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The Coursera course on Cryptography 1 has a section about Carter-Wegman MAC. Here is the image of slide: enter image description here

Now my question is both $F$ and $S$ output $n$-bit strings. We XOR two $n$-bit strings and we should get an $n$-bit string as a result. But the slide says the output result is a $2n$-bit string. How is this possible?

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The MAC consists of the pair of the n-bit random value $r$ and the n-bit value $t = F(k_1,r) \oplus S(k_2,m)$. The length of $(r,t)$ is at least $2n$ bits, partly depending on how it is encoded. If the two values are simply concatenated, the total length is $2n$, as stipulated.

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    $\begingroup$ I forgot the point that the sender should send that random number r. $\endgroup$ – Majid Azimi May 11 '16 at 9:39

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