Informal analysis of authenticated key establishment (ake) protocols was commonly accepted as the valid argument for their security in the past. Although it can provide some confidence in protocol correctness, experience has shown time and again that ake protocols are likely to contain flaws even after an informal analysis is completed. Therefore, it has become increasingly common to expect a formal analysis, and preferably a mathematical proof, of any published ake protocol in order to obtain increased confidence in its security. In this research we use an appropriate model for analysing ake protocols based on its features and properties. The model allows us to design ake protocols modularly and reuse existing protocol components. We provide a detailed description of its formalisation, operations and usage. This description also includes ways of extracting new protocol components from existing ake protocols. Following the description of the model, we propose a new unauthenticated key establishment protocol for two-party communications. By composing this protocol with authentication protocols, we can construct several new secure ake protocols. These new protocols are compared with existing protocols for their computational efficiency. The comparison shows that our new proven secure protocols are as efficient as the existing protocols with an informal security analysis. We then propose a three-party key establishment protocol which involves a trusted server and two users. We also propose a non-interactive authentication protocol and discuss it and a variant of it. These components are used to construct a secure three-party ake protocol that supports a privacy framework. This framework allows users to remain anonymous while conducting electronic transactions with an independent service provider. A new password-based authentication protocol is proposed to address the problem of authentication using passwords. This protocol carries a proof of security and satisfies a slightly relaxed definition of security. We demonstrate its application by composing it with existing key establishment protocols. To maximise its use, we modified a two-party key establishment protocol to become three-party server based. By using the server for authentication, two users within a common network domain can establish a secure session key. Only a small number of ake protocols are demonstrated in this thesis. There exist many more provably secure ake protocols that can be constructed using the protocol components presented by applying the approach of "mix and match". That is, each new component results in a number of new ake protocols depending on the number of existing components.