Related papers: Secret Sharing Schemes Based on Min-Entropies
We present information-theoretic definitions and results for analyzing symmetric-key encryption schemes beyond the perfect secrecy regime, i.e. when perfect secrecy is not attained. We adopt two lines of analysis, one based on lossless…
Min-entropy sampling gives a bound on the min-entropy of a randomly chosen subset of a string, given a bound on the min-entropy of the whole string. K\"onig and Renner showed a min-entropy sampling theorem that holds relative to quantum…
Modern statistical estimation is often performed in a distributed setting where each sample belongs to a single user who shares their data with a central server. Users are typically concerned with preserving the privacy of their samples,…
This paper considers the estimation of Shannon entropy for discrete distributions with countably infinite support. While minimax rates for finite-support distributions are established, infinite-support distributions present distinct…
The quality of image encryption is commonly measured by the Shannon entropy over the ciphertext image. However, this measurement does not consider to the randomness of local image blocks and is inappropriate for scrambling based image…
We consider a private distributed multiplication problem involving N computation nodes and T colluding nodes. Shamir's secret sharing algorithm provides perfect information-theoretic privacy, while requiring an honest majority, i.e., N \ge…
Distributed storage plays an essential role in realizing robust and secure data storage in a network over long periods of time. A distributed storage system consists of a data owner machine, multiple storage servers and channels to link…
This paper provides tight bounds on the R\'enyi entropy of a function of a discrete random variable with a finite number of possible values, where the considered function is not one-to-one. To that end, a tight lower bound on the R\'enyi…
One of the main problems in cryptography is to give criteria to provide good comparators of cipher systems. The security of a cipher system must include the security of the algorithm, the security of the key generator and management module…
Secret sharing is a new alternative for outsourcing data in a secure way.It avoids the need for time consuming encryption decryption process and also the complexity involved in key management.The data must also be protected from untrusted…
Each member of an $n$-person team has a secret, say a password. The $k$ out of $n$ gruppen secret sharing requires that any group of $k$ members should be able to recover the secrets of the other $n-k$ members, while any group of $k-1$ or…
In this work, we introduce a new technique for taking a single-secret sharing scheme with a general access structure and transforming it into an individually secure multi-secret sharing scheme where every secret has the same general access…
Entropically secure encryption is a way to encrypt a large plaintext with a small key and still have information-theoretic security, thus in a certain sense circumventing Shannon's result that perfect encryption requires the key to be at…
In this paper we consider the compressed sensing-based encryption and proposed the conditions in which the perfect secrecy is obtained. We prove when the Restricted Isometery Property (RIP) is hold and the number of measurements is more…
A new grayscale image encryption algorithm based on $(k,n)$ threshold secret sharing is proposed. The scheme allows a secret image to be transformed into $n$ shares, where any $k \le n$ shares can be used to reconstruct the secret image,…
There are several methods for constructing secret sharing schemes, one of which is based on coding theory. Theoretically, every linear code can be used to construct secret sharing schemes. However, in general, determining the access…
From the output produced by a memoryless deletion channel from a uniformly random input of known length $n$, one obtains a posterior distribution on the channel input. The difference between the Shannon entropy of this distribution and that…
Secret sharing schemes with optimal and universal communication overheads have been obtained independently by Bitar et al. and Huang et al. However, their constructions require a finite field of size q > n, where n is the number of shares,…
This paper gives upper and lower bounds on the minimum error probability of Bayesian $M$-ary hypothesis testing in terms of the Arimoto-R\'enyi conditional entropy of an arbitrary order $\alpha$. The improved tightness of these bounds over…
Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization…