Affiliation-Hiding Authenticated Key Exchange (AH-AKE) protocols enable two distrusting users, being in possession of membership credentials for some group, to establish a secure session key without leaking any information about this group to non-members. In practice, users might be members of several groups, and such protocols must be able to generate session keys between users who have one or...

This talk discusses a conjecture of R. V. Kadison and myself. Our conjecture is that each one-to-one linear map of one unital C*-algebra onto another that preserves the identity is a Jordan isomorphism if it maps the invertible elements of the first C*-algebra onto the invertible elements of the other C*-algebra. Connections are shown between this conjecture and Cartan’s uniqueness theorem. 1. ...

Linear subspace is an important representation for many kinds of real-world data in computer vision and pattern recognition, e.g. faces, motion videos, speeches. In this paper, first we define pairwise angular similarity and angular distance for linear subspaces. The angular distance satisfies non-negativity, identity of indiscernibles, symmetry and triangle inequality, and thus it is a metric....

Suppose that K is a closed, total cone in a real Banach space X, that A :X!X is a bounded linear operator which maps K into itself, and that A« denotes the Banach space adjoint of A. Assume that r, the spectral radius of A, is positive, and that there exist x ! 1 0 and m& 1 with Am(x ! ) ̄ rmx ! (or, more generally, that there exist x ! a (®K ) and m& 1 with Am(x ! )& rmx ! ). If, in addition, A...

In this paper we prove that the linear transformation

We propose a simple privacy-preserving reformulation of a linear program whose equality constraint matrix is partitioned into groups of rows. Each group of matrix rows and its corresponding right hand side vector are owned by a distinct private entity that is unwilling to share or make public its row group or right hand side vector. By multiplying each privately held constraint group by an appr...

An analytic theory of cumulative multibunch beam breakup in linear colliders is developed. Included is a linear variation of transverse focusing across the bunch train as might be applied, e.g., by chirping the radio frequency power sources or by using radio frequency quadrupole magnets. The focusing variation saturates the exponential growth of the beam breakup and establishes an algebraic dec...

The following is a short survey of the notion of a well-posed linear system. We start by describing the most basic concepts, proceed to discuss dissipative and conservative systems, and finally introduce J-energy-preserving systems, i.e., systems that preserve energy with respect to some generalized inner products (possibly semi-definite or indefinite) in the input, state and output spaces. The...

We find configurations of subspaces of a complex vector space such that any real linear map with sufficiently high rank that maps the subspaces into complex subspaces of the same dimension must be complex linear or antilinear.

Studies that combine data from multiple sources can tremendously improve the outcome of the statistical analysis. However, combining data from these various sources for analysis poses privacy risks. A number of protocols have been proposed in the literature to address the privacy concerns; however they do not fully deliver on either privacy or complexity. In this paper, we present a (theoretica...