[Busec] busec this week: Adam Smith (Wed 10AM)

Sharon Goldberg goldbe at cs.bu.edu
Mon Apr 21 08:12:41 EDT 2014

This week, we have a talk about the foundations of the RSA assumption by
our  sabbatical visitor Adam Smith from Penn State.  The talk will be at
the usual time (Wednesday 10AM), followed by the usual lunch.  See you


 BUsec Calendar:  http://www.bu.edu/cs/busec/
 BUsec Mailing list: http://cs-mailman.bu.edu/mailman/listinfo/busec
 How to get to BU from MIT: The CT2 bus or MIT's "Boston Daytime Shuttle"


Regularity of Lossy Exponentiation and Applications
Speaker: Adam Smith, Penn State.
Wednesday April 23, 2014 10AM

We study of how ``lossiness'' of the RSA trapdoor permutation under the
$\Phi$-Hiding Assumption can be used to understand the security of
classical RSA-based cryptographic systems. Under Phi-hiding, several
questions or conjectures about the security of such systems can be reduced
to bounds on the regularity  (the distribution of the primitive e-th roots
of unity mod N) of the ``lossy'' RSA map  (the mape x -> x^e where e
divides phi(N)).

Specifically, this is the case for: (i) showing that large consecutive runs
of the RSA input bits are simultaneously hardcore, (ii) showing the
widely-deployed PKCS #1 v1.5 encryption is semantically secure, (iii)
improving the security bounds of Kiltz et al. (2010) for RSA-OAEP.

We prove several results on the regularity of the lossy RSA map using both
classical techniques and recent estimates on Gauss sums over finite
subgroups, thereby obtaining new results in the above applications. Our
results deepen the connection between ``combinatorial'' properties of
exponentiation in Z_N and the security of RSA-based constructions.

This is based on joint work with Adam O'Neill and Mark Lewko and Ye Zhang.
Some of these results appeared at Eurocrypt 2013
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