In the Naive Bayes classification problem using a vertically partitioned dataset, the conventional scheme to preserve privacy of each partition uses a secure scalar product and is based on the assumption that the data is synchronized amongst common unique identities. In this paper, we attempt to discard this assumption in order to develop a more efficient and secure scheme to perform classification with minimal disclosure of private data. Our proposed scheme is based on the work by Vaidya and Clifton [2], which uses commutative encryption to perform secure set intersection so that the parties with access to the individual partitions have no knowledge of the intersection. The evaluations presented in this paper are based on experimental results, which show that our proposed protocol scales well with large sparse datasets*.

Fair exchange is an important tool to achieve “fairness” of electronic commerce. Several previous schemes satisfy universally composable security which provides security preserving property under complex networks like the Internet. In recent years, as the demand for electronic commerce increases, fair exchange for electronic vouchers (e.g., electronic tickets, moneys, etc.) to obtain services or contents is in the spotlight. The definition of fairness for electronic vouchers is different from that for general electronic items (e.g., the sender must not do duplicate use of exchanged electronic vouchers). However, although there are universally composable schemes for electronic items, there is no previous study for electronic vouchers. In this paper, we introduce a universally composable definition of fair voucher exchange, that is, an ideal functionality of fair voucher exchange. Also, we prove the equivalence between our universally composable definition and the conventional definition for electronic vouchers. Thus, our formulation of the ideal functionality is justified. Finally, we propose a new fair voucher exchange scheme from non-blocking atomic commitment as black-box, which satisfies our security definition and is adequate for mobile environments. By instantiating general building blocks with known practical ones, our scheme can be also practical because it is implemented without trusted third party in usual executions.