Abstract: An implicit certificate cryptosystem uses an implicit certificate that includes a pair of certificate components. One of the certificate components includes a public key reconstruction data that is the combination of ephemeral public keys of two entities, one of which is a trusted entity and the other of which is associated with the implicit certificate. The public key reconstruction data is then combined with the identity of the other entity and the combination encrypted to form a first certificate component. A second certificate component is generated by using the first certificate component as a message in a signature scheme and generating a signature of the trusted entity on the message. The two certificate components are provided to the other entity to permit the other entity to generate a private key using one of the certificate components. The corresponding public key can be derived from the remaining certificate component.