Question

One research topic in cryptography is to create homomorphic encryption schemes. In such schemes, it is possible to do operations on the ciphertext without performing decryption. Give an example of where homomorphic encryption would be useful. You do not have to give a specific cryptographic method but describe a situation where you would want to do computations on ciphertext. Be specific: what is the information, what is encrypted, and what the computation is.

Related concept: given an RSA scheme with plaintexts P1 and P2 and respective ciphertexts C1 and C2, show how one can find the ciphertext corresponding to P1 x P2 (“x” is multiplication) without encrypting P1 x P2.

Answer 1

Homomorphic encryption technique is technique where the recieved encrypted data is subjected to processing or calculation without decrypting. This technique wont seek the secret key used to encrypt the data for the processing. This calculation produce an encrypted data and on decrypting the data after calculation, we get the same data as done with decryption. This will help to keep the data encrypted and there by protected even at the time of processing.

There are different types of homomorphic encryption techniques:

• Partially homomorphic - Used where the evaluation of circuit consist of only 1 type of gate. (addition or multiplication)
• Somewhat homomorphic - This can can evaluate 2 types of gate for subset circuits.
• Leveled fully homomorphic - This supports arbitary circuits with bounded depth.
• Fully homomorphic - This allow evaluation of arbitaryy circuit of unbounded depth. This is the strongest homomorphic encryption.

There are several application where the input data and output data are preserved as encrypted. Homomorphic encryption technique can be used in such applications. Homomorphic encryption is used in industries like health care where to enable new services inhibiting data sharing by removing privacy barriers. For example, due to medical privacy concerns, it is hard to apply predictive analytics in heospitals. Homomophic encryption can be used to keep the data encrypted and so private. So the predictive analysis can be done without the concern of privacy.