The authors' contributions are applying distinguishing attack on linearly filtered NLFSR as a primitive or associated with filter generators. They extend the attack on linear combinations of linearly filtered NLF- SRs as well. Generally, these structures can be examined by the proposed techniques and the criteria will be achieved to design secure primitive. The attacks allow attacker to mount linear attack to distinguish the output of the cipher and recover its internal state. Also, they investigate security of the modified version of grain stream cipher to present how invulnerable is the scheme against distinguishing attacks.