In this paper, we introduce the notion of a Public-Key Encryption (PKE) Scheme that is also a Locally-Decodable Error-Correcting Code.
In particular, our construction simultaneously satisfies all of the following properties:
\begin{itemize}
\item
Our Public-Key Encryption is semantically secure under a certain number-theoretic hardness assumption
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Valiant's theory of holographic algorithms is a novel methodology
to achieve exponential speed-ups in computation. A fundamental
parameter in holographic algorithms is the dimension of the linear basis
vectors.
We completely resolve the problem of the power of higher dimensional
bases. We prove that 2-dimensional bases are universal for
holographic ... more >>>

We give a classification of block-wise symmetric signatures
in the theory of matchgate computations. The main proof technique
is matchgate identities, a.k.a. useful Grassmann-Pl\"{u}cker
identities.

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