Making ElGamal Additively Homomorphic with Elliptic Curves

The ElGamal encryption method was defined in 1985 by Tahir ElGamal:

As a discrete logarithm method, we have a private key of x and a public key of Y:

We can implement an additive and scalar multiply homomorphic encryption method by changing the ElGamal method to an elliptic curve implementation. In a standard ElGamal method, we have a secret key of x, and generate our public key with:

Y=x.G

and where G is a base point on the elliptic curve. To encrypt we generate a value scalar value (k) and a message (M). We compute:

A=k.G

B=k.Y+M

To decrypt with the private key (x), we perform:

M=B−x.A

The implementation of this is:

https://asecuritysite.com/elgamal/go_elgamal_ecc

To make homomorphically additive for two messages (M1 and M2) and two random nonce values (k1…