1. A method for joint generation of a ciphertext by devices of a data processing system, the method comprising: providing, by a first device, a first message, representing secret data of the first device, comprising at least one element of a pair of base groups G 1 , G 2 satisfying a bilinear map ê: G 1 ×G 2 →G T where G T is a target group; 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, wherein the initial consistency component is generated using the bilinear map; and sending the initial ciphertext to a second device; wherein the second device receives the initial ciphertext, provides a second message, representing secret data of the second device, comprises at least one element of the pair of base groups, generates an updated ciphertext comprising an updated blinded encrypted message and an updated consistency component for validating the updated ciphertext, wherein the updated blinded encrypted message is generated using the initial blinded encrypted message and an encryption of the second message under the public key, and wherein the updated consistency component is generated using the initial consistency component and the bilinear map, and sends the updated ciphertext to the first device; and receiving, at the first device, the updated ciphertext; unblinding the updated blinded encrypted message to obtain a final encrypted message; 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.