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We consider the secure computation problem in a minimal model, where Alice and Bob each holds an input and wish to securely compute a function of their inputs at Carol without revealing any additional information about the inputs. For this minimal secure computation problem, we propose a novel coding scheme built from two steps. First, the function to be computed is expanded such that it can be recovered while additional information might be leaked. Second, a randomization step is applied to the expanded function such that the leaked information is protected. We implement this expand-and-randomize coding scheme with two algebraic structures - the finite field and the modulo ring of integers, where the expansion step is realized with the addition operation and the randomization step is realized with the multiplication operation over the respective algebraic structures.
Secure message dissemination is an important issue in vehicular networks, especially considering the vulnerability of vehicle to vehicle message dissemination to malicious attacks. Traditional security mechanisms, largely based on message encryption
In this work, we consider the problem of secure multi-party computation (MPC), consisting of $Gamma$ sources, each has access to a large private matrix, $N$ processing nodes or workers, and one data collector or master. The master is interested in th
We consider the problem of secure distributed matrix computation (SDMC), where a textit{user} can query a function of data matrices generated at distributed textit{source} nodes. We assume the availability of $N$ honest but curious computation server
We present an introduction to the theory of algebraic geometry codes. Starting from evaluation codes and codes from order and weight functions, special attention is given to one-point codes and, in particular, to the family of Castle codes.
This paper studies the problem of repairing secret sharing schemes, i.e., schemes that encode a message into $n$ shares, assigned to $n$ nodes, so that any $n-r$ nodes can decode the message but any colluding $z$ nodes cannot infer any information ab