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We don't say this can't happen, we just say it won't happen. The only value that will decrypt to $p_2$ under $(e_2,n_2)$ is $p_2^{d_2}$, which we can call $s_2$. So, your problem comes down to asking what is the probability that $s_1=s_2$? If we assume that they're random, and that the moduli are similar enough sizes that this is even a realistic ...

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The Wikipedia article points out a good reason for using a random challenge value: preventing replay attacks. If the hash was always the same (as the hash of the symmetric key would be), then having listened in on one challenge-response cycle, a malicious listener could pass further handshake tests.

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Some devices I've been working with do indeed update biometric information. The reasons is that there may be additional information: acceptable fingerprint was scanned (required features are found), but the scan shows some area of finger not involved in previous scans. some other additional information helping make more exact scans in the future

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