Linear feedback shift registers (LFSRs) are used in manystream ciphers because of their maximal period and good statistical prop-erties. Due to the linearity of the LFSR, its output cannot be directlyused as the keystream. Dierent methods have been proposed to intro-duce the nonlinearity to the LFSR output. Irregular clocking is one ofthe methods to do this but the stream ciphers based on this method, arevulnerable to the side-channel attacks. In addition, the generation rate ofthe irregular clocked LFSRs is less than the corresponding regular ones.Jumping is a method of irregular clocking for LFSRs which may havenon of the mentioned aws but its output period cannot be determined.In this paper, using the jumping LFSRs, some new primitives will beproposed. Structures of the new primitives have the determined lowerbound of period and the resistance against the side-channel attacks. Insome of the proposed structures, the lower bound of period can be de-termined without knowledge of the jump index. These structures areapplicable when the calculation of the jump index is infeasible. The pro-posed structures can be used as primitives to design the software orientedand hardware oriented stream ciphers.