the state of being reticent, or reserved, especially with regard to speaking freely; restraint: His natural reticence seemed to disappear under the influence of alcohol.
Sometimes, reticency.

nonreticence, noun Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
reticent (ˈrɛtɪsənt)
not open or communicative; not saying all that one knows; taciturn; reserved
[C19: from Latin reticēre to keep silent, from re- + tacēre to be silent]

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
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Word Origin & History

c.1600, from Fr. réticence, from L. reticentia "silence," from reticere "keep silent," from re-, intensive prefix, + tacere "be silent" (see tact). "Not in common use until after 1830" [OED].
Online Etymology Dictionary, © 2010 Douglas Harper
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Example sentences
All my instincts run toward reticence, to protecting my family from invasions
  of our private space.
Their reticence could reflect fears of copycat crimes, or simply the old habit
  of burying news during big events.
Both parties are deservedly upbraided for their reticence on exactly how to cut
  the fiscal deficit.
The reticence partly reflects fears about consumer unease and unwelcome
  attention from regulators.
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