An open secret is a concept or idea that is "officially" (de jure) secret or restricted in knowledge, but in practice (de facto) may be widely known; or it refers to something that is widely known to be true but which none of the people most intimately concerned are willing to categorically acknowledge in public.
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Government and military
One famous "open secret" is that of Area 51, a United States military base containing an aircraft testing facility. The U.S. Government did not explicitly affirm the existence of any military facility near Groom Lake, Lincoln County, Nevada until 2013, when the CIA released documents revealing that the site was established to test spy planes. While the general location of the base is now officially acknowledged, the base does not appear on government maps or in declassified satellite photography. Yet despite this, the base was demonstrably and widely acknowledged to exist for many years before the CIA officially confirmed its existence. The immense secrecy has made it the frequent subject of conspiracy theories and a central component to UFO folklore.
Likewise, Delta Force can be considered an open secret, since its existence has been denied in the past by the United States Government.
The National Security Agency was formally established by president Truman in a memorandum of October 24, 1952, that revised National Security Council Intelligence Directive (NSCID) 9. Since President Truman's memo was a classified document, the existence of the NSA was not known to the public at that time. Due to its ultra-secrecy the U.S. intelligence community referred to the NSA as "No Such Agency".
Camp Mirage is the codename for a former Canadian Forces forward logistics facility located in Dubai, United Arab Emirates. The facility was established in late December 2001 and, though not officially acknowledged by the Canadian Forces, was considered an open secret.
The existence of the British Secret Intelligence Service (MI6) was widely known for several decades before the government's official acknowledgement of the organisation in 1994. Its Australian counterpart, ASIS, was the subject of a newspaper exposé years before its existence was officially acknowledged.
Israel is widely acknowledged to possess nuclear weapons. This can be considered an open secret, because the Israeli government has never explicitly stated whether or not it possesses a nuclear stockpile, officially maintaining a policy of deliberate ambiguity.   
Completed in 1964, the Post Office Tower was an official secret until it was officially revealed by Kate Hoey under parliamentary privilege in 1993, despite being a 177-metre (581 ft) tall structure in the middle of central London that was open to the public for about 15 years, and had already become present in popular culture by that point. Its location was, therefore, for a time, apparently prohibited from being indicated on maps (in the UK largely created by a government agency, the Ordnance Survey).
Kayfabe, or the presentation of professional wrestling as "real" or unscripted, is an open secret, kept displayed as legitimate within the confines of wrestling programs but openly acknowledged as predetermined by wrestlers and promoters in the context of interviews for decades.
In television, the primary real-world identity of The Stig, a costumed and masked television test-driver used by BBC Television for Top Gear, was an open secret until the unofficial embargo was broken by a newspaper in 2009.
- Dreamland: Fifty Years of Secret Flight Testing in Nevada By Peter W. Merlin
- Boyle, Alan (16 August 2013). "Area 51 and its purpose declassified: No UFOs, but lots of U-2 spy planes". NBC News. Retrieved 16 August 2013.
- USGS 1:24K/25K Topo map for location UTM 11 605181E 4124095N (NAD27) (map via TopoQuest.com)
- Pike, John. "Area 51 Facility Overview", Federation of American Scientists.
- "Area 51 / Catch 22" segment, 60 Minutes broadcast 17 March 1996.
- Jacobsen, Annie (2012), Area 51: An Uncensored History of America's Top Secret Military Base, Back Bay Books, ISBN 0316202304
- Truman, Harry S. (24 October 1952). "Memorandum" (PDF). National Security Agency. Archived from the original (PDF) on 21 August 2013. Retrieved 2 July 2013.
- Anne Gearan (7 June 2013). "'No Such Agency' spies on the communications of the world". The Washington Post. Retrieved 9 November 2013.
- "Secret base to be shuttered over failed airline talks: source". CTV News. 10 October 2010. Archived from the original on 12 October 2010. Retrieved 4 November 2012.
- Whitehead, Jennifer (13 October 2005). "MI6 to boost recruitment prospects with launch of first website — Brand Republic News". Brandrepublic.com. Retrieved 3 November 2012.
- Cohen, Avner (1998). Israel and the Bomb. Columbia University Press. p. 349. ISBN 0-231-10482-0.
- Korb, Lawrence (1 November 1998). "The Quiet Bomb". The New York Times. Retrieved 4 November 2012.
- Borger, Julian (15 January 2014). "The truth about Israel's secret nuclear arsenal". The Guardian. Retrieved 5 April 2020.
- Stockman, Farah (19 November 2013). "Israel's nuclear precedent". The Boston Blobe. Retrieved 5 April 2020.
- Mizokami, Kyle (9 January 2020). "Submarines Are the Key To Israel's Secret Nuclear Weapons Arsenal". TheNationalInterest.org. Retrieved 5 April 2020.
- "No title". Parliamentary Debates (Hansard). House of Commons. 19 February 1993. col. 634.
- "London Telecom Tower, formerly BT Tower and Post Office Tower, Fitzrovia, West End, London". urban75. Retrieved 19 November 2014.
- Foster, Patrick (19 January 2009). "Identity of Top Gear's The Stig revealed as Ben Collins". The Times. Retrieved 19 January 2009.
The identity of the white-suited Stig ... has been an open secret within the motoring world for some years, with newspapers refraining from publishing his name, to uphold the spirit of the programme.