Related papers: Guesswork Subject to a Total Entropy Budget
We design, implement and test a simple algorithm which computes the approximate entropy of a finite binary string of arbitrary length. The algorithm uses a weighted average of the Shannon Entropies of the string and all but the last binary…
We introduce the study of information leakage through \emph{guesswork}, the minimum expected number of guesses required to guess a random variable. In particular, we define \emph{maximal guesswork leakage} as the multiplicative decrease,…
In 2002, Russell and Wang proposed a definition of entropically security that was developed within the framework of secret key cryptography. An entropically-secure system is unconditionally secure, that is, unbreakable, regardless of the…
Attacks on classical cryptographic protocols are usually modeled by allowing an adversary to ask queries from an oracle. Security is then defined by requiring that as long as the queries satisfy some constraint, there is some problem the…
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…
The problem of compression in standard information theory consists of assigning codes as short as possible to numbers. Here we consider the problem of optimal coding -- under an arbitrary coding scheme -- and show that it predicts Zipf's…
Homomorphic encryption is a form of encryption which allows computation to be carried out on the encrypted data without the need for decryption. The success of quantum approaches to related tasks in a delegated computation setting has…
A game-theoretic model of scrip (artificial currency) systems is analyzed. It is shown that relative entropy can be used to characterize the distribution of agent wealth when all agents use threshold strategies---that is, they volunteer to…
Over the last few years, machine learning unlocked previously infeasible features for compression, such as providing guarantees for users' privacy or tailoring compression to specific data statistics (e.g., satellite images or audio…
This research note II introduces a way to understand a basic concept of the quantum enigma cipher. The conventional cipher is designed by a mathematical algorithm and its security is evaluated by the complexity of the algorithm in security…
In this work, we study interception attacks against a secret sharing protocol based on Grovers search algorithm. Unlike previous works that only give the algorithm for two and three participants, we have generalized the algorithm for any…
Given a communication system using quantum key distribution, the receiver can be seen as one who tries to guess the sender's information just as potential eavesdroppers do. The receiver-eavesdropper similarity thus implies a simple relation…
We introduce the (private) entropy of a directed graph (in a new network coding sense) as well as a number of related concepts. We show that the entropy of a directed graph is identical to its guessing number and can be bounded from below…
We study universal compression of sequences generated by monotonic distributions. We show that for a monotonic distribution over an alphabet of size $k$, each probability parameter costs essentially $0.5 \log (n/k^3)$ bits, where $n$ is the…
The secrecy capacity of a network, for a given collection of permissible wiretap sets, is the maximum rate of communication such that observing links in any permissible wiretap set reveals no information about the message. This paper…
In this work, we study the generalization capability of algorithms from an information-theoretic perspective. It has been shown that the expected generalization error of an algorithm is bounded from above by a function of the relative…
Shannon entropy is the shortest average codeword length a lossless compressor can achieve by encoding i.i.d. symbols. However, there are cases in which the objective is to minimize the \textit{exponential} average codeword length, i.e. when…
Recent work on deep neural network pruning has shown there exist sparse subnetworks that achieve equal or improved accuracy, training time, and loss using fewer network parameters when compared to their dense counterparts. Orthogonal to…
Many efficient data structures use randomness, allowing them to improve upon deterministic ones. Usually, their efficiency and correctness are analyzed using probabilistic tools under the assumption that the inputs and queries are…
The entropy of a hierarchical network topology in an ensemble of sparse random networks with "hidden variables" associated to its nodes, is the log-likelihood that a given network topology is present in the chosen ensemble.We obtain a…