32,454 research outputs found
Resettable Zero Knowledge in the Bare Public-Key Model under Standard Assumption
In this paper we resolve an open problem regarding resettable zero knowledge
in the bare public-key (BPK for short) model: Does there exist constant round
resettable zero knowledge argument with concurrent soundness for
in BPK model without assuming \emph{sub-exponential hardness}? We give a
positive answer to this question by presenting such a protocol for any language
in in the bare public-key model assuming only
collision-resistant hash functions against \emph{polynomial-time} adversaries.Comment: 19 pag
Wavelet Galerkin method for fractional elliptic differential equations
Under the guidance of the general theory developed for classical partial
differential equations (PDEs), we investigate the Riesz bases of wavelets in
the spaces where fractional PDEs usually work, and their applications in
numerically solving fractional elliptic differential equations (FEDEs). The
technique issues are solved and the detailed algorithm descriptions are
provided. Compared with the ordinary Galerkin methods, the wavelet Galerkin
method we propose for FEDEs has the striking benefit of efficiency, since the
condition numbers of the corresponding stiffness matrixes are small and
uniformly bounded; and the Toeplitz structure of the matrix still can be used
to reduce cost. Numerical results and comparison with the ordinary Galerkin
methods are presented to demonstrate the advantages of the wavelet Galerkin
method we provide.Comment: 20 pages, 0 figure
Concurrently Non-Malleable Zero Knowledge in the Authenticated Public-Key Model
We consider a type of zero-knowledge protocols that are of interest for their
practical applications within networks like the Internet: efficient
zero-knowledge arguments of knowledge that remain secure against concurrent
man-in-the-middle attacks. In an effort to reduce the setup assumptions
required for efficient zero-knowledge arguments of knowledge that remain secure
against concurrent man-in-the-middle attacks, we consider a model, which we
call the Authenticated Public-Key (APK) model. The APK model seems to
significantly reduce the setup assumptions made by the CRS model (as no trusted
party or honest execution of a centralized algorithm are required), and can be
seen as a slightly stronger variation of the Bare Public-Key (BPK) model from
\cite{CGGM,MR}, and a weaker variation of the registered public-key model used
in \cite{BCNP}. We then define and study man-in-the-middle attacks in the APK
model. Our main result is a constant-round concurrent non-malleable
zero-knowledge argument of knowledge for any polynomial-time relation
(associated to a language in ), under the (minimal) assumption of
the existence of a one-way function family. Furthermore,We show time-efficient
instantiations of our protocol based on known number-theoretic assumptions. We
also note a negative result with respect to further reducing the setup
assumptions of our protocol to those in the (unauthenticated) BPK model, by
showing that concurrently non-malleable zero-knowledge arguments of knowledge
in the BPK model are only possible for trivial languages
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