Homomorphic encryption

Homomorphic encryption is a type of encryption where the data in transit can be accessed, computed, analysed all the while the data remains encrypted. This can be extension of both symmetric and asymmetric encryption(See Symmetric and Asymmetric Encryption for more details). This can be used for outsourcing encrypted data for storage and computation to the cloud environments

 In plain language homomorphic encryption is like this - Assume there are many things in a bag and you put your hands inside, manipulate their positions, access them and sense them but you cant pull them out and see for real what they are.



 This kind of data transmission is required in healthcare where the privacy is of most concern. The same holds good for voting purposes where the data needs to be encrypted for privacy purpose but also should be assessed. In the banking sectors too this is used to protect the PII and still perform the required processing on the data.

 The computations on the data are represented by either Boolen or arithmetic circuits.

 Types of homomorphic encryption 

 Partially homomorphic encryption: 

 encompasses schemes that support the evaluation of circuits consisting of only one type of gate, e.g., addition or multiplication.

 Somewhat homomorphic encryption:
can evaluate two types of gates, but only for a subset of circuits

 Leveled fully homomorphic encryption :
supports the evaluation of arbitrary circuits of bounded (pre-determined) depth

 Fully homomorphic encryption(FHE): 
allows the evaluation of arbitrary circuits of unbounded depth, and is the strongest notion of homomorphic encryption

 For the majority of homomorphic encryption schemes, the multiplicative depth of circuits is the main practical limitation in performing computations over encrypted data.

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