| Summary: | Homomorphic encryption system (HES) schemes are anticipated to play a significant role in cloud-based applications. Moving to cloud-based storage and analytic services securely are two of the most important advantages of HES. Several HES schemes have been recently proposed. However, the majority of them either have limited capabilities or are impractical in real-world applications. Various HES schemes provide the ability to perform computations for statistical analysis (e.g. average, mean and variance) on encrypted data. Domingo-Ferrer is one scheme that has privacy homomorphism properties to perform the basic mathematical operations (addition, subtraction and multiplication) in a convenient and secure way. However, it works only in the positive numbers’ range which is considered as a limitation because several applications require both positive and negative ranges in which to work, especially those that have to implement analytical services in cloud computing. In this paper, we extend Domingo-Ferrer’s scheme to be able to perform arithmetic operations for both positive and negative numbers. We also propose using a lightweight data aggregation function to compute both maximum and minimum values of the aggregated data that works for both positive and negative numbers.
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