Mitra Fatemi

Efficient multistage secret sharing scheme using bilinear map

In a multistage secret sharing (MSSS) scheme, the authorised subsets of participants could recover a number of secrets in different stages. A one-stage multisecret sharing (OSMSS) scheme is a special case of MSSS schemes in which all the secrets are recovered simultaneously. In these schemes, in addition to the individual shares, the dealer should provide the participants with a number of public values associated with the secrets. The less the number of public values, the more efficient is the scheme. It is desired that the MSSS and OSMSS schemes provide computational security. In this study, the authors show that in the OSMSS schemes any unauthorised coalition of the participants can reduce the uncertainty of the secrets. In addition, in MSSS schemes recovering a secret causes reducing uncertainty of the unrecovered secrets. Furthermore, by introducing a new multi-use MSSS scheme based on weil pairing, they reduce the number of public values comparing with the previous schemes.

Anonymous roaming in universal mobile telecommunication system mobile networks

A secure roaming protocol for mobile networks is proposed. Roaming has been analysed in some schemes from the security point of view; however, there are vulnerabilities in most of them and so the claimed security level is not achieved. The scheme offered by Wan et al. recently is based on hierarchical identity-based encryption, in which the roaming user and the foreign network mutually authenticate each other without the help of the home network. Although the idea behind this proposal is interesting, it contradicts technical considerations such as routing and billing. The proposed protocol makes use of similar functions used in Wan et al.s scheme but contributes a distinguished structure that overcomes the previous shortcomings and achieves a higher possible level of security in mobile roaming as well as enhancing the security of the key issuing procedure.

Sampling and Reconstruction of Shapes With Algebraic Boundaries

We present a sampling theory for a class of binary images with finite rate of innovation (FRI). Every image in our model is the restriction of 1{p≤0} to the image plane, where 1 denotes the indicator function and p is some real bivariate polynomial. This particularly means that the boundaries in the image form a subset of an algebraic curve with the implicit polynomial p. We show that the image parameters-i.e., the polynomial coefficientssatisfy a set of linear annihilation equations with the coefficients being the image moments. The inherent sensitivity of the moments to noise makes the reconstruction process numerically unstable and narrows the choice of the sampling kernels to polynomial reproducing kernels. As a remedy to these problems, we replace conventional moments with more stable generalized moments that are adjusted to the given sampling kernel. The benefits are threefold: 1) it relaxes the requirements on the sampling kernels; 2) produces annihilation equations that are robust at numerical precision; and 3) extends the results to images with unbounded boundaries. We further reduce the sensitivity of the reconstruction process to noise by taking into account the sign of the polynomial at certain points, and sequentially enforcing measurement consistency. We consider various numerical experiments to demonstrate the performance of our algorithm in reconstructing binary images, including low to moderate noise levels and a range of realistic sampling kernels.

Shapes From Pixels

Continuous-domain visual signals are usually captured as discrete (digital) images. This operation is not invertible in general, in the sense that the continuous-domain signal cannot be exactly reconstructed based on the discrete image, unless it satisfies certain constraints (e.g., bandlimitedness). In this paper, we study the problem of recovering shape images with smooth boundaries from a set of samples. Thus, the reconstructed image is constrained to regenerate the same samples (consistency), as well as forming a shape (bilevel) image. We initially formulate the reconstruction technique by minimizing the shape perimeter over the set of consistent binary shapes. Next, we relax the non-convex shape constraint to transform the problem into minimizing the total variation over consistent non-negative-valued images. We also introduce a requirement (called reducibility) that guarantees equivalence between the two problems. We illustrate that the reducibility property effectively sets a requirement on the minimum sampling density. We also evaluate the performance of the relaxed alternative in various numerical experiments.

A multi-stage secret sharing scheme using all-or-nothing transform approach

A multi-stage secret sharing (MSS) scheme is a method of sharing a number of secrets among a set of participants, such that any authorized subset of participants could recover one secret in every stage. The first MSS scheme was proposed by He and Dawson in 1994, based on Shamirs well-known secret sharing scheme and one-way functions. Several other schemes based on different methods have been proposed since then. In this paper, the authors propose an MSS scheme using All-Or-Nothing Transform (AONT) approach. An AONT is an invertible map with the property that having “almost all” bits of its output, one could not obtain any information about the input. This characteristic is employed in the proposed MSS scheme in order to reduce the total size of secret shadows, assigned to each participant. The resulted MSS scheme is computationally secure. Furthermore, it does not impose any constraint on the order of secret reconstructions. A comparison between the proposed MSS scheme and that of He and Dawson indicates that the new scheme provides more security features, while preserving the order of public values and the computational complexity.

Randomized recovery for boolean compressed sensing

We consider the problem of boolean compressed sensing, which is also known as group testing. The goal is to recover a small number of defective items in a large set from a few collective binary tests. This problem can be formulated as a binary linear program, which is NP hard in general. To overcome the computational burden, it was recently proposed to relax the binary constraint on the variables, and apply a rounding to the solution of the relaxed linear program. In this paper, we introduce a randomized algorithm to replace the rounding procedure. We show that the proposed algorithm considerably improves the success rate with only a slight increase in computational cost.

Equivalence of synthesis and atomic formulations of sparse recovery

Recovery of sparse signals from linear, dimensionality reducing measurements broadly falls under two well-known formulations, named the synthesis and the analysis formulations. Recently, Chandrasekaran et al. introduced a new algorithmic sparse recovery framework based on the convex geometry of linear inverse problems, called the atomic norm formulation. In this paper, we prove that atomic norm formulation and synthesis formulation are equivalent for closed atomic sets. Hence, it is possible to use the synthesis formulation in order to obtain the so-called atomic decompositions of signals. In order to numerically observe this equivalence we derive exact linear matrix inequality representations, also known as the theta bodies, of the centrosymmertic polytopes formed from the columns of the simplex and their antipodes. We then illustrate that the atomic and synthesis recovery results agree on machine precision on randomly generated sparse recovery problems.