相关论文: Secret Sharing Schemes Based on Min-Entropies
Quantum secret sharing (QSS) allows a dealer to distribute a secret quantum state among a set of parties so that certain subsets can reconstruct the secret, while unauthorized subsets obtain no information. While QSS was introduced over…
A restriction on quantum secret sharing (QSS) that comes from the no-cloning theorem is that any pair of authorized sets in an access structure should overlap. From the viewpoint of application, this places an unnatural constraint on secret…
Disjunctive Hierarchical Secret Sharing (DHSS)} scheme is a type of secret sharing scheme in which the set of all participants is partitioned into disjoint subsets, and each subset is said to be a level with different degrees of trust and…
In this paper, some general properties of Shannon information measures are investigated over sets of probability distributions with restricted marginals. Certain optimization problems associated with these functionals are shown to be…
Estimation of Shannon and R\'enyi entropies of unknown discrete distributions is a fundamental problem in statistical property testing and an active research topic in both theoretical computer science and information theory. Tight bounds on…
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…
In this paper, we investigate the index coding problem in the presence of an eavesdropper. Messages are to be sent from one transmitter to a number of legitimate receivers who have side information about the messages, and share a set of…
A secret sharing scheme (SSS) was introduced by Shamir in 1979 using polynomial interpolation. Later it turned out that it is equivalent to an SSS based on a Reed-Solomon code. SSSs based on linear codes have been studied by many…
It is well established that the notion of min-entropy fails to satisfy the \emph{chain rule} of the form $H(X,Y) = H(X|Y)+H(Y)$, known for Shannon Entropy. Such a property would help to analyze how min-entropy is split among smaller blocks.…
Current security techniques can be implemented with either secret key exchange or physical layer wiretap codes. In this work, we investigate an alternative solution for MIMO wiretap channels. Inspired by the artificial noise (AN) technique,…
A ($t$, $n$) threshold quantum secret sharing (QSS) is proposed based on a single $d$-level quantum system. It enables the ($t$, $n$) threshold structure based on Shamir's secret sharing and simply requires sequential communication in…
We revisit the well-studied problem of estimating the Shannon entropy of a probability distribution, now given access to a probability-revealing conditional sampling oracle. In this model, the oracle takes as input the representation of a…
A probabilistic secret sharing scheme is a joint probability distribution of the shares and the secret together with a collection of secret recovery functions. The study of schemes using arbitrary probability spaces and unbounded number of…
We conclude a sequence of work by giving near-optimal sketching and streaming algorithms for estimating Shannon entropy in the most general streaming model, with arbitrary insertions and deletions. This improves on prior results that obtain…
Secret image sharing deals with splitting confidential images into several shares and the original image can be reconstructed from the qualified subset of the shares. Secret sharing schemes are used in transmission and storage of private…
In this paper, we consider the case that sharing many secrets among a set of participants using the threshold schemes. All secrets are assumed to be statistically independent and the weak secure condition is focused on. Under such…
We calculate an achievable secret key rate for quantum key distribution with a finite number of signals, by evaluating the min-entropy explicitly. The min-entropy can be expressed in terms of the guessing probability, which we calculate for…
We demonstrate a new construction for perfect quantum secret sharing (QSS) schemes based on imperfect "ramp" secret sharing combined with classical encryption, in which the individual parties' shares are split into quantum and classical…
We present a detailed derivation of some estimators of Shannon entropy for discrete distributions. They hold for finite samples of N points distributed into M "boxes", with N and M -> oo, but N/M < oo. In the high sampling regime (<< 1…
Secret sharing is an instrumental tool for sharing secret keys in distributed systems. In a classical threshold setting, this involves a dealer who has a secret/key, a set of parties/users to which shares of the secret are sent, and a…