This question concerns the field GF$(256)$

$.$ The modulus is P$($x$)=$x$8+$x$4+$x$3+$x$+1$

$.$

Please answer the following questions about arithmetic in this field.

a$)$ If p$($x$)=$x$7+$x$5+$x$4+$x$3+$x$2+$x

$,$ what is the corresponding hexadecimal representation? Please prepend an $"0$x$"$ on your answer and use lowercase letters $($if letters occur$).$

b$)$ If p$($x$)=$x$7+$x$4+$x$3+$x$2+$x

$,$ what is the corresponding hexadecimal representation? Please prepend an $"0$x$"$ on your answer and use lowercase letters $($if letters occur$).$

c$)$ Consider the hex byte $0$x$26$

$.$ What is the corresponding element of GF$(256)($as a polynomial$)?$

d$)$ Consider the hex byte $0$x$5$c

$.$ What is the corresponding element of GF$(256)($as a polynomial$)?$