Key Predistribution Schemes Based On A Class Of Orthogonal Arrays

In 1947,statistician Rao introduced orthogonal array and used it for orthogonal exper-imental design.Subsequently,orthogonal experimental design gradually emerged among many experimental design methods and became the mainstream method in industrial and agricultural production and scientific experiments.Orthogonal arrays are popular for their simple definition and beautiful structure.They are not only essential in statistics but also useful in the fields of computer science,cryptography,codes and network security.Orthog-onal arrays have usually close connection to finite fields,number theory,finite geometry,etc.Many combinatorial mathematicians and statisticians are devoted to the research on orthogonal arrays,and obtain abundant achievementsWith the deep study of orthogonal arrays,their applications have penetrated into many fields,one of which is to construct key predistribution schemes for distributed sensor networks.The key predistribution scheme needs to distribute the keys to each sensor node before the nodes are deployed.It is challenging to find an efficient way of distributing keys to sensor nodes.This dissertation studies the Hamming distances of orthogonal arrays,and explores the orthogonal arrays with unique Hamming distance distribution to construct secure and effective schemes,so that the schemes can adapt to different network scenarios The concrete content is summarized as follows(1)For the study on Hamming distances of orthogonal arrays,two definitions of the Hamming distance distribution of an orthogonal array and its uniqueness are proposed Furthermore,we present some orthogonal arrays with unique Hamming distance distribu-tion,including schematic orthogonal arrays,symmetric and asymmetric orthogonal arrays The concepts can help to simplify the analysis of network connectivity and resilience in a scheme.(2)Key predistribution schemes based on orthogonal arrays with unique Hamming distance distribution are proposed.Their simplified calculation formulas of the network connectivity and resilience are given.And two specific key predistribution schemes are constructed.We analyze the resulting schemes and compare them with existing ones.It is shown that the proposed schemes have better connectivity or resilience.