On Generalization of Geffe's Generator

Summary We present a new construction of a pseudorandom generator based on a simple combination of q+1 LFSRs over GF(q), which is a generalization of Geffe’s generator is presented by P. R. Geffe. The construction has attractive properties as simplicity (conceptual and implementation-wise), scalability (hardware and security), proven minimal security conditions (period, linear complexity). In order to resist Siegenthaler's correlation attack, we introduce a new shrinking generator (called Geffe’s shrinking generator) over GF(q), a conjecture for period of Geffe’s shrinking generator is proposed.