ElGamal — Applying Multiple Public Key Operations (ECC)

We hardly ever use discrete logs these days, as Elliptic Curve Cryptography is just so much more efficient and faster. And, so I love converting discrete log proofs with Elliptic Curve methods. Basically, we convert a power into a multiplicative operation for the base point:

and where G is the base point of the curve. Then a multiplication is replaced with a point addition, and a division is replaced with a point subtraction:

Now, here’s an example. On the left hand side we have the discrete log proof, and the right hand side has the equivalent elliptic curve proof:

Coding

The coding is [here]:

package main
import (
    "fmt"
    "os"
    "go.dedis.ch/kyber/v3/group/edwards25519"
    "go.dedis.ch/kyber/v3/util/random"
)

func main() {
    message:="Testing"
    argCount := len(os.Args[1:])
    if (argCount>0) {message= string(os.Args[1])}
    
    suite := edwards25519.NewBlakeSHA256Ed25519()

    // Alice's key pair (x,Y)
    x := suite.Scalar().Pick(suite.RandomStream()) 
    Y := suite.Point().Mul(x, nil)                 
    M := suite.Point().Embed([]byte(message)…