A Framework for Efficient Signatures, Ring Signatures and Identity Based Encryption in the Standard Model
Speaker: Zvika Brakerski , Weizmann Institute
Date: November 5 2010
Time: 10:00AM to 12:00PM
Location: 32-G449 Patil/Kiva
Host: Shafi Goldwasser, CSAIL, MIT
Contact: Be Blackburn , 3-6098, imbe@mit.edu
In this work, we present a generic framework for constructing
efficient signature schemes, ring signature schemes, and identity
based encryption schemes, all in the standard model (without relying
on random oracles). We start by abstracting the recent work of
Hohenberger and Waters (Crypto 2009), and specifically their ``prefix
method''. We show a transformation taking a signature scheme with a
very weak security guarantee (a notion that we call a-priori-message
unforgeability under static chosen message attack) and producing a
fully secure signature scheme (i.e., existentially unforgeable under
adaptive chosen message attack).
Our transformation uses the notion of chameleon hash functions,
defined by Krawczyk and Rabin (NDSS 2000) and the ``prefix
method''. Constructing such weakly secure schemes seems to be
significantly easier than constructing fully secure ones, and we
present {\em simple} constructions based on the RSA assumption, the
{\em short integer solution} (SIS) assumption, and the {\em
computational Diffie-Hellman} (CDH) assumption over bilinear groups.
Next, we observe that this general transformation also applies to the
regime of ring signatures. Using this observation, we construct new
(provably secure) ring signature schemes: one is based on the {\em
short integer solution} (SIS) assumption, and the other is based on
the CDH assumption over bilinear groups.
As a building block for these constructions, we define a primitive
that we call \emph{ring trapdoor functions}. We show that ring
trapdoor functions imply ring signatures under a weak definition,
which enables us to apply our transformation to achieve full security.
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