Private computation of the Schulze voting method over the cloud
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Private computation of the Schulze voting method over the cloud Vijay Kumar Yadav1 • Anshul Anand1 • Shekhar Verma1 • S. Venkatesan1 Received: 28 September 2019 / Revised: 13 November 2019 / Accepted: 2 December 2019 Springer Science+Business Media, LLC, part of Springer Nature 2019
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. Keywords Homomorphic encryption Fully homomorphic encryption Cloud computing Schulze voting method Ring learning with error
1 Introduction Recently, there is a trend of delegating or outsourcing of digital data to the cloud platforms for the computation [1]. On the sidelines of this development, we can see an increasing concern about a user’s privacy. Extracting sensitive information from a collection of useful looking data is also now a possibility [2–4]. Hence, there is a dichotomy where the user wants to perform cloud-based or serverbased computing due to computational constraints and also keep its sensitive data and the result of the computation as private to prevent the breach of privacy. For example, a scientific lab might want to outsource the computation of fingerprint matching but would not want to reveal the & Vijay Kumar Yadav [email protected] 1
sensitive biometric information to the cloud server as the cloud server might not be a compl
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