IACR News item: 27 May 2013
Vadim Lyubashevsky, Chris Peikert, Oded Regev
ePrint Reportdevelopment of ring-based primitives such as ring-$\\lwe$, have made it
possible to design cryptographic schemes whose efficiency is
competitive with that of more traditional number-theoretic ones, along
with entirely new applications like fully homomorphic encryption.
Unfortunately, realizing the full potential of ring-based cryptography
has so far been hindered by a lack of practical algorithms and
analytical tools for working in this context. As a result, most
previous works have focused on very special classes of rings such as
power-of-two cyclotomics, which significantly restricts the possible
applications.
We bridge this gap by introducing a toolkit of fast, modular
algorithms and analytical techniques that can be used in a wide
variety of ring-based cryptographic applications, particularly those
built around ring-\\lwe. Our techniques yield applications that work
in \\emph{arbitrary} cyclotomic rings, with \\emph{no loss} in their
underlying worst-case hardness guarantees, and very little loss in
computational efficiency, relative to power-of-two cyclotomics. To
demonstrate the toolkit\'s applicability, we develop two illustrative
applications: a public-key cryptosystem and a ``somewhat homomorphic\'\'
symmetric encryption scheme. Both apply to arbitrary cyclotomics, have
tight parameters, and very efficient implementations.
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