I don't know why, but I think this sounds a bit more natural.

http://www.prescient.net/pdf/PrivacySecurityRelationalDataba...

http://ithandbook.ffiec.gov/it-booklets/operations/risk-miti...

--------------------------------------------------
Note added at 1 day10 hrs (2012-09-23 16:45:37 GMT)
--------------------------------------------------

I have suggested an answer for the asker's question. No more, no less. 'Confidential database number' or 'confidential information number' sound rather strange to my ears.

Taking into account that the whole phrase is: 'Número de Bolsa de información confidencial', the final version would read

The number of the database storing confidential information.

(The) confidential information database number.

(The) number of the confidential information database.

(The) number of the database containing confidential information, etc.



ARIN Directory Services Databases

The ARIN Public Information Database (APID) is a collection of information created and collected by ARIN during the due course of business which the ARIN membership has deemed public information and decided to publish.

The ARIN Confidential Information Database (ACID) is a collection of information created and collected by ARIN during the due course of business which the ARIN membership has deemed is confidential information that should be kept under a strict privacy policy.

https://www.arin.net/policy/proposals/2005_2.html

Medical practices are prime targets: They house what is arguably the most comprehensive database of confidential information about Americans - valuable personal, clinical and financial data. To make matters worse, they're often protected by relatively modest information technology.

http://professional.medtronic.com/rm/pmr/is/ASSETS_150885#.U...