Optimal Information Rate Research Articles

Improving the trade-off between storage and communication in broadcast encryption schemes*1

The most important point in the design of broadcast encryption schemes (BESs) is to obtain a good trade-off between the amount of secret information that must be stored by every user and the length of the broadcast message, which are measured, respectively, by the information rate ρ and the broadcast information rate ρ B . In this paper, we present a simple method to combine two given BESs in order to improve the trade-off between ρ and ρ B by finding BESs with good information rate ρ for arbitrarily many different values of the broadcast information rate ρ B . We apply this technique to threshold ( R , T )-BESs and we present a method to obtain, for every rational value 1/ R ⩽ ρ B ⩽1, a ( R , T )-BES with optimal information rate ρ among all ( R , T )-BESs that can be obtained by combining two of the ( R , T )-BESs proposed by Blundo et al. (Lecture Notes in Comput. Sci. 1190 (1996) 387–400).

Lower bounds on the information rate of secret sharing schemes with homogeneous access structure

We present some new lower bounds on the optimal information rate and on the optimal average information rate of secret sharing schemes with homogeneous access structure. These bounds are found by using some covering constructions and a new parameter, the k- degree of a participant, that is introduced in this paper. Our bounds improve the previous ones in almost all cases.

Secret sharing schemes with bipartite access structure

We study the information rate of secret sharing schemes whose access structure is bipartite. In a bipartite access structure there are two classes of participants and all participants in the same class play an equivalent role in the structure. We characterize completely the bipartite access structures that can be realized by an ideal secret sharing scheme. Both upper and lower bounds on the optimal information rate of bipartite access structures are given. These results are applied to the particular case of weighted threshold access structure with two weights.

Weighted threshold secret sharing schemes

In a secret sharing scheme, each participant receives a share of a secret in such a way that only authorized subsets can reconstruct the secret. The information rate of a secret sharing scheme is the ratio between the size of the secret and the size of the shares given to the participants. In a weighted threshold scheme each participant has his or her own weight. A subset of participants is authorized to reconstruct the secret if the sum of their weights is greater than or equal to the threshold. This paper deals with weighted threshold schemes, mainly the properties related to the information rate. A complete characterization of the access structures of weighted threshold schemes when all the minimal authorized subsets have at most two elements is presented. Lower bounds for the optimal information rate of these access structures are given.

More information theoretical inequalities to be used in secret sharing?

The efficiency of secret sharing schemes is measured by means of the average or worst-case information rate. It has been shown that information theoretical inequalities can be used to upper bound these rates. Recently, Jackson and Martin studied the optimal average and worst-case information rate of access structures on five participants. Using combinatorial arguments they showed that information theoretically derived upper bounds for certain optimal average information rates can never be met with equality. This led to the search of new information theoretical inequalities to be used in secret sharing. In this letter we discuss one example from Jackson and Martins' paper. We improve the optimal average information rate by introducing new inequalities.

On the information rate of secret sharing schemes

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).

Graph decompositions and secret sharing schemes

In this paper we continue a study of secret sharing schemes for-access structures based on graphs. Given a graph G, we require that a subset of participants can compute a secret key if they contain an edge of G; otherwise, they can obtain no information regarding the key. We study the information rate of such schemes, which measures how much information in being distributed as shares compared with the size of the secret key, and the average information rate, which is the ratio between the secret size and the arithmetic mean of the size of the shares. We give both upper and lower bounds on the optimal information rate and average information rate that can be obtained. Upper bounds arise by applying entropy arguments due to Capocelli et al. [15]. Lower bounds come from constructions that are based on graph decompositions. Application of these constructions requires solving a particular linear programming problem. We prove some general results concerning the information rate and average information rate for paths, cycles, and trees. Also, we study the 30 (connected) graphs on at most five vertices, obtaining exact values for the optimal information rate in 26 of the 30 cases, and for the optimal average information rate in 28 of the 30 cases.

An explication of secret sharing schemes

This paper is an explication of secret sharing schemes, emphasizing combinatorial construction methods. The main problem we consider is the construction of perfect secret sharing schemes, for specified access structures, with the maximum possible information rate. In this paper, we present numerous direct constructions for secret sharing schemes, such as the Shamir threshold scheme, the Boolean circuit construction of Benaloh and Leichter (for general access structures), the vector space construction of Brickell, and the Simmons geometric construction. We discuss the connections between ideal schemes (i.e., those with information rate equal to one) and matroids. We also mention the entropy bounds of Capocelli et al. Then we give a very general construciton, called the decomposition construction, and numerous applications of it. In particular, we study schemes for access structures based on graphs and the many interesting bounds that can be proved; and we determine the exact value of the optimal information rate for all access structures on at most four participants.

The Optimization of Astronautical Vehicle Detection Systems through the Application of Search Theory

A generalized theory of detection system performance is developed and applied to the analysis of collision warning and the optimal allocation of search effort for astronautical vehicles. The kinematic basis of the relative frequency of intercepts with randomly moving particles is presented. The pronounced variation in warning system effectiveness if the possible contact space is uniformly scanned is displayed by investigating the functional behavior of the weighted mean acquisition range and cumulative probability of detection by some minimal detection barrier in the hypervelocity closure rate, low signal amplitude operational environment. Fixing the search system frame time, it is shown that the probability of acquiring a closing particle by some critical range determined by the system response delay may be made independent of the bearing angle of the relative approach path by choosing search system dwell times that are proportional to the second or fourth power of the mean anticipated closure rate, the exponent being dependent upon whether the sensor is active or passive. The rational choice of the frame time is investigated in terms of the information rate out of the sensor and the requirements of the decision-making apparatus. The latter is assumed to be an unsaturated, bandwidth and memory limited data processing subsystem. The probability of track retention and the variance of the best estimate of the contact-bearing angle are related to the cumulative probability of detection. It is shown that the required system reaction times are in conflict with the optimal detection system information rates.