On Equivalence with Output Sequence of Grain Model

Grain is one of the hardware-oriented finalists of the eSTREAM. A generalized definition of all Grain-like stream ciphers is proposed in this paper, namely Grain Model. We construct equivalent sequences to the outputting and structures to the model, not only in key generation phase but also in initialization phase. A design proposal on tap selection and some particular properties, such us shift equivalence, one-to-one correspondence, et al. are also proposed.