The security is so important for both storing and transmitting the digital data, the choice of parameters is critical for a security system, that is, a weak parameter will make the scheme very vulnerable to attacks, for example the use of supersingular curves or anomalous curves leads to weaknesses in elliptic curve cryptosystems, for RSA cryptosystem there are some attacks for low public exponent or small private exponent. In certain circumstances the secret sharing scheme is required to decentralize the risk. In the context of the security of secret sharing schemes, it is known that for the scheme of Shamir, an unqualified set of shares cannot leak any information about the secret. This paper aims to show that the well-known Shamir’s secret sharing is not always perfect and that the uniform randomization before sharing is insufficient to obtain a secure scheme. The second purpose of this paper is to give an explicit construction of weak polynomials for which the Shamir’s (k, n) threshold scheme is insecure in the sense that there exist a fewer than k shares which can reconstruct the secret. Particular attention is given to the scheme whose threshold is less than or equal to 6. It also showed that for certain threshold k, the secret can be calculated by a pair of shares with the probability of 1/2. Finally, in order to address the mentioned vulnerabilities, several classes of polynomials should be avoided.

Graph matching is a comparison process of two objects represented as graphs through finding a correspondence between vertices and edges. This process allows defining a similarity degree (or dissimilarity) between the graphs. Generally, graph matching is used for extracting, finding and retrieving any information or sub-information that can be represented by graphs. In this paper, a new consistency rule is proposed to tackle with various problems of graph matching. After, using the proposed rule as a necessary and sufficient condition for the graph isomorphism, we generalize it for subgraph isomorphism, homomorphism and for an example of inexact graph matching. To determine whether there is a matching or not, a backtracking algorithm called CRGI2 is presented who checks the consistency rule by exploring the overall search space. The tree-search is consolidated with a tree pruning technique that eliminates the unfruitful branches as early as possible. Experimental results show that our algorithm is efficient and applicable for a real case application in the information retrieval field. On the efficiency side, due to the ability of the proposed rule to eliminate as early as possible the incorrect solutions, our algorithm outperforms the existing algorithms in the literature. For the application side, the algorithm has been successfully tested for querying a real dataset that contains a large set of e-mail messages.

This paper introduces a new approach of hybrid meta-heuristics based optimization technique for decreasing the computation time of the shortest paths algorithm. The problem of finding the shortest paths is a combinatorial optimization problem which has been well studied from various fields. The number of vehicles on the road has increased incredibly. Therefore, traffic management has become a major problem. We study the traffic network in large scale routing problems as a field of application. The meta-heuristic we propose introduces new hybrid genetic algorithm named IOGA. The problem consists of finding the k optimal paths that minimizes a metric such as distance, time, etc. Testing was performed using an exact algorithm and meta-heuristic algorithm on random generated network instances. Experimental analyses demonstrate the efficiency of our proposed approach in terms of runtime and quality of the result. Empirical results obtained show that the proposed algorithm outperforms some of the existing technique in term of the optimal solution in every generation.