Private computation of the Schulze voting method over the cloud

Abstract

In this work, we propose an algorithm that computes the Schulze voting method privately and finds the winner of the candidate without revealing the preferences of the voter. Users often outsource data to the cloud to get the result of an intended computation. Many a time, the user would like to keep the data and the result of the delegated computation private due to its sensitive nature. It is possible using data analytics to extract private information from a person. Hence, there is a need to perform computation on encrypted data, which can protect from a leak of private information. Homomorphic encryption (HE), allows computation on encrypted data. HE scheme takes input data in encrypted form and produces output in encrypted form. This encrypted output can not be decrypted without the private key. The Schulze method involves computation of a more complex function known as strength of strongest path. This is challenging to implement privately because it requires the evaluation of several functions over the ciphertexts. We use the Levelled-Brakerski–Gentry–Vaikuntanathan (BGV) fully homomorphic encryption (FHE) scheme to privately compute the strongest paths in a weighted graph using a modified image result of the Floyd–Warshall algorithm. We evaluated our proposed algorithm using an FHE library HElib. Besides, we implemented it for various parameters like time and number of levels in the modulus chain and also evaluated the size of the public key and secret key used for encryption and decryption. From the implementation results, we found that if we increase the number of levels, then the computation and communication complexity will also increase. Therefore, for efficient computation, we need to choose the optimal level.