Fully homomorphic encryption: a general framework and implementations. Issue 5 (2nd September 2020) - Akl, Selim G.
ABSTRACT: Two data items a and b are stored on an untrusted database in their encrypted forms E ( a ) and E ( b ), respectively. It is required that the encryption function be fully homomorphic, that is, E must satisfy the conditions E ( a ) + E ( b ) = E ( a + b ) and E ( a ) × E ( b ) = E ( a × b ) . This would allow the owner of the data, as well as an untrusted party operating the database on behalf of the owner, to perform operations directly on the encrypted data without the need for decryption. We propose a general framework that allows the derivation of such fully homomorphic functions. Two implementations of the general framework are then described that, in addition to being secure, enjoy the property of being efficient to compute.