Secure Scalar Product for Big-Data in MapReduce

Organizations and individuals nowadays are more and more willing to outsource their data to save storage and management costs, especially with the push of cloud computing which offers both storage and computation scalability. However, the data, once being released to a server, is no longer under its owner´s control, and its privacy and security herein become a primary concern. To this end, users usually encrypt the private data before outsourcing it, which however makes cloud data mining be very thorny and challenging as data is both big and encrypted. Under such new circumstance, we consider secure scalar product in this paper, which is a building block of data mining used to compute the sum of the products of corresponding values of two vectors. Existing methods either prevent privacy violation in the price of sacrificing accuracy, or requires users to take huge overhead. So, we propose a protocol called Secure Scalar Product in MapReduce (S²PM), which is able to perform massive data processing for encrypted big-data securely. S²PM lets the cloud be responsible for most of the operations while user only need to carry out a decryption operation to get the final result. We formally proved that S²PM can return the correct result and is secure. We also conducted performance analysis for S²PM.