Security, privacy and data integrity are the critical issues in Big Data application of IoT-enable environment and cloud-based services. There are many upcoming challenges to establish secure computations for Big Data applications. Authenticated encryption (AE) plays one of the core roles for Big Data’s confidentiality, integrity, and real-time security. However, many proposals exist in the research area of authenticated encryption. Generally, there are two concepts of nonce respect and nonce reuse under the security notion of the AE. However, recent studies show that nonce reuse needs to sacrifice security bound of the AE. In this paper, we consider nonce respect scheme and probabilistic encryption scheme which are more efficient and suitable for big data applications. Both schemes are based on keyed function. Our first scheme (FS) operates in parallel mode whose security is based on nonce respect and supports associated data. Furthermore, it needs less call of functions/block-cipher. On the contrary, our second scheme is based on probabilistic encryption. It is expected to be a light solution because of weaker security model construction. Moreover, both schemes satisfy reasonable privacy security bound.
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