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An illegal number is a number that represents information which is illegal to possess, utter or propagate. Any piece of information is representable as a number, and therefore if the information itself is illegal in some way, the pure number itself may be illegal.
An illegal number may represent some type of classified information or trade secret, legal to possess only by certain authorized persons. An AACS encryption key that came to prominence in May 2007 is an example of a number claimed to be a secret, and whose publication or inappropriate possession is claimed to be illegal in the United States. It allegedly assists in the decryption of any HD DVD or Blu-ray Disc released before this date. The issuers of a series of cease-and-desist letters claim that the key itself is therefore a copyright circumvention device, and that publishing the key violates Title 1 of the US Digital Millennium Copyright Act.
In part of the DeCSS court order and in the AACS legal notices, the claimed protection for these numbers is based on their mere possession and the value or potential use of the numbers. This makes their status and legal issues surrounding their distribution quite distinct from that of mere copyright infringement.
Any image file or an executable program can be regarded as simply a very large binary number. In certain jurisdictions, there are images that are illegal to possess, due to obscenity or secrecy/classified status, so the corresponding numbers could be illegal.
In 2011 Sony sued George Hotz and members of fail0verflow for jailbreaking the PlayStation 3. Part of the lawsuit complaint was that they had published PS3 keys. Sony also threatened to sue anyone who distributed the keys. Sony later accidentally tweeted an older dongle key through its fictional Kevin Butler character.
Flags and steganography 
As a protest of the DeCSS case, many people created "steganographic" versions of the illegal information. Dave Touretzky of Carnegie Mellon University created a "Gallery of DeCSS descramblers". In the AACS encryption key controversy, a "free speech flag" was created. The illegal number was so short that a simple flag (pictured above) could be created by using the numbers as red-green-blue colors. The argument is that if short numbers can be made illegal, then anything based on those numbers also becomes illegal, like simple patterns of colors, etc.
In the Sony Computer Entertainment v. Hotz case, many bloggers (including one at Yale Law School) made a "new free speech flag" in homage to the AACS free speech flag. Most of these were based on the "dongle key" rather than the keys Hotz actually released. Several users of other websites posted similar flags.
See also 
- Illegal prime
- HDCP master key release
- Texas Instruments signing key controversy
- Normal number
- Infinite monkey theorem
- The Library of Babel
- Prior art
- Streisand effect
- Phil Carmody. "An Executable Prime Number?". Archived from the original on 2007-03-29. Retrieved 2007-05-08. "Maybe I was reading something between the lines that wasn't there, but if arbitrary programs could be expressed as primes, the immediate conclusion is that all programs, including ones some people wished didn't exist, can too. I.e. the so called 'circumvention devices' of which my previous prime exploit was an example."
- Thomas C Greene (2001-03-19). "DVD descrambler encoded in ‘illegal’ prime number". The Register. Retrieved 2007-05-08. "The question, of course, is whether an interesting number is illegal merely because it can be used to encode a contraband program."
- "The Prime Glossary: illegal prime". Retrieved 2007-05-09. "The bottom line: If distributing code is illegal, and these numbers contain (or are) the code, doesn't that make these number [sic] illegal?"
- "AACS licensor complains of posted key". Chilling Effects. Retrieved 2007-05-08. "Illegal Offering of Processing Key to Circumvent AACS Copyright Protection [...] are thereby providing and offering to the public a technology, product, service, device, component, or part thereof that is primarily designed, produced, or marketed for the purpose of circumventing the technological protection measures afforded by AACS (hereafter, the "circumvention offering"). Doing so constitutes a violation of the anti-circumvention provisions of the Digital Millennium Copyright Act (the "DMCA")"
- Memorandum Order, in MPAA v. Reimerdes, Corley and Kazan (NY; Feb. 2, 2000)
- "Prime Curios: 48565...29443 (1401-digits)". Retrieved 2007-05-09. "What folks often forget is a program (any file actually) is a string of bits (binary digits)—so every program is a number."
- "Criminal Justice Act 1988 + amendments". Retrieved 2007-05-09.
- Aniconism in Islam
- Jyllands-Posten Muhammad cartoons controversy#Aniconism
- Sony follows up, officially sues Geohot and fail0verflow over PS3 jailbreak. Nilay Patel, Engadget (2011-01-12). Retrieved on 2011-02-16.
- See also File:sonyvhotz.djvu
- "Sony lawyers now targeting anyone who posts PlayStation 3 hack". Arstechnica. February 8, 2011.
- "PS3 'jailbreak code' retweeted by Sony's Kevin Butler". Engadget. February 9, 2011.
- 46-dc-ea-d3-17-fe-45-d8-09-23-eb-97-e4-95-64-10-d4-cd-b2-c2 by Ben S, Yale Law Tech, 2011 March
- See File:Free-speech-flag-ps3.svg description
- Monolith, muddying the waters of the digital copyright debate
- Why the 09ers Are So Upset
- "What Colour are your bits?". Retrieved 2007-05-03.
- Guadamuz, Andres L., Trouble with Prime Numbers: DeCSS, DVD and the Protection of Proprietary Encryption Tools . Journal of Information, Law & Technology, Vol. 3, 2002
- "A Great Debate: Is Computer Code Protected Speech?". Retrieved 2007-05-09.
- Becky Hogge (2007-05-09). "Digging in". openDemocracy. Retrieved 2007-05-10.
- "Illegal Number" Triggers Flood of MPAA Cease-and Desist Letters
- Censorship backfires: thanks to MPAA takedown notice "illegal number" becomes popular on digg.com
- DVD descrambler encoded in ‘illegal’ prime number
- Steganography Wing of the Gallery of CSS Descramblers, Carnegie Mellon University, Dave Touretzky
- US judge rules that you can't copyright pi by New Scientist
- Could Quantum Computing Kill Copyright? by TorrentFreak
- We are in Digits of Pi and Live Forever by Clifford A. Pickover
- Grime, James. "Illegal Numbers". Numberphile. Brady Haran.