Effecting reissue in a data processing system of a cryptographic credential certifying a set of attributes, the credential being initially bound to a first secret key stored in a first processing device. A backup token is produced using the first device and comprises a commitment to said set of attributes and first proof data permitting verification that the set of attributes in said commitment corresponds to the set of attributes certified by said credential. At a second processing device, a second secret key is stored and blinded to produce a blinded key. A credential template token produced from the backup token and the blinded key is sent to a credential issuer where said verification is performed using the first proof data and the credential template token is used to provide a reissued credential, certifying said set of attributes, to the second device, the reissued credential being bound to the second secret key.