I was reading an online editorial a week or so ago in which its author employed an awesome word, the meaning of which was "to intentionally and deliberately withhold information [essential to the endeavor at hand, with the underlying purpose of misleading others by its omission]". Yeah, all of that in one word.
Alas, I can't seem to find the editorial online anymore, I've now I forgotten the word!
Best Answer
I think you're looking for dissimulate (or dissemble); alternatives include prevaricate (avoid a direct answer) equivocate (give an ambiguous answer: "you will emerge from the war with the Romans victorious"), and obfuscate (give a confusing answer that serves to hide the real information), but all of those require you to say something. Only dissimulate implies you say nothing at all: a lie of omission (cf. lie of commission).
On a different tack, there is both non-disclosure and maintaining confidentiality, which both mean to purposefully withhold information, but usually the intent is to protect one's own interests, rather than mislead.
To keep mum (and synonyms) is similar, except that's typically applied to someone who has transgressed (or knows about someone who has) in some way.