Distributed computing frameworks are used to harvest distributed resources to process big data more efficiently. As the popularity of the frameworks increases, it is anticipated that some of the data they are used to process are private or sensitive, therefore require more stringent security protections. As authentication is the first-line of defence in any computing system, providing an effective and efficient authentication service to safeguard data processed or used in a distributed computing framework is paramount to the wide scale application of the framework, and this is still an open issue. To investigate and address this open issue, the author of this thesis has chosen one of the most widely used distributed computing framework, the MapReduce (MR) application framework (or MR application for short), and designed an effective and efficient authentication solution for this framework. This thesis has examined a use-case scenario of MR computation and presented a generic computational model of MR to capture the characteristics of MR application framework, the main components, process and interactions of a job computation (i.e. job submission and execution). Using this model, the thesis analyses the threats related to the job submission and execution. From the threat analysis a set of requirements for an effective and efficient authentication solution is specified. Based on these requirements, the thesis critically analyses the state-of-the-art authentication solutions used or proposed for the MR application identifying limitations and gaps for improvement. Existing solutions do not adequately capture the characteristics of MR being deployed in a distributed and resource-sharing environment, they largely use centralised approach to authentication and based on a password single factor authentication, and most of them assume that the clients are already identified locally to the MR application and the communication among MR components is through a trusted network. To address these limitations and gaps, the thesis has made the following contributions. Firstly, a Generic MapReduce Computation (GMC) model is constructed. The main novelty of this model is that it classifies and captures two classes of MR components. One is MR components that are job-independent, and the other is MR components that are job-dependent. As the MR components are distributed and in a resource-sharing environment, their interactions should all be authenticated to safeguard the job resources (i.e. data). Facilitating authentication of these interactions effectively in such an environment is a complex task. To address this complex task, the second novel contribution has been made, that is the proposal of a novel authentication model, called MR Layered Authentication Model (MR-LAM). It uses a layered approach to authentication. The model consists of two layers. The first is the MR-Infrastructure domain authentication layer and it is responsible for a job-independent MR components authentication. The second is the MR-Job domain authentication layer and it is responsible for job-dependent MR components authentication. The third novel contribution of this thesis, our proposed solution for MR-Job domain authentication layer, is the design of a Virtual Domain based Authentication Framework (VDAF) to secure, in term of authentication, the job-resource access in the distributed and resource-sharing environment. At the centre of the VDAF lies our novel authentication method, called Password and Token-based Multi-factor Multi-point Authentication (PT2M-AuthN) method. In this method, two main ideas are used; the principle of separation of duty-and-credential and the key wrap-and-swap operation to support mutual authentication for both job submission and execution. To implement the VDAF function and this novel authentication method, four sets of protocols that are collectively referred to as the Lightweight VDAF Authentication Protocol (LVAP) suite, are proposed. The first set consists of MR-Client Primary Credential Establishment (CPCrE) protocol, the second set consists of MR-Job Components Primary Credentials Establishment (JCPCrE) and MR-Clients Authentication (MR-CAuthN) protocols, the third and fourth sets consist of MR-Job Components Authentication (MR-JCAuthN) protocols and MR-Data Authentication (MR-DAuthN) protocols, respectively. The effectiveness (security) and the efficiency of the design have been evaluated. The security evaluation is done by using an informal security analysis and formal security verification using the Automated Validation of Internet Security Protocols and Applications (AVISPA) tool. The performance evaluation is done by using theoretical and experimental methods, and the latter uses the Riverbed Modeller simulation tool. The evaluation results have been compared with those of related work. The comparison results show that our authentication method provides a stronger level of protection as a result of using two-factor authentication and key wrap-and-swap operation that provide mutual authentication. With regard to performance, the comparison results show that when our authentication method is used, our protocol execution time (PET) is 20% shorter than that of when the most related authentication method is used.