Q$2$: As shown in the figure below, suppose Eve intercepts the ciphertext $c=(11111011000001{)}_2$ from Alice to Bob. She knows that the plaintext begins with $m=(1100$dots${)}_2.$

$[6$ points$]$

a$.$ Eve suspects that a stream cipher is implemented with LCG generator, and it is generated by a recursive formula: $S_{i+1}-=5S_i+1$mod$16.$ If that's the case, show how Eve can break the cipher and determine the remaining plaintext, i$.$e$.,$ the remaining $10$ bits.

a$.$ On second thought, Eve thinks a stream cipher is implemented using an LFSR using the polynomial: $P(x)=x^3+x^2+1.$ If that's the case what would be the plaintext?