Algorithms for Implementing Repeated Homomorphic Operations on Restricted Data Type Ranges

Abstract

Security is the primary concern for cloud-based data storage. While the data is stored in the cloud, it is queried and retrieved regularly from various remote locations. Various cloud providers come with built-in security features for all the data stored in the cloud. Even though cloud providers offer different security methods, organizations can’t rely on them when it comes to sensitive data. In various enterprise applications, there can be a requirement of performing different operations on data stored in coded form. In this situation, homomorphic ciphering techniques are useful. Different homomorphic encryption methods enable execution of operations on encrypted data without first decrypting it. Typically, these calculations include performing arithmetic operations on encrypted cloud-based data. When the data to be stored is structured and its elements are to be stored in various data type fields, there is a restriction on the range of values stored in the respective data type. Using existing homomorphic techniques, direct operations between two or more encrypted values cause the result value’s size to increase by that many bits. The size of the result is proportional to the number of times the operation performed. It is therefore challenging to enable numerous additions or multiplications over encrypted numeric values stored in databases. In this paper, we propose a methodology to support an unlimited number of homomorphic operations on encrypted data without increase in size of the final result by incorporating few changes in implementation of various operations. Our proposed work guarantees that it supports unlimited additions or multiplications over encrypted data such that the final result does not exceed the storage size of the data by more than the number of bits. This article provides algorithms for additive homomorphic with Paillier and multiplicative homomorphic with RSA.