Flexible and Robust Privacy-Preserving Implicit Authentication

Implicit authentication consists of a server authenticating a user based on the user's usage profile, instead of/in addition to relying on something the user explicitly knows (passwords, private keys, etc.). While implicit authentication makes identity theft by third parties more difficult, it requires the server to learn and store the user's usage profile. Recently, the first privacy-preserving implicit authentication system was presented, in which the server does not learn the user's profile. It uses an ad hoc two-party computation protocol to compare the user's fresh sampled features against an encrypted stored user's profile. The protocol requires storing the usage profile and comparing against it using two different cryptosystems, one of them order-preserving; furthermore, features must be numerical. We present here a simpler protocol based on set intersection that has the advantages of: i) requiring only one cryptosystem; ii) not leaking the relative order of fresh feature samples; iii) being able to deal with any type of features (numerical or non-numerical). Keywords: Privacy-preserving implicit authentication, privacy-preserving set intersection, implicit authentication, active authentication, transparent authentication, risk mitigation, data brokers.Comment: IFIP SEC 2015-Intl. Information Security and Privacy Conference, May 26-28, 2015, IFIP AICT, Springer, to appea

Accurate computations with Lupas matrices

Lupas q-analogues of the Bernstein functions play an important role in Approximation Theory and Computer Aided Geometric Design. Their collocation matrices are called Lupas matrices. In this paper, we provide algorithms for computing the bidiagonal decomposition of these matrices and their inverses to high relative accuracy. It is also shown that these algorithms can be used to perform to high relative accuracy several algebraic calculations with these matrices, such as the calculation of their inverses, their eigenvalues or their singular values. Numerical experiments are included

On factorization of a special type of vandermonde rhotrix

Vandermonde matrices have important role in many branches of applied mathematics such as combinatorics, coding theory and cryptography. Some authors discuss the Vandermonde rhotrices in the literature for its mathematical enrichment. Here, we introduce a special type of Vandermonde rhotrix and obtain its LR factorization namely left and right triangular factorization, which is further used to obtain the inverse of the rhotrix

On Factorization of a Special type of Vandermonde Rhotrix

Vandermonde matrices have important role in many branches of applied mathematics such as combinatorics, coding theory and cryptography. Some authors discuss Vandermonde rhotrices in the literature for its mathematical enrichment. Here, we introduce a special type of Vandermonde rhotrix and obtain its LR factorization, namely left and right triangular factorization which is further used to obtain the inverse of the rhotrix

Accurate computation of the Moore-Penrose inverse of strictly totally positive matrices

The computation of the Moore-Penrose inverse of structured strictly totally positive matrices is addressed. Since these matrices are usually very ill-conditioned, standard algorithms fail to provide accurate results. An algorithm based on the factorization and which takes advantage of the special structure and the totally positive character of these matrices is presented. The first stage of the algorithm consists of the accurate computation of the bidiagonal decomposition of the matrix. Numerical experiments illustrating the good behavior of our approach are included.Numerical experiments illustrating the good behavior of our approach are included

Total positivity and accurate computations with Gram matrices of Said-Ball bases

In this article, it is proved that Gram matrices of totally positive bases of the space of polynomials of a given degree on a compact interval are totally positive. Conditions to guarantee computations to high relative accuracy with those matrices are also obtained. Furthermore, a fast and accurate algorithm to compute the bidiagonal factorization of Gram matrices of the Said-Ball bases is obtained and used to compute to high relative accuracy their singular values and inverses, as well as the solution of some linear systems associated with these matrices. Numerical examples are included