The answer from Sebastian Fischer should be extended:  Big Data (analysis) and encryption is a problem, this is correct. But it is not only the performance that creates problems: If someone performs analysis on (big) data she has to perform some operation on the data. If the data are encrypted  (using traditionally encryption) we cannot do any (useful) operations on the data. There are encryption schemes that allow to operate on encrypted data like fully homomorphic encryption. Homomorphic enc. has an efficiency problem - and so the circle from Sebastians answer is complete ;-)

If you are interested in FHE the paper from Gentry is a must-read:

"Craig Gentry. Fully Homomorphic Encryption Using Ideal Lattices. In the 41st ACM Symposium on Theory of Computing (STOC), 2009."

Just as a last hint: In many (big) data scenarios, there is no need for FULLY homomorphic encryption: We just have to query data/ columns etc. within a database and/or do one very specific operation on the data. We do not need to execute ALL possible processor operations on the data; that means we do not need FULLY homom. enc. For these latter cases cryptography provides "relaxed" schemes that are faster than FHE. 

To mention one of the several publications in this field see a paper from MIT:

Stephen Tu, M. Frans Kaashoek, Samuel Madden, and Nickolai Zeldovich. 2013. Processing analytical queries over encrypted data. In Proceedings of the 39th international conference on Very Large Data Bases (PVLDB'13), Michael Böhlen and Christoph Koch (Eds.). VLDB Endowment 289-300.

The traditional security mechanism may not suitable for Big Data due to 3V's, So security issues must be implemented from scratch. Some of the challenges are providing security for - data storage, non-relation data set, transaction logs.

There are many security issues, including data confidentiality and integrity. Looking at specific type of data may help to start a good research ground. I am concern on data ownership... also... the security and privacy standard. There will be major security issues due to the use of cloud computing

There is a document from CSA with exactly the title you are looking for:  "Expanded Top 10 Big Data Security Challenges"

https://cloudsecurityalliance.org/download/expanded-top-ten-big-data-security-and-privacy-challenges/

A big challenge is the encryption. To work with big data, you basically need a good performance, so you don't encrypt the data.

But collecting a lot of data and store it plain is bad for the security. If someone gets it, they can read it without any problems.

The answer from Sebastian Fischer should be extended:  Big Data (analysis) and encryption is a problem, this is correct. But it is not only the performance that creates problems: If someone performs analysis on (big) data she has to perform some operation on the data. If the data are encrypted  (using traditionally encryption) we cannot do any (useful) operations on the data. There are encryption schemes that allow to operate on encrypted data like fully homomorphic encryption. Homomorphic enc. has an efficiency problem - and so the circle from Sebastians answer is complete ;-)

If you are interested in FHE the paper from Gentry is a must-read:

"Craig Gentry. Fully Homomorphic Encryption Using Ideal Lattices. In the 41st ACM Symposium on Theory of Computing (STOC), 2009."

Just as a last hint: In many (big) data scenarios, there is no need for FULLY homomorphic encryption: We just have to query data/ columns etc. within a database and/or do one very specific operation on the data. We do not need to execute ALL possible processor operations on the data; that means we do not need FULLY homom. enc. For these latter cases cryptography provides "relaxed" schemes that are faster than FHE. 

To mention one of the several publications in this field see a paper from MIT:

Stephen Tu, M. Frans Kaashoek, Samuel Madden, and Nickolai Zeldovich. 2013. Processing analytical queries over encrypted data. In Proceedings of the 39th international conference on Very Large Data Bases (PVLDB'13), Michael Böhlen and Christoph Koch (Eds.). VLDB Endowment 289-300.

Heterogeneous cryptographic approaches are of great challenge. Interchangeability of security schemes render weakness in data security hence posing challenge to big data.  

Top Big Data Challenges:

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