Incomplete character sums over finite fields and their application to the interpolation of the discrete logarithm by Boolean functions
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 participants allows us to investigate their abstract properties, to connect the topic to other branches of mathematics, and to discover new design paradigms. A scheme is perfect if unqualified subsets have no information on the secret, that is, their total share...
This paper deals with the concept of the “size“ or “extent“ of the information in the sense of measuring the improvement of our knowledge after obtaining a message. Standard approaches are based on the probabilistic parameters of the considered information source. Here we deal with situations when the unknown probabilities are subjectively or vaguely estimated. For the considered fuzzy quantities valued probabilities we introduce and discuss information theoretical concepts.
The structures of the fuzzy information theory are focused on the concept of fuzzy entropy, where the individual information of symbols is considered only implicitely. This paper aims to fill this gap and to study the concepts of fuzzy information. Special attention is paid to the typical fuzzy set theoretical paradigma of monotonicity of operations.
The measurement of information emitted by sources with uncertainty of random type is known and investigated in many works. This paper aims to contribute to analogous treatment of information connected with messages from other uncertain sources, influenced by not only random but also some other types of uncertainty, namely with imprecision and vagueness. The main sections are devoted to the characterization and quantitative representation of such uncertainties and measures of information produced...