Certification of Dl/ec Keys

It is shown that the explicit certification of public keys in customary DL/EC (Discrete-Log/ Elliptic-Curve) applications, ranging from digital signatures of the DSA type to keyagreements of the DH type, can be abolished. This facilitates highly efficient implementations in terms of the total number of exponentiations needed to be executed, the ability of having parallel processing, and communication overhead. At the fundamental level it is shown how to integrate the processing of the public key of the trusted third party (needed, by definition, in establishing the validity of static public values submitted by a user) and the dynamic processing associated with the actual cryptographic process. This reduces, by a factor of at least 2, the processing time when compared to standard signature and key-agreement techniques, while further reducing communication overhead. It is then shown how the performance of the introduced key-agreement techniques is further enhanced, by utilizing a principle termed "you are OK if I am OK". Here, the processing of the public key of Alice’s trusted third party is not performed by Bob after he receives the values submitted by Alice, as customarily done. Instead, Bob refers to the said public key prior to his communication with Alice (utilizing the realistic observation under which Bob is supposed to know in any case the public key of Alice’s trusted third party regardless of his communication with Alice). Here, if Bob is assured that his secret and public values are valid then he is subsequently assured that the public values submitted by Alice are valid as well.