The rapid advancement of Generative AI (GenAI) technologies offers transformative opportunities within Australia's critical technologies of national interest while introducing unique security challenges. This paper presents SecGenAI, a comprehensive security framework for cloud-based GenAI applications, with a focus on Retrieval-Augmented Generation (RAG) systems. SecGenAI addresses functional, infrastructure, and governance requirements, integrating end-to-end security analysis to generate specifications emphasizing data privacy, secure deployment, and shared responsibility models. Aligned with Australian Privacy Principles, AI Ethics Principles, and guidelines from the Australian Cyber Security Centre and Digital Transformation Agency, SecGenAI mitigates threats such as data leakage, adversarial attacks, and model inversion. The framework's novel approach combines advanced machine learning techniques with robust security measures, ensuring compliance with Australian regulations while enhancing the reliability and trustworthiness of GenAI systems. This research contributes to the field of intelligent systems by providing actionable strategies for secure GenAI implementation in industry, fostering innovation in AI applications, and safeguarding national interests.