Abstract: A method of performing IBE cryptography comprising the steps of a key generation server transmitting a master public key to a processor, the processor generating or retrieving a fresh master public key derived from the master public key transmitted by the key generation centre, and the processor using the fresh master public key to generate a public key for transmitting a message to a recipient device having a corresponding private key. The processor may store the fresh master public key in a read only memory for repeated use or it may dynamically generate it. To dynamically generate the fresh master public key the processor multiplies the original master public key by a curve co-factor. The processor may be incorporated into a hand-held card, and it may transfer information to a linked second processor for performing some of the calculations.