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...
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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:
1.3 (Of a person) choosing not to reveal their thoughts and feelings to others: he was a very private man
1 (Of a person) not willing to divulge information: the sergeant seemed unforthcoming, so he enquired at the gate
Cautious and having possible reservations: he has given a guarded welcome to the idea
We might call this person reserved:
formal or self-restrained in manner and relationship; avoiding familiarity or intimacy with others: a quiet, reserved man.
We often call such a person a very private person.
One very private person was Josephine Tey.
That person might be closed or guarded.