203,488 research outputs found
Evolving Secret Sharing Schemes Based on Polynomial Evaluations and Algebraic Geometry Codes
A secret sharing scheme enables the dealer to share a secret among parties. A classic secret sharing scheme takes the number of parties and the secret as the input. If is not known in advance, the classic secret sharing scheme may fail. Komargodski, Naor, and Yogev \cite[TCC 2016]{KNY16} first proposed the evolving secret sharing scheme that only takes the secret as the input. In the work \cite[TCC 2016]{KNY16}, \cite[TCC 2017]{KC17} and \cite[Eurocrypt 2020]{BO20}, evolving threshold and ramp secret sharing schemes were extensively investigated. However, all of their constructions except for the first construction in \cite{BO20} are inspired by the scheme given in \cite{KNY16}, namely,
these schemes rely on the scheme for st-connectivity which allows to generate infinite number of shares.
In this work, we revisit evolving secret sharing schemes and present three constructions that take completely different approach. Most of the previous schemes mentioned above have more combinatorial flavor, while our schemes are more algebraic in nature. More precisely speaking, our evolving secret sharing schemes are obtained via either the Shamir secret sharing or arithmetic secret sharing from algebraic geometry codes alone. Our first scheme is an evolving -threshold secret sharing scheme with share size for any constant . Thus, our scheme achieves almost the same share size as in \cite[TCC 2016]{KNY16}.
Moreover, our scheme is obtained by a direct construction while the scheme in \cite[TCC 2016]{KNY16} that achieves the share size is obtained by a recursive construction which makes their structure complicated.
Our second scheme is an evolving -threshold secret sharing scheme with any sequence of threshold values that has share size . This scheme improves the share size by given in \cite{KC17} where a dynamic evolving -threshold secret sharing scheme with the share size was proposed. In addition, we also show that if the threshold values grow in rate for a real , then we have a dynamic evolving threshold secret sharing scheme with the share size . For , this scheme has sub-linear share size which was not known before.
Our last scheme is an evolving (\Ga t,\Gb t)-ramp secret sharing scheme with constant share size. One major feature of this ramp scheme is that it is multiplicative as the scheme is also an arithmetic secret sharing scheme. We note that the same technique in \cite{KC17} can also transform all of our schemes to a robust scheme as our scheme is linear.\footnote{We note that by replacing the building block scheme with an arithmetic secret sharing scheme, the evolving (\Ga t,\Gb t)-ramp secret sharing scheme in \cite{BO20} can also be multiplicative. However, their share size is much bigger than ours as each party hold multiple shares.
Dynamic Tardos Traitor Tracing Schemes
We construct binary dynamic traitor tracing schemes, where the number of
watermark bits needed to trace and disconnect any coalition of pirates is
quadratic in the number of pirates, and logarithmic in the total number of
users and the error probability. Our results improve upon results of Tassa, and
our schemes have several other advantages, such as being able to generate all
codewords in advance, a simple accusation method, and flexibility when the
feedback from the pirate network is delayed.Comment: 13 pages, 5 figure
Near-optimal adjacency labeling scheme for power-law graphs
An adjacency labeling scheme is a method that assigns labels to the vertices
of a graph such that adjacency between vertices can be inferred directly from
the assigned label, without using a centralized data structure. We devise
adjacency labeling schemes for the family of power-law graphs. This family that
has been used to model many types of networks, e.g. the Internet AS-level
graph. Furthermore, we prove an almost matching lower bound for this family. We
also provide an asymptotically near- optimal labeling scheme for sparse graphs.
Finally, we validate the efficiency of our labeling scheme by an experimental
evaluation using both synthetic data and real-world networks of up to hundreds
of thousands of vertices
Dynamic Rate Adaptation for Improved Throughput and Delay in Wireless Network Coded Broadcast
In this paper we provide theoretical and simulation-based study of the
delivery delay performance of a number of existing throughput optimal coding
schemes and use the results to design a new dynamic rate adaptation scheme that
achieves improved overall throughput-delay performance.
Under a baseline rate control scheme, the receivers' delay performance is
examined. Based on their Markov states, the knowledge difference between the
sender and receiver, three distinct methods for packet delivery are identified:
zero state, leader state and coefficient-based delivery. We provide analyses of
each of these and show that, in many cases, zero state delivery alone presents
a tractable approximation of the expected packet delivery behaviour.
Interestingly, while coefficient-based delivery has so far been treated as a
secondary effect in the literature, we find that the choice of coefficients is
extremely important in determining the delay, and a well chosen encoding scheme
can, in fact, contribute a significant improvement to the delivery delay.
Based on our delivery delay model, we develop a dynamic rate adaptation
scheme which uses performance prediction models to determine the sender
transmission rate. Surprisingly, taking this approach leads us to the simple
conclusion that the sender should regulate its addition rate based on the total
number of undelivered packets stored at the receivers. We show that despite its
simplicity, our proposed dynamic rate adaptation scheme results in noticeably
improved throughput-delay performance over existing schemes in the literature.Comment: 14 pages, 15 figure
Optimal sequential fingerprinting: Wald vs. Tardos
We study sequential collusion-resistant fingerprinting, where the
fingerprinting code is generated in advance but accusations may be made between
rounds, and show that in this setting both the dynamic Tardos scheme and
schemes building upon Wald's sequential probability ratio test (SPRT) are
asymptotically optimal. We further compare these two approaches to sequential
fingerprinting, highlighting differences between the two schemes. Based on
these differences, we argue that Wald's scheme should in general be preferred
over the dynamic Tardos scheme, even though both schemes have their merits. As
a side result, we derive an optimal sequential group testing method for the
classical model, which can easily be generalized to different group testing
models.Comment: 12 pages, 10 figure
Dynamic Traitor Tracing Schemes, Revisited
We revisit recent results from the area of collusion-resistant traitor
tracing, and show how they can be combined and improved to obtain more
efficient dynamic traitor tracing schemes. In particular, we show how the
dynamic Tardos scheme of Laarhoven et al. can be combined with the optimized
score functions of Oosterwijk et al. to trace coalitions much faster. If the
attack strategy is known, in many cases the order of the code length goes down
from quadratic to linear in the number of colluders, while if the attack is not
known, we show how the interleaving defense may be used to catch all colluders
about twice as fast as in the dynamic Tardos scheme. Some of these results also
apply to the static traitor tracing setting where the attack strategy is known
in advance, and to group testing.Comment: 7 pages, 1 figure (6 subfigures), 1 tabl
Efficient Probabilistic Group Testing Based on Traitor Tracing
Inspired by recent results from collusion-resistant traitor tracing, we
provide a framework for constructing efficient probabilistic group testing
schemes. In the traditional group testing model, our scheme asymptotically
requires T ~ 2 K ln N tests to find (with high probability) the correct set of
K defectives out of N items. The framework is also applied to several noisy
group testing and threshold group testing models, often leading to improvements
over previously known results, but we emphasize that this framework can be
applied to other variants of the classical model as well, both in adaptive and
in non-adaptive settings.Comment: 8 pages, 3 figures, 1 tabl
- …