Research on Cryptography and Key Management Strategies in Cloud Computing focuses on ensuring the confidentiality, integrity, and authenticity of data and communications in cloud environments through advanced cryptographic techniques and secure key management practices. This area addresses challenges such as multi-tenancy, dynamic resource allocation, distributed storage, and the risk of insider and outsider attacks. Key research directions include designing scalable and efficient encryption schemes (e.g., symmetric, asymmetric, homomorphic, and attribute-based encryption), secure key generation, distribution, storage, and rotation strategies, and lightweight cryptographic protocols for resource-constrained cloud and edge devices. Other emerging topics involve blockchain-assisted key management, privacy-preserving computation, multi-cloud and hybrid cloud cryptographic frameworks, and post-quantum cryptography integration. Additionally, research on access control policies, key recovery and revocation mechanisms, and AI-driven anomaly detection for cryptographic operations represents significant avenues for advancing secure, resilient, and trustworthy cloud computing infrastructures.