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Non-malleable codes are kind of encoding schemes which are resilient to tampering attacks. The main idea behind the non-malleable coding is that the adversary can't be able to obtain any valuable information about the message. Non-malleable codes are used in tamper resilient cryptography and protecting memory against tampering attacks. Several kinds of definitions for the non-malleability exist in the literature. The Continuous non-malleability is aiming to protect messages against the adversary who issues polynomially many tampering queries. The first continuous non-malleable encoding scheme has been proposed by Faust et al. (FMNV) in 2014. In this paper, we propose a new method for proving... 

A non-malleable encoding scheme is a keyless encoding scheme which is resilient to tampering attacks. Such a scheme is said to be continuously secure if the scheme is resilient to attacks containing more than one tampering procedure. Moreover, such a scheme is said to have the T-tamper-detection property if any kind of tampering attack by an adversary chosen from a predetermined class of algorithms T is detected. Faust et al. have introduced a continuous non-malleable encoding scheme based on non-interactive zero-knowledge (NIZK) which is secure in a strong model for which the adversary receives the tampered codeword as a response to its tampering query if the tampered codeword is not... 

Hall's condition for the existence of a proper vertex list-multicoloring of a simple graph G has recently been used to define the fractional Hall and Hall-condition numbers of G, and . Little is known about , but it is known that , where ‘⩽’ means ‘is a subgraph of’ and α(H) denotes the vertex independence number of H. Let and denote the fractional chromatic and choice (list-chromatic) numbers of G. (Actually, Slivnik has shown that these are equal, but we will continue to distinguish notationally between them.) We give various relations among , , , and , mostly notably that , when G is a line graph. We give examples to show that this equality does not necessarily hold when G is... 

Given a weighted graph G=(V,E) with weight functions c:E→R+ and π:V→R+, and a subset U⊆V, the normalized cut value for U is defined as the sum of the weights of edges exiting U divided by the weight of vertices in U. The mean isoperimetry problem, ISO1(G,k), for a weighted graph G is a generalization of the classical uniform sparsest cut problem in which, given a parameter k, the objective is to find k disjoint nonempty subsets of V minimizing the average normalized cut value of the parts. The robust version of the problem seeks an optimizer where the number of vertices that fall out of the subpartition is bounded by some given integer 0≤ρ≤|V|. The problem may also be considered as the...