ABSTRACT We give an abstraction of multisecret sharing based on Lagrange interpolating polynomial that is accessible to a fully mechanized analysis. This abstraction is formalized in the applied pi‐calculus by using an equational theory that characterizes the cryptographic semantics of multisecret sharing based on Lagrange interpolating polynomial. We also present an encoding from the equational theory into a convergent rewriting system, which is suitable for the automated protocol verifier ProVerif. Finally, we verify the Yang–Chang–Hwang (YCH) protocol in ProVerif. Copyright © 2013 John Wiley & Sons, Ltd.

We present a new multi-dimensional data structure, which we call the skip quadtree (for point data in R2) or the skip octree (for point data in Rd, with constant d > 2). Our data structure combines the best features of two well-known data structures, in that it has the well-defined "box"-shaped regions of region quadtrees and the logarithmic-height search and update hierarchical structure of skip lists. Indeed, the bottom level of our structure is exactly a region quadtree (or octree for higher dimensional data). We describe efficient algorithms for inserting and deleting points in a skip quadtree, as well as fast methods for performing point location, approximate range, and approximate nearest neighbor queries.