Homomorphic Encryption: Computing on encrypted data

Abstract

Homomorphic encryption is the ability to compute mathematical functions on encrypted data without decryption. The output of the computations is itself in encrypted form which when decrypted is identical to the output had the computation been performed on the plaintexts directly. A homomorphic encryption scheme is said to be fully homomorphic if mathematical functions of arbitrary complexity can be computed on encrypted data. Fully homomorphic encryption (FHE) has several applications in security and privacy since computations can be outsourced to a third (untrusted) party while the data is still in encrypted form. For the usability of FHE in various applications, it is needed that these schemes are thoroughly studied and implemented to be able to use in practice. However, not all schemes in the literature are implemented yet. In this thesis, we implemented the basic encryption operation and homomorphic addition property of the FHE scheme, proposed by Dowerah et.al in her PhD dissertation. Further, we explored the possibility of extending the scheme to a multi-key setting for the basic encryption scheme. Multikey homomorphic encryption (MK-HE) enables separate parties to utilize distinct keys for encryption, different from traditional homomorphic encryption scheme which assesses the arithmetic circuits of ciphertexts encrypted with the same key.