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Hasttte avatar Crypto

Mifare Classic, authentification protocol question

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Hasttte

Thanks to reverse engineering papers on Mifare Classic, one can study the authentication protocol. However, I have a problem understanding how it works.

In the above document, after the reader responds with $\{n_R\}$ $\{a_R\}$, the tag can now calculate $b_{32}$ (keystream) to $b_{63}$ (thanks to $n_T$, $\text{uid}$ and the tag's key) so XOR it with $\{n_R\}$ to retrieve $n_R$. But how can we be sure that the $n_R$ is the same as the reader's?

The keys in the reader and the tag are not necessarily the same.

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fgrieu avatar Crypto
ng flag
fgrieu

How can we be sure that the $n_R$ is the same as the reader's?

What the tag can do is decipher $\{a_R\}$ and compare to the true $a_R$, which is a function of $n_T$ that the tag knows. If that check passes, which is highly improbable if the reader and tag keys do not match, the tag presumably assumes $\{n_R\}$ deciphers to the reader's $n_R$; I see no way that it can further check, given that $n_R$ is random.

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Hasttte avatar
gb flag
Hasttte
Oh i understand that's clever ! Thanks a lot ! Now let's go understand nested attacks
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