To improve the security of an LFSR-based stream cipher it has been suggested to use two LFSRs and combine their outputs using a non-linear logic gate (e.g., AND gate) to generate the next bit of the key stream. Check the potential benefits of this scheme using two LFSR with the polynomial x^3 +x+1 (a primitive polynomial with a length 7 sequence): one with the initial state c0,c1,c2=001 (i.e, it will first produce the output 0) and the second with the initial state 110. What will be the length of the sequence at the output of AND gate: What is the probability of a key bit (output of the AND gate) being 1? Write it as a fraction like 4/7. Repeat the above for an OR gate: length of sequence is and probability of key bit=1 is Would you recommend at least one of these schemes? Write Y or N

To improve the security of an LFSR-based stream cipher it has been suggested to use two LFSRs and combine their outputs using a nonlinear logic gate (e.g., AND gate) to generate the next bit of the key stream. Check the potential benefits of this scheme using two LFSR with the polynomial x3+x+1 (a primitive polynomial with a length 7 sequence): one with the initial state c0,c1,c2=001 (i.e, it will first produce the output 0 ) and the second with the initial state 110 . What will be the length of the sequence at the output of AND gate: What is the probability of a key bit (output of the AND gate) being 1 ? Write it as a fraction like 4/7. Repeat the above for an OR gate: length of sequence is and probability of key bit=1 is Would you recommend at least one of these schemes? Write Y or N