Homomorphic Encryption

Today, a lot of data is stored in the cloud. But what is a cloud? It is basically someone else’s computer with lot more storage space than regular laptops and desktop computers. Knowing this, some people encrypt the data before sending it to the cloud so that neither the owner of the cloud or a hacker who obtains access to the cloud can read the data. But what if the data that is encrypted is a file which you want to modify after uploading to the cloud?

One way would be to download the file from the cloud, decrypt it, modify it and then upload the modified file back to the cloud. Another way would be to decrypt the file online and modify it. But this would leave the file vulnerable. Thus this method can be ruled out. The first method is viable if the file is of the size that your computer can handle. What if you want to search for a keyword in a large number of files that you have encrypted and stored in the cloud? Assuming that these files are confidential, the only reason you are storing them in the cloud is due to lack of space on your computer, it is not viable to download the entire database and find the files with the keyword. So what will you do?

You can use homomorphic encryption. Homomorphic encryption is a form of encryption which allows processing of encrypted data and generate an encrypted result which, when decrypted, matches the result of operations performed on the plaintexts. It was first mentioned in 1978 by Rivest, Adleman and Dertouzo in their paper  “On data banks and privacy homomorphisms”, but it took three decades for the first fully homomorphic encryption scheme to be proposed. In those thirty years, partially homomorphic schemes were proposed. RSA cryptosystem, that is widely used today, in its unpadded form is multiplicatively homomorphic, wherein the multiplication of two ciphertexts on decryption gives the product of plaintexts. ElGamal cryptosystem is another multiplicatively homomorphic scheme while Paillier cryptosystem is one of the additively homomorphic cryptosystems.

Image Source: http://www.americanscientist.org/issues/pub/2012/5/alice-and-bob-in-cipherspace/1