The term “cloud computing” refers to a vast network of linked, virtually hosted, and easily updatable computer resources. That are capable of consisting of a number of different apps and offering a number of different services to customers, and that have the potential to do so. Customers are required to pay for the cost of using the Services in accordance with the company's “pay-for-use only” policy. However, there are certain firms, such as Google Inc, that provide customers with particular free storage space even though the services provided by the company are limited, specifically with regard to the public cloud. A third-party service provider frequently owns and maintains the infrastructure required to run cloud computing services. But because more and more data and files pertaining to individuals and businesses are being stored in the cloud, worries have started to grow about how safe it actually is. Among these are the protection of software for virtualization and distributed computing, the safety of application software, the administration of identities, and the authentication and restriction of access. Nevertheless, efficient user authentication is the most essential need of cloud computing, as it limits unauthorized usage of a cloud server. Cloud computing has become increasingly popular in recent years. In this research, we present a new authentication method between users and online computing systems that is based on the suggested secure hash algorithm (SHA-3) and makes use of the lightweight Sosemanuk method. We created this technique. That system is going to be known as the SoSha3 system. The design that has been proposed for the system deals with data in three different sizes: 128, 256, and 512 bits. In order to make these authentication systems suitable for cloud computing at high rates, some modifications were made to them. The three-dimensional chaotic system, also known as the Lorenz system, will be combined with the authentication architecture that was presented earlier in order to achieve the goal of achieving high hashing security.