Prove that $\{0,1\}$

$\backslash$lambda

is a group with respect to the xor operator. What is the identity

element, and what is the inverse of a value x in $\{0,1\}$

$\backslash$lambda

$?$

$($b$)$ Fill in the details of the Dec algorithm and prove $($using the group axioms$)$ that the

scheme satises correctness.

$($c$)$ Prove that the scheme satises one$-$time secrecy