6.897 Spring 2004
Homework 4
Handed out: 5/6/2004
Due: 5/12/2004 (last day of class!)

This homework problem relates to pairing-based cryptography;
see the readings available on the class web site.

Problem.
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Part A:

Give a careful definition of a "trapdoor pairing" (like a 
standard bilinear map except that the pairing can only be
computed if you have certain "trapdoor information").

Part B:

Give an application of trapdoor pairings.  (Try to make it
interesting...)

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NOTE: As far as I know, the notion of a trapdoor pairing
      doesn't (yet) exist in the literature...  Thus, this
      homework poses two "open problems".  If your solution
      is really good, maybe you can turn it into a 
      paper for Asiacrypt (submission deadline May 21st) or
      the Cryptography track of the RSA conference (submission
      deadline June 1st).  Of course, the obvious question I
      didn't ask here is: can you implement a trapdoor pairing?