Method add

src/main/java/com/thealgorithms/ciphers/ECC.java:187–208

Add two points on the elliptic curve.

(ECPoint other, BigInteger p, BigInteger a)

         * Add two points on the elliptic curve.
         */
        public ECPoint add(ECPoint other, BigInteger p, BigInteger a) {
            if (this.x.equals(BigInteger.ZERO) && this.y.equals(BigInteger.ZERO)) {
                return other; // If this point is the identity, return the other point
            }
            if (other.x.equals(BigInteger.ZERO) && other.y.equals(BigInteger.ZERO)) {
                return this; // If the other point is the identity, return this point
            }

            BigInteger lambda;
            if (this.equals(other)) {
                // Special case: point doubling
                lambda = this.x.pow(2).multiply(BigInteger.valueOf(3)).add(a).multiply(this.y.multiply(BigInteger.valueOf(2)).modInverse(p)).mod(p);
            } else {
                // General case: adding two different points
                lambda = other.y.subtract(this.y).multiply(other.x.subtract(this.x).modInverse(p)).mod(p);
            }

            BigInteger xr = lambda.pow(2).subtract(this.x).subtract(other.x).mod(p);
            BigInteger yr = lambda.multiply(this.x.subtract(xr)).subtract(this.y).mod(p);

            return new ECPoint(xr, yr);
        }

        /**
         * Subtract two points on the elliptic curve.