We discuss nonlinear vectorial primitive recursive sequences. First we consider the nonlinearly filtered multiple-recursive matrix generator for producing pseudorandom vectors based on some nonlinear schemes and give lower bounds for their componentwise linear complexity. Moreover, we obtain certain results concerning the jump multiple-recursive matrix generator and establish that sequences generated by them have better period and componentwise linear complexity as compared to usual multiple-recursive matrix generator sequences. We also include analogous results for transformation shift registers for generating pseudorandom vectors.

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Cryptography and Communications
School of Mathematics and Statistics

Hasan, S.U. (Sartaj Ul), Panario, D, & Wang, Q. (2018). Nonlinear vectorial primitive recursive sequences. Cryptography and Communications, 10(6), 1075–1090. doi:10.1007/s12095-017-0265-2