n12 - CS 70 Discrete Mathematics for CS Spring 2008 David...

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Unformatted text preview: CS 70 Discrete Mathematics for CS Spring 2008 David Wagner Note 12 Fingerprinting Suppose we just finished transmitting an enormous file to the Moon. Wed like to verify that our file got there correctly, without any errors. We could of course re-send the file a second time, but bandwidth to the Moon is hard to come by, so this would take a long time. Itd be nice to have a better solution. So, the problem is this: if we have a n-bit bitstring s on Earth, and a n-bit bitstring s on the Moon, how can we efficiently verify that s = s ? We will measure the efficiency of a solution by the number of bits that need to be sent between the Earth and Moon to finish this task. We will assume that the Earth and Moon have a reliable but low-bandwidth channel that they can use to communicate. The approach The gist of our idea is for the Earthlings to compute a short fingerprint of their data, and then send that fingerprint to the Moon. The Moon can compute the fingerprint of their own copy of the data and check that it matches the fingerprint received from the Earth. We will denote the fingerprint of data s by F ( s ) , so the Earth computes F ( s ) and sends F ( s ) to the Moon; the Moon computes F ( s ) ; and then the Moon checks whether F ( s ) = F ( s ) . If there is a mismatch in the fingerprints ( F ( s ) negationslash = F ( s ) ), then we can conclude that the two endpoints do not have the same data ( s negationslash = s ). If the two fingerprints do match ( F ( s ) = F ( s ) ), what can we conclude? In this case, there is no guarantee that the two endpoints definitely have the same data. Since we want the fingerprint F ( s ) to be shorter than the data s , the function F ( ) cannot possibly be one-to-one (injective), so it is possible that...
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This note was uploaded on 04/09/2008 for the course CS 70 taught by Professor Papadimitrou during the Spring '08 term at University of California, Berkeley.

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n12 - CS 70 Discrete Mathematics for CS Spring 2008 David...

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