Primitives Based on Jumping LFSRs with Determined Period

Linear feedback shift registers (LFSRs) are used in many stream ciphers because of their maximal period and good statistical properties. Due to the linearity of the LFSR, its output cannot be directly used as the keystream. Different methods have been proposed to utilize LFSRs in construction of stream ciphers. Jumping is one of these methods which is used in some stream ciphers like Mickey and Pomaranch but the period for this method cannot be generally determined. In this paper, using the jumping LFSRs, some new primitives are proposed. According to the properties of these new primitives, a lower bound for their period can be computed. In some of the proposed primitives, this lower bound can be determined without the knowledge of the jump index. These primitives are applicable when the calculation of the jump index is infeasible. The proposed primitives can be used as building blocks to design the software oriented and the hardware oriented stream ciphers.