The invention provides a method and a system for signcrypting data based on elliptic curve cryptography. In a head-end system, data is encrypted using a random point R and digitally signed using the random point R. Only the x-coordinate R x of the random point R and only the signature components signature of the signature are added to the data after signcrypting the data. In a smartcard the signcrypted data is verified using the random point R and decrypted using the random point R.