A method of operating an identity based directoryless key-code cryptographic communication system having two users A and B and a universal authority U, involving the generation of a public modulus M, being the product of two primes P and Q, and the operation of a publicly available secure one way hash function, #. User A presents his identity to U who uses #, M, P and Q to generate a decryption key, r, which is only made available to A. User B, who wishes to transmit a message to A, can encrypt data by using the #, M and A's identity. User A can recover the data by using r.