Person who doesn't share

What is the equivalent word for a person who doesn't want to communicate to share any of his/her secrets, life's stories or personal information?

Need some words related to the above described description...

This person would be called private.

"Private" is used to describe not only information, but also people who don't share personal information freely.

There are a variety of expressions to describe someone who does not wish to disclose other types of information, such as "secretive," "tight-lipped," and "discreet." However, "private" seems the best for the situation you've described.

Two other possible candidates are unforthcoming and guarded.

From Oxford Dictionaries online:

private

1.3 (Of a person) choosing not to reveal their thoughts and feelings to others: he was a very private man

unforthcoming

1 (Of a person) not willing to divulge information: the sergeant seemed unforthcoming, so he enquired at the gate

guarded

Cautious and having possible reservations: he has given a guarded welcome to the idea

We often call such a person a very private person.

One very private person was Josephine Tey.

That person might be closed or guarded.

We might call this person reserved:

formal or self-restrained in manner and relationship; avoiding familiarity or intimacy with others: a quiet, reserved man.

An adjective is secretive ( person):

• Having or marked by an inclination to secrecy; not open, forthright, or frank.

also , according to context, an introvert :

• a shy person; a person concerned primarily with inner thoughts and feelings rather than with the physical or social environment.