Methods and apparatus are provided for cryptographically encoding secret data in a data processing system. The secret data is encoded in accordance with a verifiable encryption process to produce a cryptographic construction (θ) having a decryption constraint dependent on the occurrence of a predetermined event. An event-dependent decryption constraint is thereby built into the cryptography, so that there is an intrinsic restriction on the ability to decrypt the encoded secret data which is dependent on occurrence of the predetermined event. Decoding apparatus for such a cryptographic construction is also provided, as well as distributed trust data processing systems providing accountable privacy based on use of such cryptographic constructions.