A method of generating a public key in a secure digital communication system, having at least one trusted entity CA and subscriber entities A. For each entity A, the trusted entity selects a unique identity distinguishing the entity A. The trusted entity then generates a public key reconstruction public data of the entity A by mathematically combining public values obtained from respective private values of the trusted entity and the entity A. The unique identity and public key reconstruction public data of the entity A serve as A's implicit certificate. The trusted entity combines the implicit certificate information with a mathematical function to derive an entity information f and generates a value k.sub.A by binding with f with private values of the trusted entity. The trusted entity transmits the value k.sub.A to the entity to permit A to generate a private key from k.sub.A, A's private value and A's implicit certificate. The entity A's public key information may be reconstructed from public information, and A's implicit certificate.