we use the indistinguishability notion to prove that, despite the substantially high bound for ITS, the WCA scheme with an ${\varepsilon}'$-perfect key is indistinguishable from the ideal authentication, except with probability ${\varepsilon}+{\varepsilon}'$. As a natural consequence, Universally Composable (UC) security of the WCA scheme with an ${\varepsilon}'$-perfect key directly follows from our proof of indistinguishability.

(-2.6,0) node\[fill=black!10,minimum width=2cm,minimum height=.8cm\]; (2.6,0) node\[fill=black!10,minimum width=2cm,minimum height=.8cm\]; (-3,0) node\[draw,minimum width=1cm,fill=white\](a) [Alice]{}; (3,0)node\[draw,minimum width=1cm,fill=white\](b) [Bob]{}; (0, 0)node\[draw,minimum width=3cm,fill=white\](f) [${\mathcal{F}}$]{}; (a) to node\[above\][$m$]{} (f); ($(f.south)+(-1,0)$) to\[bend right=45\] node\[below left\][$m$]{} ++(.5,-.5); ($(f.south)+(-1,0)$)++(.5,-.5) to ++(1,0); ($(f.south)+(-1,0)$)++(.5,-.5)++(1,0) to\[bend right=45\] node\[below right\][$m'$]{} ($(f.south)+(1,0)$); (f) to node\[above\][$m,\bot$]{} (b);

(-2,0) node\[fill=black!10,minimum width=3cm,minimum height=.8cm\]; (2,0) node\[fill=black!10,minimum width=3.1cm,minimum height=.8cm\]; (-3,0) node\[draw,minimum width=1cm,fill=white\](a) [Alice]{}; (3,0)node\[draw,minimum width=1cm,fill=white\](b) [Bob]{}; (0, 1)node\[draw,rounded rectangle, minimum width=1.3cm\](k) [Key]{}; (-1,0)node\[draw,rectangle,minimum width=1cm,fill=white\](T) [TAG]{}; (1,0)node\[draw,rectangle,minimum width=1cm,fill=white\](V) [VRFY]{}; (0,.5) node\[draw,dotted,minimum width=3cm,minimum height=1.7cm\] +(1.2,.75)node[WCA]{}; (a) to node\[above\][$m$]{} (T); (T.south) to\[bend right=45\] node\[below left\][$(m,t)$]{} ++(.5,-.5); (T.south)++(.5,-.5) to ++(1,0); (T.south)++(.5,-.5)++(1,0) to\[bend right=45\] node\[below right\][$(m',t')$]{} (V.south); (V) to node\[above\][$m',\bot$]{} (b); (k.south) to node\[above right,at end\][$k$]{} (T.north); (k.south) to node\[above left,at end\][$k$]{} (V.north);

The ideal functionality of authentication, an *authentic* channel ${\mathcal{F}}$, connects Alice and Bob in such a way that Bob can be certain that any message output from the channel was sent by Alice. If the message 