If you don't like sharing information or letting other people know how you feel, you're secretive. Secretive people probably make the best spies.
When a person is secretive, they seem mysterious because they don't reveal much about themselves. You can also be secretive about something specific — you might be suspicious of your sister's secretive behavior until you realize she's been planning a surprise party for your birthday. Secretive existed in the same form in Middle English, from the Latin root secretus, "withdrawn, hidden, concealed, or private."