An authenticated, ID-based private/public key pair, with a self-certified public key, is generated using Kummer arithmetic without bilinear pairings. Two or more parties can generate such key pairs and use them as their respective long-term key pairs which, when combined with the parties' short-term key pairs, can allow the parties to establish an authenticated, short-term shared key. Some embodiments are suitable for connected vehicles communicating with each other and/or with other systems. Other features are also provided.