Pseudonym digital certificates (160p) are generated for devices (110/150) by a Pseudonym Certificate Authority (PCA), which communicates with devices via another entity—registration authority (RA)—so that the PCA and RA cannot associate certificates with devices. Each certificate is associated with a public signature key, and with a public encryption key used by PCA to encrypt the certificate to hide it from the RA. Both keys are derived by PCA from a single key. For example, the signature key can be derived from the public encryption key rather than generated independently. However, high security is obtained even when the PCA does not sign the encrypted certificate. Reduced bandwidth and computational costs are obtained as a result. Other embodiments are also provided.