Abstract
Consider the following problem. A and B each have a N-element set of bit-strings. They wish to find all collisions, in other words to find the common strings of their sets or to establish that there are none. How much data must A and B exchange to do this?
Problems of this type arise in the context of Merkle puzzles, for example where A and B propose to use the collision between two randomly constructed lists to construct a cryptographic key.
Here we give a protocol for finding all the collisions. Provided the number of collisions is small relative to N/ log2 N the protocol requires on the order of log2 N messages and the total amount of data which A and B need exchange is about 4.5N bits. The collision set can also be determined in three messages containing a total of at most 9N bits provided N < 21023.
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© 2002 Springer-Verlag Berlin Heidelberg
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Christianson, B., Wheeler, D. (2002). Merkle Puzzles Revisited — Finding Matching Elements between Lists. In: Christianson, B., Malcolm, J.A., Crispo, B., Roe, M. (eds) Security Protocols. Security Protocols 2001. Lecture Notes in Computer Science, vol 2467. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45807-7_13
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DOI: https://doi.org/10.1007/3-540-45807-7_13
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