations. Arithmetical progressions will play a central part. This approach clarifies the underlying structures and makes it easier to determine the minimal periods of the sequences generated by the symmetric shift registers. Key words: Shift registers, nonlinear difference equations, periods, arithmetical progressions, GF(2).