Related papers: Symmetries in Linear Programming for Information I…
This paper is on developing some computer-assisted proof methods involving non-classical inequalities for Shannon entropy. Two areas of the applications of information inequalities are studied: Secret sharing schemes and hat guessing games.…
We discuss linear programming techniques that help to deduce corollaries of non classic inequalities for Shannon's entropy. We focus on direct applications of the copy lemma. These applications involve implicitly some (known or unknown)…
Determining information ratios of access structures is an important problem in secret sharing. Information inequalities and linear rank inequalities play an important role for proving bounds. Characteristic-dependent linear rank…
A common approach of system identification and machine learning is to generate a model by using training data to predict the test data instances as accurate as possible. Nonetheless, concerns about data privacy are increasingly raised, but…
This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of…
Linear error-correcting codes can be used for constructing secret sharing schemes; however finding in general the access structures of these secret sharing schemes and, in particular, determining efficient access structures is difficult.…
Secret sharing is a cryptographic discipline in which the goal is to distribute information about a secret over a set of participants in such a way that only specific authorized combinations of participants together can reconstruct the…
Most current distributed processing research deals with improving the flexibility and convergence speed of algorithms for networks of finite size with no constraints on information sharing and no concept for expected levels of signal…
Secret sharing is an important building block in cryptography. All explicitly defined secret sharing schemes with known exact complexity bounds are multi-linear, thus are closely related to linear codes. The dual of such a linear scheme, in…
Linear programming is a fundamental tool in a wide range of decision systems. However, without privacy protections, sharing the solution to a linear program may reveal information about the underlying data used to formulate it, which may be…
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric linear and integer programs are studied from a group theoretical viewpoint. We show that for any linear program there exists an optimal solution…
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…
Missing values are unavoidable in many applications of machine learning and present challenges both during training and at test time. When variables are missing in recurring patterns, fitting separate pattern submodels have been proposed as…
Linear codes have diverse applications in secret sharing schemes, secure two-party computation, association schemes, strongly regular graphs, authentication codes and communication. There are a large number of linear codes with few weights…
The problem of detecting and quantifying the presence of symmetries in datasets is useful for model selection, generative modeling, and data analysis, amongst others. While existing methods for hard-coding transformations in neural networks…
Nowadays, the utilization of the ever expanding amount of data has made a huge impact on web technologies while also causing various types of security concerns. On one hand, potential gains are highly anticipated if different organizations…
We consider the setting of a master server who possesses confidential data (genomic, medical data, etc.) and wants to run intensive computations on it, as part of a machine learning algorithm for example. The master wants to distribute…
Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help reduce the problem dimension, cut…
This work investigates the design of sparse secret sharing schemes that encode a sparse private matrix into sparse shares. This investigation is motivated by distributed computing, where the multiplication of sparse and private matrices is…
A dealer aims to share a secret with participants so that only predefined subsets can reconstruct it, while others learn nothing. The dealer and participants access correlated randomness and communicate over a one-way, public, rate-limited…