Privacy-Preserving Bayesian Network for Horizontally Partitioned Data

Construction of learning structures for Bayesian networks is considered in this work when data is securely maintained by different parties, not willing to reveal their individual private data to each other. We propose a privacy-preserving protocol for Bayesian network from data which is homogeneously partitioned among two or more parties by using K2 algorithm, a heuristic algorithm typically used to construct Bayesian network. Three secure building blocks are also presented to use inside the main protocol; Secure Exponentiation, Secure Multi-party Factorial and Secure Product Comparison. We have also modified two existing building blocks which are used in this paper, Secure Multi-Party Addition and Multiplication, to improve their resistance against colluding attack. These protocols have the added advantage that they can even be used over public channels. That is, channels over which any party is able to see any messages exchanged between any two or more parties.