Increasing System Security with Full Homo-morphic Encryption using Lagrange's Functions

Homo-morphic systems present a novel way to encrypt data, via which operations performed on the encrypted data are fully/partially reflected in the decrypted data. For example, if the input data D is homo-morphically encrypted to E, and if we perform X=E+N, then while decrypting X, we are bound to get D+N. Such a kind of encryption helps data owners to safely share their data among different analysers, without the risk of any kind of data leakages. Data analysers usually perform mathematical operations on the data which include addition, subtraction, multiplication and division. Homo-morphic systems which support addition & subtraction but do not support multiplication and division are termed as partially homo-morphic systems. While systems which support all the operations are termed as fully homo-morphic systems. In this paper, we have implemented a fully homo-morphic system based on Lagrange’s functions. These functions help in improving the overall security of the system by adding stochastics to the input data, which ensures that the same input data has different cipher text, and full homo-morphism is achieved. Security of overall system increased by 40% by using FHE.