Private Equality Test Using Ring-LWE Somewhat Homomorphic Encryption

Abstract

We propose two secure protocols namely private equality test (PET) for single comparison and private batch equality test (PriBET) for batch comparisons of l-bit integers. We ensure the security of these secure protocols using somewhat homomorphic encryption (SwHE) based on ring learning with errors (ring-LWE) problem in the semi-honest model. In the PET protocol, we take two private integers input and produce the output denoting their equality or non-equality. Here the PriBET protocol is an extension of the PET protocol. So in the PriBET protocol, we take single private integer and another set of private integers as inputs and produce the output denoting whether single integer equals at least one integer in the set of integers or not. To serve this purpose, we also propose a new packing method for doing the batch equality test using few homomorphic multiplications of depth one. Here we have done our experiments at the 140-bit security level. For the lattice dimension 2048, our experiments show that the PET protocol is capable of doing any equality test of 8-bit to 2048-bit that require at most 107 milliseconds. Moreover, the PriBET protocol is capable of doing about 600 (resp., 300) equality comparisons per second for 32-bit (resp., 64-bit) integers. In addition, our experiments also show that the PriBET protocol can do more computations within the same time if the data size is smaller like 8-bit or 16-bit.