| Summary: | Fully homomorphic encryption is an encryption scheme where a party can receive encrypted data and perform arbitrary operations on this data efficiently.The data remains encrypted throughout, but the operations can be done regardless, without having to know the decryption key.Such a scheme would be very advantageous, for example in ensuring the privacy of data that is sent to a third-party service.This is in contrast with schemes like Paillier where you can not perform a multiplication of encrypted data without decrypting the data first, or ElGamal where you can not perform an addition of encrypted data without decrypting the data first.This thesis acts as a survey of the most recent fully homomorphic encryption schemes. We study some of the latest fully homomorphic encryption schemes, make an analysis of them and make a comparison.These schemes have some elements in common:1. An efficient lattice-based cryptosystem, with security based on the hardness of well-known lattice problems. 2. An evaluation function with definitions for $c_{add}$ and $c_{mult}$, such that the noise does not rapidly increase.3. Techniques to make the scheme fully homomorphic with this evaluation function. Whenever possible, we rewrite the main results of these schemes in a more detailed and readable format.Apart from Gentry's scheme, the schemes that we choose to discuss are very new. The earliest one was published in October 2011, while some are still only available as eprints. We hope this work can help readers be up to date with the field of fully homomorphic encryption, paving way to further advances in the field.
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