On the calculation of the linear equivalence bias of jump controlled linear finite state machines

Jump controlled linear finite state machines were introduced several years ago as building blocks for stream ciphers that can efficiently be implemented in hardware and have intrinsically good side channel resistance. These constructions have found their way in concrete stream cipher designs. The bias in the distribution of linear relations of low degree in the key stream is important for the cryptographic strength of these stream ciphers. Recently, an algorithm was presented by the author to determine this bias. In this paper a new algorithm is introduced, that makes use of the properties of jump registers and has sub exponential order in the degree of the characteristic polynomial of the linear finite state machine.