A method of a trusted entity CA facilitating generation of a public key by an entity A in an electronic data communication system using implicit certificates. The trusted entity CA selects a unique identity distinguishing the entity A. The trusted entity CA then generates a public key reconstruction public data of the entity A by mathematically combining a private value of said trusted entity CA and information made public by said trusted entity CA. The unique identity and public key reconstruction public data of file entity A serve as A's implicit certificate. The trusted entity CA generates a private key for said entity A using said implicit certificate and said private value of said trusted entity CA. The trusted entity CA then transmits the unique identity, public key reconstruction public data, and private key to the entity A to permit A to generate a public key from the public key reconstruction public data and the private key.