Secret computation of purchase history data using somewhat homomorphic encryption

We consider secret computation of purchase history data among two companies of different type of business in order to identify purchase patterns without revealing customer information of each company. Among several privacy-preserving approaches, we focus on homomorphic encryption, which is public-key encryption supporting meaningful computations on encrypted data. In particular, we apply the somewhat homomorphic encryption scheme proposed by Brakerski and Vaikuntanathan (CRYPTO 2011), which can support a limited number of both additions and multiplications over polynomials. The main contribution is to introduce a practical packing method in the scheme to efficiently compute the set intersection of purchase history data over packed ciphertexts. Furthermore, we implemented the scheme for several parameters corresponding to various security levels, and demonstrate the efficiency of our packing method. We hope that this work would give the first practical usage of somewhat homomorphic encryption in marketing analysis.