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A backup system ought to be able to handle several scenarios including file deletion, theft, natural disaster and file corruption. [http://en.wikipedia.org/wiki/Data_loss]

In terms of file corruption, the obvious way to check whether a backup is adequate is with a file checksum. If the backup is corrupted, the chance that the backup matches with the original is negligible (unless of course the original is corrupted as well, but let's assume it is not). Is it possible for a checksum comparison to fail to detect file corruption?

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It is possible for a checksum comparison to fail to detect file corruption, but it's very unlikely. The corrupted file would need to produce the same checksum as the original. If the checksum produces an n-bit value, the probability of a false negative is 2-n. (I'm assuming that you're trying to detect random failures, not purposeful tampering.)

So even a simple 32-bit checksum has only a 10-10 (approximately) probability of false negatives.

See section 12.5 of Information Theory, Inference, and Learning Algorithms for detailed explanations of the limits of error detection using checksums.

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