Users A and B want to use the Diffie$-$Hellman system to fix a common key over a public channel. They use

F$2[$x$]/($x$^10+$ x$^3+1)$ as representation of GF$(2^10).$ User B makes cB $=0100010100$ public, which stands for

the field element x $+$ x$5^+$ x$^7.$ If mA $=2,$ what will be the common key that A and B use for their

communication