Annalisa De Bonis

Improved Schemes for Visual Cryptography

A (k,n)-threshold visual cryptography scheme ((k,n)-threshold VCS, for short) is a method to encode a secret image SI into n shadow images called shares such that any k or more shares enable the “visual” recovery of the secret image, but by inspecting less than k shares one cannot gain any information on the secret image. The “visual” recovery consists of xeroxing the shares onto transparencies, and then stacking them. Any k shares will reveal the secret image without any cryptographic computation.In this paper we analyze visual cryptography schemes in which the reconstruction of black pixels is perfect, that is, all the subpixels associated to a black pixel are black. For any value of k and n, where 2 ≤ k ≤ n, we give a construction for (k,n)-threshold VCS which improves on the best previously known constructions with respect to the pixel expansion (i.e., the number of subpixels each pixel of the original image is encoded into). We also provide a construction for coloured (2,n)-threshold VCS and for coloured (n,n)-threshold VCS. Both constructions improve on the best previously known constructions with respect to the pixel expansion.

Constructions of generalized superimposed codes with applications to group testing and conflict resolution in multiple access channels

In this paper we introduce a parameterized generalization of the well known superimposed codes. We give algorithms for their construction and provide non-existential results. We apply our new combinatorial structures to the efficient solution of new group testing problems and access coordination issues in multiple access channels.

Improved algorithms for group testing with inhibitors

Abstract Recent biological applications motivate a new group testing model where in addition to the category of the positive samples and the one of the negative samples, there is a third class of samples called inhibitors. The presence of positives in a test set cannot be detected if the test set contains one or more inhibitors. Let n be the total number of samples and p and r denote the number of positive and inhibitor samples, respectively. Farach et al. (1997), who introduced this model, have given a lower bound of Ω(log(( p n )( r n − p ))) on the number of tests required to find the p positives. They have also described a randomized algorithm to find the p positives which achieve this bound when p + r ⪡ n. In this paper, we give a better lower bound on the number of tests required to find the p positives by uncovering a relation between this group testing problem and cover-free families. We also provide efficient deterministic algorithms to find the positive samples.

Largest Families Without an r-Fork

Let [n] = { 1,2,...,n} be a finite set,

Largest family without A ∪ B ⊆ C ∩ D

{\cal F}

Group testing with unreliable tests

a family of its subsets, 2 ≤ r a fixed integer. Suppose that

Metering Schemes with Pricing

{\cal F}

Dynamic Multi-threshold Metering Schemes

contains no r + 1 distinct members F, G1,..., Gr such that F ⊂ G1,...,F ⊂ Gr all hold. The maximum size

Optimal detection of a counterfeit coin with multi-arms balances

|{\cal F}|

Combinatorial group testing for corruption localizing hashing

is asymptotically determined up to the second term, improving the result of Tran.