I’m just seeking a better understanding as to the logic behind design of the A5/1 cipher’s keystream generator. Why are the registers degree chosen in such a fashion (19,22 and 23 bits long respectively)? I have heard because they are co-prime but have little understanding how this may influence the system.
The reason I ask this is because I was asked a question today relating to a hypothetical stream cipher key-stream generator with 2 LFSRs, 17 bits and 25 bits in length respectively, with a 40 bit key input. I was needing to explain why these register sizes were chosen over something like a 7 bit and 35 bit register pair or two 21 bit registers but couldn’t find an appropriate line of reasoning.