174 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
An Improvement over the GVW Algorithm for Inhomogeneous Polynomial Systems
The GVW algorithm is a signature-based algorithm for computing Gr\"obner
bases. If the input system is not homogeneous, some J-pairs with higher
signatures but lower degrees are rejected by GVW's Syzygy Criterion, instead,
GVW have to compute some J-pairs with lower signatures but higher degrees.
Consequently, degrees of polynomials appearing during the computations may
unnecessarily grow up higher and the computation become more expensive. In this
paper, a variant of the GVW algorithm, called M-GVW, is proposed and mutant
pairs are introduced to overcome inconveniences brought by inhomogeneous input
polynomials. Some techniques from linear algebra are used to improve the
efficiency. Both GVW and M-GVW have been implemented in C++ and tested by many
examples from boolean polynomial rings. The timings show M-GVW usually performs
much better than the original GVW algorithm when mutant pairs are found.
Besides, M-GVW is also compared with intrinsic Gr\"obner bases functions on
Maple, Singular and Magma. Due to the efficient routines from the M4RI library,
the experimental results show that M-GVW is very efficient
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