Does ElGamal Encryption Do Homomorphic Addition and Subtraction?

Well, yes, but with a small modification …

Homomorphic encryption provides us with a way to encrypt values and then to be able to process them. Let’s say we have Bob the Data Processor and Alice the Consumer. With this, Alice could encrypt the values that she has with her public key, and then Bob can process these values with mathematical operations and then give the result back to Alice, who will then decrypt the result.

For given methods, such as for RSA and ElGamal, we can have partial homomorphic encryption (PHE), and where we implement a few of the arithmetic operations. For example, ElGamal naturally supports multiplication and division:

https://asecuritysite.com/elgamal/el_homomorphic01

But what about addition and subtraction? Well, with a tweak, we can modify ElGamal to support addition and subtraction.

Homomorphic addition using the ElGamal method

With ElGamal encryption, initially, Bob creates his public key by selecting a g value and a prime number (p) and then selecting a private key (x). He then computes Y which is:

His public key is (Y,g,p) and he will send this to Alice. Alice then creates a message (M) and…