Analysis and Comparison of Fully Homomorphic Encryption Approaches Over Integers

Bozkurt, Cansu
The time period after the mid-20th century was named as information age or digital age. In that age, the world is being digitalized very fastly. The amount of data transferred and processed online is increasing rapidly. As a result, data protection became an essential topic for researchers. To process or make a computation on the encrypted data deciphering ciphertext first causes a security flaw. Homomorphic encryption (HE) algorithms were designed to make computations on data without deciphering it. However, HE algorithms are able to work for a limited amount of processing steps. Fully homomorphic encryption (FHE) algorithms are developed to solve this problem. It is feasible to apply any accurately calculable operation on encrypted data. This thesis presents definitions, properties, applications of FHE. Some constructions of FHE schemes based on the integers are also analyzed. Furthermore, the computational complexity of two algorithms, namely the DGHV scheme and Batch DGHV scheme has been computed, and their efficiency is compared based on the complexities. While the DGHV scheme encrypts the one-bit message, the batch DGHV scheme encrypts an ℓ-bit message vector m at a time. The primary purpose is to research which option is more efficient for encrypting l-bit messages. The first option is to use the DGHV scheme for l-times. The second option is to use the batch DGHV scheme one time. We conclude that for message size l when security parameter l ≤ λ^3/2 using the batch scheme is more efficient than using DGHV scheme.


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Citation Formats
C. Bozkurt, “Analysis and Comparison of Fully Homomorphic Encryption Approaches Over Integers,” M.S. - Master of Science, Middle East Technical University, 2022.