Cryptanalysis of the "grain" family of stream ciphers

Let us have an NLFSR with the feedback function g(x) and an LFSR with the generating polynomial f(x). The function g(x) is a Boolean function on the state of the NLFSR and the LFSR, at any time instance t. Whenever the LFSR has good statistical properties, it is used for controlling the randomness of the NLFSR's state machine. In this paper we define and study the general class of "Grain" family of stream ciphers, where the keystrearn bits are generated by another Boolean function h(y) on the states of the NLFSR and the LFSR. We show that the cryptographic strength of this family is related to the general decoding problem, when a key-recovering attack is considered. A proper choice of the functions f