Introduction to Homomorphic Encryption

Introduction to Homomorphic Encryption

Homomorphic Encryption is a mechanism which allows computationally expensive calculations to be performed on sensitive data by a third party by encrypting it using polynomials and matrices, so that the content of the data is not accessible to the third party performing the calculations, only the encrypted file. This has a broad range of applications such as processing of health, government and financial data. This encrypted data goes through a boolean series which is either an additive process, multiplicative, or combined in the case of fully homomorphic encryption. This ciphertext output, while not meaningful in any way to the processing server, can be decrypted by the client’s key to reveal the processed data. Within this article the mechanisms which enables the functionality of Homomorphic encryption will be explored as well as the history of the technology dating back to 1978 in which the current day homomorphic technology was iteratively improved from

Bootstrapping and noise generation

When performing calculations on encrypted data, the level of "noise" increases, if the noise level becomes too high, the data will become unable to be deciphered. Bootstrapping can act as a way to continuously reset the noise level. It works by taking plain text "x" and encrypting it with a "red" key (colour is purely to differentiate for example's sake), then some calculations are performed on the data which increases the noise level. In order to reset the noise level back down, this function is now encrypted with the "blue" key. This layered function is then simplified with the decryption function which consists of the red key encrypted by the blue key. This "unwraps" the function, so that it preserves the initial data and partial calculations, while remaining only encrypted by the blue key, so that more calculations can be performed on this data, and this process can go on continuously, theoretically allowing an unlimited amount of calculations to be performed on the data. The issue is that bootstrapping is a slow process, alternatively an adequate noise budget can be set on which a limited amount of calculations can be performed on the data and while limited, this is a more practical approach