Regular covers of complete graphs which are 2-arc-transitive are investigated. A classification is given of all such graphs whose group of covering transformations is either cyclic or isomorphic to Z p _Z p , where p is a prime and whose fibrepreserving subgroup of automorphisms acts 2-arc-transitively. As a result two new families of 2-arc-transitive graphs are obtained. Academic Press

Abstract. The purpose of this paper is to investigate fixed-point arithmetic in ring-based Somewhat Homomorphic Encryption (SHE) schemes. We provide three main contributions: firstly, we investigate the representation of fixed-point numbers. We analyse the two representations from Dowlin et al, representing a fixed-point number as a large integer (encoded as a scaled polynomial) versus a polynomial-based fractional representation. We show that these two are, in fact, isomorphic by presenting an explicit isomorphism between the two that enables us to map the parameters from one representation to another. Secondly, given a computation and a bound on the fixed-point numbers used as inputs and scalars within the computation, we achieve a way of producing lower bounds on the plaintext modulus p and the degree of the ring d needed to support complex homomorphic operations. Finally, as an application of these bounds, we investigate homomorphic image processing.

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