An illegal number is a number that represents information which is illegal to possess, utter, propagate, or otherwise transmit in some legal jurisdiction. Any piece of digital information is representable as a number; consequently, if communicating a specific set of information is illegal in some way, then the number may be illegal as well.
A number may represent some type of classified information or trade secret, legal to possess only by certain authorized persons. An AACS encryption key (09 F9 11 02 9D 74 E3 5B D8 41 56 C5 63 56 88 C0) 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 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 retweeted 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 (i.e. hiding them in some form in flags etc.). Dave Touretzky of Carnegie Mellon University created a "Gallery of DeCSS descramblers". In the AACS encryption key controversy, a "free speech flag" was created. Some illegal numbers are so short that a simple flag (shown in the image) could be created by using triples of components as describing red-green-blue colors. The argument is that if short numbers can be made illegal, then any representation of 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.
An illegal prime is an illegal number which is also prime. One of the earliest illegal prime numbers was generated in March 2001 by Phil Carmody. Its binary representation corresponds to a compressed version of the C source code of a computer program implementing the DeCSS decryption algorithm, which can be used by a computer to circumvent a DVD's copy protection.
Protests against the indictment of DeCSS author Jon Lech Johansen and legislation prohibiting publication of DeCSS code took many forms. One of them was the representation of the illegal code in a form that had an intrinsically archivable quality. Since the bits making up a computer program also represent a number, the plan was for the number to have some special property that would make it archivable and publishable (one method was to print it on a T-shirt). The primality of a number is a fundamental property of number theory and is therefore not dependent on legal definitions of any particular jurisdiction.
The large prime database of the PrimePages website records the top 20 primes of various special forms; one of them is proof of primality using the elliptic curve primality proving (ECPP) algorithm. Thus, if the number were large enough and proved prime using ECPP, it would be published.
There are other contexts in which smaller numbers have run afoul of laws or regulations, or drawn the attention of authorities.
- In 2012, it was reported that the numbers 89, 6, and 4 each became banned search terms on search engines in China, because of the date (1989-06-04) of the June Fourth Massacre in Tiananmen Square.
- Due to the association with gangs, in 2012 a school district in Colorado banned the wearing of jerseys that bore the numbers 18, 14, or 13 (or the reverse, 81, 41, or 31).
- In 2017, far-right Slovak politician Marian Kotleba was criminally charged for donating 1,488 euros to a charity. The number is a reference to a white supremacist slogan and the Nazi salute.
- Carmody, Phil. "An Executable Prime Number?". Retrieved December 30, 2018.
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.
- Greene, Thomas C. (March 19, 2001). "DVD descrambler encoded in 'illegal' prime number". The Register. Retrieved December 30, 2018.
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 December 30, 2018.
The bottom line: If distributing code is illegal, and these numbers contain (or are) the code, doesn't that make these number illegal?
- "AACS licensor complains of posted key". Lumen. April 17, 2007. Retrieved December 30, 2018.
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". February 2, 2000. Retrieved December 30, 2018.
- "Prime Curios: 48565...29443 (1401-digits)". Retrieved December 30, 2018.
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". Retrieved December 30, 2018.
- Wells, David (2011). "Illegal prime". Prime Numbers: The Most Mysterious Figures in Math. Wiley. pp. 126–127. ISBN 9781118045718.
- Patel, Nilay (January 12, 2011). "Sony follows up, officially sues Geohot and fail0verflow over PS3 jailbreak". Engadget. Retrieved December 30, 2018.
- Kravets, David (February 8, 2011). "Sony lawyers now targeting anyone who posts PlayStation 3 hack". Ars Technica. Retrieved December 30, 2018.
- Miller, Ross (February 9, 2011). "PS3 'jailbreak code' retweeted by Sony's Kevin Butler, no punchline needed". Engadget. Retrieved December 30, 2018.
- S., Ben (March 1, 2011). "46-dc-ea-d3-17-fe-45-d8-09-23-eb-97-e4-95-64-10-d4-cd-b2-c2". Yale Law Tech. Retrieved December 30, 2018.
- See File:Free-speech-flag-ps3.svg description.
- "Prime glossary - Illegal prime". Primes.utm.edu. 1999-10-06. Retrieved 2013-03-26.
- Hamilton, David P. "Banned Code Lives in Poetry and Song"
- MacKinnon, Mark (June 4, 2012). "Banned in China on Tiananmen anniversary: 6, 4, 89 and 'today'". The Globe and Mail. Retrieved December 30, 2018.
- Meyer, Jeremy P. (September 5, 2012). "Greeley school ban on gang numbers includes Peyton Manning's 18". The Denver Post. Retrieved December 30, 2018.
- "Police charge leader of Slovak far-right party with extremism". Reuters. July 28, 2017. Retrieved December 30, 2018.
- Skala, Matthew; Bonfield, Brett; Torpey, Mary Fran (February 15, 2008). "Mediating between law and technology requires vigilance and education, not a technical solution". Library Journal. Archived from the original on March 30, 2013.
- Guadamuz, Andrés (2002). "Trouble with Prime Numbers: Decss, Dvd and the Protection of Proprietary Encryption Tools". Journal of Information, Law & Technology. 3. SSRN 569103.
- "A Great Debate: Is Computer Code Protected Speech?". November 30, 2001. Retrieved December 30, 2018.
- Hogge, Becky (May 9, 2007). "Digging in". openDemocracy. Retrieved December 30, 2018.
- Touretzky, Dave. "Steganography Wing of the Gallery of CSS Descramblers". Carnegie Mellon University. Retrieved December 30, 2018.
- Ornes, Stephen (March 16, 2012). "US judge rules that you can't copyright pi". New Scientist. Retrieved December 30, 2018.
- Masnick, Mike (June 25, 2013). "American Bankers' Association Claims Routing Numbers Are Copyrighted". TechDirt. Retrieved December 30, 2018.
- Ernesto (October 27, 2015). "Orwell Estate Sends Copyright Takedown Over the Number "1984"". TorrentFreak. Retrieved December 30, 2018.
- Pickover, Clifford A. "We are in Digits of Pi and Live Forever". Retrieved December 30, 2018.
- Haran, Brady. "Illegal Numbers- feat. James Grime". Numberphile. Archived from the original on July 24, 2018. Retrieved December 30, 2018.