A method and system for accelerated decryption of a cryptographically protected user data unit, wherein a transmitter initially generates a cryptographic key that is provided with a related key identification. The transmitter then performs asymmetrical encryption of the generated cryptographic key using a public cryptographic key and encryption of at least one user data unit using the generated cryptographic key. The encrypted user data unit, the asymmetrically encrypted cryptographic key and the related key identification of the cryptographic key are transported to a receiver that decrypts the received asymmetrically encrypted key using a private key, if verification of the received related key identification of the cryptographic key indicates the cryptographic key is not present in a decrypted state in the receiver. The receiver then decrypts the received cryptographically encrypted user data unit using the cryptographic key in the receiver or with the cryptographic key decrypted using the private key.