non-disclosure; withholding of information
Used in formal or legal contexts to indicate that information is not being disclosed or released.
You can request non-disclosure of personal information.
There is an obligation to explain the reason for non-disclosure.
秘密 is a general word for 'secret' or 'confidential'. 不開示 is more about the formal withholding of information rather than the information itself being secret.
Compound of 不 (fu, 'not') + 開示 (kaiji, 'disclosure'). The term is a straightforward Sino-Japanese formation.