A method for joint generation of a ciphertext by devices of a data processing system includes providing, by a first device, a first message, representing secret data of the first device, generating an initial ciphertext comprising an initial blinded encrypted message, in which the first message is encrypted under a public key of a trusted entity, and an initial consistency component for validating the initial ciphertext using the bilinear map; and sending the initial ciphertext to a second device; wherein the second device provides a second message, representing secret data of the second device, generates an updated ciphertext comprising an updated blinded encrypted message and an updated consistency component for validating the updated ciphertext, and generating a final ciphertext comprising the final encrypted message and a final consistency component for validating the final ciphertext, wherein the final consistency component is generated using the updated consistency component and the bilinear map.