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How it works or what it is? It’s a form of encryption where the encrypted data can have computational performed on it without the person/computer performing the computations knowing the underlying data. The output of the computations can be decrypted like normal to give the result of the computations on the original data.

Let’s say my encryption is adding 1 to a number, and my secret number is 7. The encrypted number is now 8. I can tell a data company that my encrypted number is 8 and they’ll never know the secret number. Now they can do some math like adding 12 to the number. They tell me the output of their calculation is 20, so to find the final answer I just subtract 1 to get 19. The same answer if the calculation would have been done on 7. This example is only partially homomorphic because addition and subtraction work but not multiplication or division.

With RSA cryptography, there is a special way to implement multiplication, so that the decrypted answer is the correct result, and the person doing the computation never finds the unencrypted data, but this is still only partially homomorphic. The main problem is that homomorphic encryption requires a lot of computation to do simple calculations.