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Carlo Blundo

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8 papers

1 author row

TCS Journal 2006 Journal Article

Visual cryptography schemes with optimal pixel expansion

Carlo Blundo
Stelvio Cimato
Alfredo De Santis

A visual cryptography scheme encodes a black and white secret image into n shadow images called shares which are distributed to the n participants. Such shares are such that only qualified subsets of participants can “visually” recover the secret image. Usually, the reconstructed image will be darker than the background of the image itself. In this paper we consider visual cryptography schemes satisfying the model introduced by Tzeng and Hu [A new approach for visual cryptography, Designs, Codes and Cryptography 27 (3) (2002) 207–227]. In such a model, the recovered secret image can be darker or lighter than the background. We prove a lower bound on the pixel expansion of the scheme and, for ( 2, n ) -threshold visual cryptography schemes, we provide schemes achieving the bound. Our schemes improve on the ones proposed by Tzeng and Hu.

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TCS Journal 2004 Journal Article

Bounds and constructions for unconditionally secure distributed key distribution schemes for general access structures

Carlo Blundo
Paolo D'Arco
Vanessa Daza
Carles Padró

In this paper we investigate the issues concerning the use of a single server across a network, the key distribution center (KDC) to enable private communications within groups of users. After providing several motivations, showing the advantages related to the distribution of the task accomplished by this server, we describe a model for such a distribution, and present bounds on the amount of resources required in a real-world implementation: random bits, memory storage, and messages to be exchanged. Moreover, we introduce a linear algebraic approach to design optimal schemes distributing a KDC, and we point out that some previous constructions belong to the proposed framework.

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TCS Journal 2001 Journal Article

Extended capabilities for visual cryptography

Giuseppe Ateniese
Carlo Blundo
Alfredo De Santis
Douglas R. Stinson

An extended visual cryptography scheme (EVCS), for an access structure (Γ Qual, Γ Forb ) on a set of n participants, is a technique to encode n images in such a way that when we stack together the transparencies associated to participants in any set X∈Γ Qual we get the secret message with no trace of the original images, but any X∈Γ Forb has no information on the shared image. Moreover, after the original images are encoded they are still meaningful, that is, any user will recognize the image on his transparency. The main contributions of this paper are the following: • A trade-off between the contrast of the reconstructed image and the contrast of the image on each transparency for (k, k)-threshold EVCS (in a (k, k)-threshold EVCS the image is visible if and only if k transparencies are stacked together). This yields a necessary and sufficient condition for the existence of (k, k)-threshold EVCS for the values of such contrasts. In case a scheme exists we explicitly construct it. • A general technique to implement EVCS, which uses hypergraph colourings. This technique yields (k, k)-threshold EVCS which are optimal with respect to the pixel expansion. Finally, we discuss some applications of this technique to various interesting classes of access structures by using relevant results from the theory of hypergraph colourings.

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I&C Journal 1998 Journal Article

Perfectly Secure Key Distribution for Dynamic Conferences

Carlo Blundo
Alfredo De Santis
Amir Herzberg
Shay Kutten
Ugo Vaccaro
Moti Yung

In this paper we analyze perfectly secure key distribution schemes for dynamic conferences. In this setting, anymember of a group oftusers can compute a common key using only his private initial piece of information and theidentitiesof the othert−1 users in the group. Keys are secure against coalitions of up tokusers; that is, even ifkusers pool together their pieces they cannot compute anything about a key of any conference comprised oftother users. First we consider a noninteractive model where users compute the common key without any interaction. We prove the tight bound on the size of each user's piece of information of[formula]times the size of the common key. Then, we consider the model where interaction is allowed in the common key computation phase and show agapbetween the models by exhibiting a one-round interactive scheme in which the user's information is onlyk+t−1 times the size of the common key. Finally, we present its adaptation to network topologies with neighbourhood constraints and to asymmetric (e. g. , client-server) communication models.

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TCS Journal 1996 Journal Article

Fully dynamic secret sharing schemes

Carlo Blundo
Antonella Cresti
Alfredo De Santis
Ugo Vaccaro

We consider secret sharing schemes in which the dealer is able (after a preprocessing stage) to activate a particular access structure out of a given set and/or to allow the participants to reconstruct different secrets (in different time instants) by sending them the same broadcast message. In this paper we establish a formal setting to study secret sharing schemes of this kind. The security of the schemes presented is unconditional, since they are not based on any computational assumption. We give bounds on the size of the shares held by participants, on the size of the broadcast message, and on the randomness needed in such schemes.

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TCS Journal 1996 Journal Article

On the information rate of secret sharing schemes

Carlo Blundo
Alfredo De Santis
Luisa Gargano
Ugo Vaccaro

We derive new limitations on the information rate and the average information rate of secret sharing schemes for access structure represented by graphs. We give the first proof of the existence of access structures with optimal information rate and optimal average information rate less than 1 2 + ε, where ε is an arbitrary positive constant. We also consider the problem of testing if one of these access structures is a substructure of an arbitrary access structure and we show that this problem is NP-complete. We provide several general lower bounds on information rate and average information rate of graphs. In particular, we show that any graph with n vertices admits a secret sharing scheme with information rate Ω((log n)/n).

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I&C Journal 1996 Journal Article

Randomness in Distribution Protocols

Carlo Blundo
Alfredo De Santis
Ugo Vaccaro

Randomness is a useful computation resource due to its ability to enhance the capabilities of other resources. Its interaction with resources such as time, space, interaction with provers and its role in several areas of computer science has been extensively studied. In this paper we give a systematic analysis of the amount of randomness needed by secret sharing schemes and secure key distribution schemes. We give both upper and lower bounds on the number of random bits needed by secret sharing schemes. The bounds are tight for several classes of secret sharing schemes. For secure key distribution schemes we provide a lower bound on the amount of randomness needed, thus showing the optimality of a recently proposed key distribution protocol.

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I&C Journal 1996 Journal Article

Visual Cryptography for General Access Structures

Giuseppe Ateniese
Carlo Blundo
Alfredo De Santis
Douglas R. Stinson

A visual cryptography scheme for a set P ofnparticipants is a method of encoding a secret imageSIintonshadow images called shares, where each participant in P receives one share. Certain qualified subsets of participants can “visually” recover the secret image, but other, forbidden, sets of participants have no information (in an information-theoretic sense) onSI. A “visual” recovery for a setX⊆ P consists of xeroxing the shares given to the participants inXonto transparencies, and then stacking them. The participants in a qualified setXwill be able to see the secret image without any knowledge of cryptography and without performing any cryptographic computation. In this paper we propose two techniques for constructing visual cryptography schemes for general access structures. We analyze the structure of visual cryptography schemes and we prove bounds on the size of the shares distributed to the participants in the scheme. We provide a novel technique for realizingkout ofnthreshold visual cryptography schemes. Our construction forkout ofnvisual cryptography schemes is better with respect to pixel expansion than the one proposed by M. Naor and A. Shamir (Visual cryptography, in“Advances in Cryptology—Eurocrypt '94” CA. De Santis, Ed.), Lecture Notes in Computer Science, Vol. 950, pp. 1–12, Springer-Verlag, Berlin, 1995) and for the case of 2 out ofnis the best possible. Finally, we consider graph-based access structures, i. e. , access structures in which any qualified set of participants contains at least an edge of a given graph whose vertices represent the participants of the scheme.

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