The data perturbation technique apply to preserve privacy on Big Data are Some of the commonly used techniques for privacy preserving in cloud are

1) Reconstruction method 2) Anonymization method 3) Cryptographic method The Reconstruction Method Reconstruction is popular method for the Privacy Preserving Data Mining technique. The sensitive data are transformed or masked by adding additional data to the original data.

The Anonymization Method In this method the individual record is made indistinguishable using Suppression and Generalization techniques. K- anonymity is a common algorithm for this process. K-anonymity conceals the records which are commonly used as the unique identifier for the data.

The Cryptographic Method This method is mainly used when data mining is mutually done by different parties on the same data. This case requires preserving the privacy data mining of the parties. Several algorithms have been developed for this privacy preserving data mining

Data Perturbation is the technique to perturb(modify) the sensitive data to preserve privacy. In this era of Big Data, it is applied to Big Data by using following techniques:

With best of my knowledge applying perturbation to large amount of data is not feasible. Therefore, anonymization is used in majority of privacy preserving big data publishing approaches. However, differential privacy is gaining popularity in big data privacy area.

Here is a paper related to differential privacy with respect to big data: https://www.usenix.org/legacy/event/nsdi10/tech/full_papers/roy.pdf

I am not aware of any standard paper related to perturbation in big data but I recently did my PhD with thesis titled, "scalable anonymization approaches for privacy preserving big data publishing". If you are interested you may study my papers and ask for any help.

Thanks

An interesting issue, because the issue of information security and privacy in data collected in Big Data database systems is currently an important issue determining the development of Big Data applications in analytical processes.

Best wishes

The Perturbation techniques varies based on the data-set type. As Perturbation for structured data set, Semi-Structured Data-set,UN-structured Data set,