Homomorphic encryption is the conversion of data into ciphertext that can be analyzed and worked with as if it were still in its original form.  

Homomorphic encryptions allow complex mathematical operations to be performed on encrypted data without compromising the encryption. In mathematics, homomorphic describes the transformation of one data set into another while preserving relationships between elements in both sets.  The term is derived from the Greek words for "same structure." Because the data in a homomorphic encryption scheme retains the same structure, identical mathematical operations -- whether they are performed on encrypted or decrypted data --  will yield equivalent results.

Homomorphic encryption is expected to play an important part in cloud computing, allowing companies to store encrypted data in a public cloud and take advantage of the cloud provider’s analytic services.

Here is a very simple example of how a homomorphic encryption scheme might work in cloud computing:

• Business XYZ has a very important data set (VIDS) that consists of the numbers 5 and 10.  To encrypt the data set, Business XYZ multiplies each element in the set by 2, creating a new set whose members are 10 and 20.
• Business XYZ sends the encrypted VIDS set to the cloud for safe storage.  A few months later, the government contacts Business XYZ and requests the sum of VIDS elements.   
• Business XYZ is very busy, so it asks the cloud provider to perform the operation.  The cloud provider, who only has access to the encrypted data set,  finds the sum of 10 + 20 and returns the answer 30.
• Business XYZ decrypts the cloud provider’s reply and provides the government with the decrypted answer, 15.

17 Aug 2011