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in the presence of an eavesdropper. In this paper we focus on the cryptographic aspects of AlphaEta and its variants. Moreover, we propose a new protocol for which we can provide a rigorous proof
that the eavesdropper obtains neglible information. In comparison to single-photon quantum cryptography, AlphaEta provide much higher throughputs combined with a well-known technology.
These strategies involve building a secret branch of the block-tree and publishing it opportunistically, aiming to replace the top of the main branch and rip the reward associated with the secretly mined blocks. We identify two types of block-hiding strategies and chart the parameter space where those are more beneficial than the standard mining strategy described in Nakamoto\'s paper.
Our analysis suggests a generalization of the notion of the relative hashing power as a measure for a miner\'s influence on the network. Block-hiding strategies are beneficial only when this measure of influence exceeds a certain threshold.
In order to study perfect and non-perfect secret sharing schemes with all generality, we describe the structure of the schemes through their access function, a real function that measures the amount of information that every subset of participants knows about the secret value. We present new tools for the construction of secret sharing schemes. In particular, we construct a secret sharing scheme for every access function.
We extend the connections between polymatroids and perfect secret sharing schemes to the non-perfect ones to find new results on the information ratio. We find a new lower bound on the information ratio that is better than the ones previously known. In particular, this bound is tight for uniform access functions. The access function of a secret sharing scheme is uniform if all participants play the same role in a scheme (e.g. ramp secret sharing schemes). Moreover, we construct a secret sharing scheme with optimal information ratio for every rational uniform access function.
Algebraic properties of modular addition modulo a power of two have been studied for two operands by Braeken in fse\'05. Also, the authors of this paper, have studied this operator, in some special cases, before. In this paper, taking advantage of previous researches in this area, we generalize the algebraic properties of this operator for more than two summands. More precisely, we
determine the algebraic degree of the component Boolean functions of modular addition of arbitrary number of summands modulo a power of two, as a vectorial Boolean function, along with the number of terms and variables in these component functions. As a result, algebraic degrees of the component Boolean functions of Generalized Pseudo-Hadamard Transforms are driven.