Homomorphic Encryption

Abstract

Important types of encryption schemes are those that fall into the homomorphic encryption (HE) category, which allows calculations to be computed directly on the encrypted data, without needing a preceding decryption operation. The most important condition in homomorphic encryption is that the value achieved by decrypting the result obtained by applying the calculations over the encrypted data must be the same as the value achieved by applying the same calculations on the plain data. With these properties, the HE schemes are considered to have great potential because they enable third-party entities to apply functions (therefore, to apply algorithms) on the encrypted data, but without the need for any access of the plain data. In this way, the data is protected and secured while being processed. For a real-life example, suppose you are on vacation into a foreign city and you want to search the Internet, using your phone or another device, for local attractions such as museums, exhibitions, art galleries, and so on. Even this simple search on the Internet may reveal a lot of information about you, such as your exact location, your cultural interests, the time of the search query, and so on. If the search engine used a homomorphic approach, then nothing would be revealed to anyone including the search engine itself, because all of the information and even the search query would be encrypted. The results that you receive would be also encrypted, therefore only you could decrypt them. Homomorphic encryption has applications in many areas, such as finance/business, healthcare, and any domain that works with sensitive data. Further, some formal aspects of homomorphic encryption are given.