Homomorphic Encryption Case Study

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The so-called fully homomorphic encryption is considered the Holy Grail of Cryptography. Addition and multiplication are the main building blocks of computers, and the ability to make calculations on encrypted data without decrypting it, would lead to a whole new level of security.
So, a company, for example, could send an encrypted database to a cloud computing provider, which would work on that data without decrypting it. If a customer wanted then to perform a search on their personal database, it could be performed in spite of the encryption, the result would then be encoded and sent to the authorized person, and the latter can then decrypt it on their own computer. Similarly, the content of other Internet applications such as web-mail could
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Smart and Vercauteren [2] built their approach in order to make it possible to test Gentry's idea on a desktop computer. They managed to implement the system and encrypt the data and even do a little of addition and multiplication. Around 30 sequential operations were thus possible. But still, there are some limitations of this technique. If additional operations are performed, its following encrypted answers deteriorate, they are "dirty" (which is known as a noise). This means that the current version of the technology is not really fully homomorphic because calculations aren't all possible to be performed.

In this paper, we propose a secure and efficient data Access control mechanism. Also, we're going to address an important subject in the Cloud, risk management.

II. ABSTRACT STRUCTURE OF THE
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They are all confined to a particular mathematical operation, either addition or multiplication. A fully homomorphic method, which allows arbitrary operations on encrypted data, has made a breakthrough, encoded data are manipulated as desired, and the results are correctly translated back into plaintext. This could mean a breakthrough for cloud computing. However, the process eats up lots of computing power and is therefore not yet appropriate for current computing in the cloud.
Gentry has already developed a method that periodically "cleans" the data so it can be self-corrected (noise reduction), thus, it creates a fully homomorphic system. However, an implementation of this method is still required so it can cover a certain number of calculations. Therefore, Gentry and his IBM colleague Shai Helevi are experimenting currently with their own version of Smart’s approach [4] and hope to still report initial results and improvements in the near future. Smart currently tries to find the right parameters of his approach, to find out what really works best. For example, the generation of the key is very slow, which can be optimized, it is a bit like tuning a race car, you work on the engine and then suddenly discovered that the wheels are the

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