Efficient integer division computation protocols based on partial homomorphic encryption

In cloud environment, designing the efficient outsourced calculation protocols to serve the machine learning or data mining is a hot topic. At the same time, homomorphic encryption allows operations on encrypted data, and is a natural primitive to implement outsourced computation. Most existing protocols consider all operands being secret data. While in practice, the operations may occur between public data and private data since some of them is publicly known to all, and only partial data is confidential. To address the partially encrypted computation, it is necessary to design new protocols. In this paper, we consider the integer division calculation and design two protocols based on the partial homomorphic encryption, one of which caters to the division with public divisor and private dividend, and the other caters to the division with public dividend and private divisor. The quotient and the remainder are computed in ciphertext. The security of the protocols is proved within the ideal/real paradigm, and the performance analysis shows the efficiency of the protocols compared with the full-encrypted division