Abstract
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.
Highlights
For a tantamount degree of security, the encryption and decoding activities of an absolutely homomorphic encryption plot are a few sets of size more slow than a standard open key framework, and homomorphically assessing a circuit are regularly essentially all the more burdening
Flattening was recently introduced by Gentry, Sahai& Waters (2013), this technique is based on the modulus switching, the variation here is that the ciphertext is presented in matrix form while the encryption key is in vector form, it was a trivial transformation where vectors are modified without affecting their dot product, making a better bound of the growth of the error
Security factor: This is the total length of the cipher text to the length of the input text
Summary
In the present period of "distributed computing", quite a bit of people's and organizations' information is put away and figured on by outsiders like Google, Microsoft, Apple, Amazon, Facebook, Dropbox and loads of others. For a tantamount degree of security, the encryption and decoding activities of an absolutely homomorphic encryption plot are a few sets of size more slow than a standard open key framework, and (contingent upon its unpredictability) homomorphically assessing a circuit are regularly essentially all the more burdening Be that as it may, this is frequently a quick advancing field, and as of since 2009 huge improvements are found that decreased the computational and capacity overhead by numerous sets of extents. During this arrangement eventually the private key resides on the cloud supplier's PCs, and along these lines the customer must confide in the security of the enclave Speaking, this may give sensible protection from remote programmers, yet (dissimilar to FHE) most likely not against modern aggressors (e.g., governments) that have physical access to the server.
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