Embodiments include 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 Rx of the random point R and only the signature component ssignature 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.