In this paper we present a new scheme for verifiable delegation of polynomials in a cloud computing scenario. The security of our scheme is based on a standard assumption, the subgroup membership one. Furthermore, the scheme is highly efficient since the number of operations is independent of the degree of the polynomial. We also propose a second scheme that allows to hide the polynomial to be delegated and that improves the efficiency of the scheme by Benabbas et al. in [BGV11]. Moreover, we give a third polynomial delegation scheme which is the first that allows the client to hide the input point.

An encryption scheme should satisfy semantic security or indistinguishability of encryptions against chosen plaintext attack (IND-CPA). We propose an elliptic curve scheme over the ring /spl Zopf/(n/sup 2/), which is efficient and semantically secure in the standard model. It is based on factoring, and it has expansion factor 2 (previous schemes with these features present expansion factors greater than or equal to 4). Demytko's primitive has been used to obtain efficiency and probabilistic encryption. Semantic security of this scheme is based on a new decisional assumption, namely, the decisional small root assumption. Confidence in this assumption is also discussed.

The purpose of this paper is to find fault-tolerant fixed routings in some families of digraphs that have been widely considered into the design of interconnection networks. A routing $\rho$ in a digraph G assigns to each pair of vertices a fixed path (called a route) between them. For a given set of faulty vertices and/or arcs, the vertices of the surviving route digraph are the nonfaulty vertices and there is an arc between two vertices if and only if there are no faults on the route between them. The diameter of the surviving route digraph measures the fault tolerance of the routing. In this work, sufficient conditions are found for a digraph to have a routing such that for any set of faults with a bounded number of elements the diameter of the surviving route digraph is at most 3. These results are applied to prove the existence of routings with this property in the generalized de Bruijn and Kautz digraphs, the bipartite digraphs BD(d,n), and general iterated line digraphs.

The aim of this note is to present some counterexamples to the results in the paper by Du, Lyuu, and Hsu (see ibid., vol.42, no.5, p.612-16, May 1993).