QUESTION $2$

a$)$ Write your UB number as a $32-$bit vector by converting each digit in the number into a $4-$bit binary number $($see example below$).$ This will be the plaintext for this question.

$[2$ marks$]$

$\backslash$table$[[$UB number:,$0,8,0,1,2,3,5,2],[$Bit vector:,$0000,1000,0000,0001,0010,0011,0101,0010]]$

b$)$ Write out the first $32$ bits of the output sequence produced by the linear feedback shift register $R_1=($:$4,1+D+D^3$:$)$ with initial state $1,0,0,1.($Hint: the sequence has period $7.)[6$ marks$]$

c$)$ The keystream for the synchronous stream cipher in figure $1$ is generated by an alternating step generator, with $R_1$ being the LFSR from part $b)$ above, $R_2$ produces an infinite output sequence of period $6$ with cycle $1,0,0,1,1,1,$ and $R_3$ produces an infinite output sequence of period $5$ with cycle $1,1,0,0,1.$ Write out the first $32$ bits of the keystream.

$[10$ marks$]$

Figure $1$: Synchronous stream cipher

d$)$ Write out the ciphertext that results from encrypting the bit vector you constructed as your answer to part a$)$ using the synchronous stream cipher in figure $1.$

$[2$ marks$]$