SummaryCloud Computing (CC) and big data are growing technology in the business. Big data is demonstrated in terms of volume, variety, and velocity. CC is employed for storing, processing, and accessing data. Many cryptographic techniques have been developed to enhance big data security in cloud computing. However, security and privacy are the primary concerns in protecting data, as it is highly sensitive. Yet, it faces the major problems of inefficient performance, increased time consumption, and lack of data confidentiality and integrity. To address this issue, proposed Extreme Learning with Projection Relational Algebraic Secured Data Transmission (ELPRA‐SDT) is introduced to secure data transactions from cloud users to cloud servers with enhanced data confidentiality and reduced time consumption for big cloud data. The proposed ELPRA‐SDT consists of two major processes namely registration and key generation. At first, the user's IP address is registered employing a transitive advanced set relation theory graph model in a cloud server (CS) for retrieving the numerous services. The CS generates private and public keys for each registered user's IP address using the Transitive Operational and Time Synchronized Random Winternitz Key generation model. After, the user sends a request to the CS for acquiring data. The CS validates the requested user based on security policy attributes. Second, the Projection Relational Algebraic Signcryption and Unsigncryption algorithm performs signature verification to ensure secure data access for protecting the data. Results of experiments carried out by using Coburg Intrusion Detection Data Sets‐001 dataset in Java. ELPRA‐SDT method is more efficient and more suitable for providing security and privacy to network traces in the Cloud. The result shows maximum performance with data confidentiality by 10% and data integrity by 13%. In addition, delay is reduced by 32%, and data delivery time and communication complexity is decreased by 28% and 24% to other existing methods.