public function generate(PrivateKey $privateKey = null)
    {
        if ($privateKey instanceof PrivateKey) {
            $this->setPrivateKey($privateKey);
        }

        if (!empty($this->hex)) {
            return $this;
        }

        if (is_null($this->privateKey)) {
            throw new \Exception('Please `setPrivateKey` before you generate a public key');
        }

        if (!$this->privateKey->isGenerated()) {
            $this->privateKey->generate();
        }

        if (!$this->privateKey->isValid()) {
            throw new \Exception('Private Key is invalid and cannot be used to generate a public key');
        }

        $point = new Point(
            '0x'.substr(Secp256k1::G, 2, 64),
            '0x'.substr(Secp256k1::G, 66, 64)
        );

        $R = Util::doubleAndAdd(
            '0x'.$this->privateKey->getHex(),
            $point
        );

        $RxHex = Util::encodeHex($R->getX());
        $RyHex = Util::encodeHex($R->getY());

        $RxHex = str_pad($RxHex, 64, '0', STR_PAD_LEFT);
        $RyHex = str_pad($RyHex, 64, '0', STR_PAD_LEFT);

        $this->x   = $RxHex;
        $this->y   = $RyHex;
        $this->hex = sprintf('%s%s', $RxHex, $RyHex);
        $this->dec = Util::decodeHex($this->hex);

        return $this;
    }