Generation of Cryptographic Sequences by means of Difference Equations

In the present work, it is shown that the sequences obtained from cryptographic generators based on decimation are just particular solutions of a kind of linear difference equations. Moreover, all these sequences are simple linear combinations of a class of basic sequences (binomial sequences). Cryptographic parameters of decimated sequences, e.g. period, linear complexity or balancedness, can be analyzed in terms of solutions to linear equations. In brief, difference equations are useful tools for the generation of new cryptographic sequences with application in stream ciphers.