Cloud computing has become one of the leading computing paradigms in the current era. Most of the enterprises, business people, academia, and even individuals use the cloud as a convenient platform for storing their data. Since cloud incorporates many computing technologies, the security issues associated with those technologies will be carried over to the cloud too. Loss of control over the data stored in public Cloud Service Providers (CSPs) and the lack of trust in the service providers increase the risk of storing data with public CSPs. The commonly used solution for data security is encryption, but most of the cases it consumes a large amount of time. More than that, the size of the data will be increased when it is encrypted. Since the whole data is encrypted and stored in a public CSP for a long time, the security of the data depends on the trustworthiness of the CSP and the strength of the encryption algorithm. In this paper, a Sudoku puzzle inspired Data Scrambling method (SiDS) is proposed to improve the data security using data splitting and N-Cloud architecture. The SiDS provides fast and efficient data splitting mechanism, by which the data is split into multiple chunks and stored into N number of CSPs. The use of N-cloud architecture eliminates the vulnerability of single-point-failure. The performance of the proposed system is analyzed with various security metrics and found giving better results, and the execution time of the proposed algorithm consumes less time than various block cipher encryption algorithms.