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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.


Background

A number may represent some type of
classified information Classified information is material that a government body deems to be sensitive information that must be protected. Access is restricted by law or regulation to particular groups of people with the necessary security clearance and need to know, ...
or
trade secret Trade secrets are a type of intellectual property that includes formulas, practices, processes, designs, instruments, patterns, or compilations of information that have inherent economic value because they are not generally known or readily asc ...
, 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 HD DVD (short for High Definition Digital Versatile Disc) is an obsolete high-density optical disc format for storing data and playback of high-definition video. Supported principally by Toshiba, HD DVD was envisioned to be the successor to the ...
or
Blu-ray Disc The Blu-ray Disc (BD), often known simply as Blu-ray, is a digital optical disc data storage format. It was invented and developed in 2005 and released on June 20, 2006 worldwide. It is designed to supersede the DVD format, and capable of stori ...
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 The Digital Millennium Copyright Act (DMCA) is a 1998 United States copyright law that implements two 1996 treaties of the World Intellectual Property Organization (WIPO). It criminalizes production and dissemination of technology, devices, or s ...
. In part of the
DeCSS DeCSS is one of the first free computer programs capable of decrypting content on a commercially produced DVD video disc. Before the release of DeCSS, open source operating systems (such as BSD and Linux) could not play encrypted video DVDs. ...
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 A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" ( one). The base-2 numeral system is a positional notation ...
. In certain jurisdictions, there are images that are illegal to possess, due to
obscenity An obscenity is any utterance or act that strongly offends the prevalent morality of the time. It is derived from the Latin ''obscēnus'', ''obscaenus'', "boding ill; disgusting; indecent", of uncertain etymology. Such loaded language can be us ...
or secrecy/classified status, so the corresponding numbers could be illegal. In 2011 Sony sued
George Hotz George Francis Hotz (born October 2, 1989), alias geohot, is an American security hacker, entrepreneur, and software engineer. He is known for developing iOS jailbreaks, reverse engineering the PlayStation 3, and for the subsequent lawsuit br ...
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 A dongle is a small piece of computer hardware that connects to a port on another device to provide it with additional functionality, or enable a pass-through to such a device that adds functionality. In computing, the term was initially synonym ...
key through its fictional Kevin Butler character.


Flags and steganography

As a protest of the DeCSS case, many people created "
steganographic Steganography ( ) is the practice of representing information within another message or physical object, in such a manner that the presence of the information is not evident to human inspection. In computing/electronic contexts, a computer file, ...
" 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 controversy surrounding the AACS cryptographic key arose in April 2007 when the Motion Picture Association of America and the Advanced Access Content System Licensing Administrator, LLC (AACS LA) began issuing cease and desist letters to we ...
, a "
free speech Freedom of speech is a principle that supports the freedom of an individual or a community to articulate their opinions and ideas without fear of retaliation, censorship, or legal sanction. The right to freedom of expression has been recogn ...
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 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 Yale Law School (Yale Law or YLS) is the law school of Yale University, a private research university in New Haven, Connecticut. It was established in 1824 and has been ranked as the best law school in the United States by '' U.S. News & World Re ...
) 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.


Illegal primes

An illegal prime is an illegal number which is also
prime A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...
. One of the earliest illegal prime numbers was generated in March 2001 by
Phil Carmody Phil may refer to: * Phil (given name), a shortened version of masculine and feminine names * Phill, a given name also spelled "Phil" * Phil, Kentucky, United States * ''Phil'' (film), a 2019 film * -phil-, a lexical fragment, used as a root ter ...
. Its
binary Binary may refer to: Science and technology Mathematics * Binary number, a representation of numbers using only two digits (0 and 1) * Binary function, a function that takes two arguments * Binary operation, a mathematical operation that ta ...
representation corresponds to a compressed version of the C
source code In computing, source code, or simply code, is any collection of code, with or without comments, written using a human-readable programming language, usually as plain text. The source code of a program is specially designed to facilitate the w ...
of a computer program implementing the
DeCSS DeCSS is one of the first free computer programs capable of decrypting content on a commercially produced DVD video disc. Before the release of DeCSS, open source operating systems (such as BSD and Linux) could not play encrypted video DVDs. ...
decryption algorithm, which can be used by a computer to circumvent a DVD's
copy protection Copy protection, also known as content protection, copy prevention and copy restriction, describes measures to enforce copyright by preventing the reproduction of software, films, music, and other media. Copy protection is most commonly found o ...
. Protests against the indictment of DeCSS author
Jon Lech Johansen Jon Lech Johansen (born November 18, 1983 in Harstad, Norway), also known as DVD Jon, is a Norwegian programmer who has worked on reverse engineering data formats. He wrote the DeCSS software, which decodes the Content Scramble System used for ...
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 A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...
of a number is a fundamental property of
number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathe ...
and is therefore not dependent on legal definitions of any particular jurisdiction. The large prime database of The
Prime Pages The PrimePages is a website about prime numbers maintained by Chris Caldwell at the University of Tennessee at Martin. The site maintains the list of the "5,000 largest known primes", selected smaller primes of special forms, and many "top twenty" ...
website records the top 20 primes of various special forms; one of them is proof of primality using the
elliptic curve primality proving In mathematics, elliptic curve primality testing techniques, or elliptic curve primality proving (ECPP), are among the quickest and most widely used methods in primality proving. It is an idea put forward by Shafi Goldwasser and Joe Kilian in 1986 a ...
(ECPP)
algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...
. Thus, if the number were large enough and proved prime using ECPP, it would be published.


Other examples

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 Colorado (, other variants) is a state in the Mountain West subregion of the Western United States. It encompasses most of the Southern Rocky Mountains, as well as the northeastern portion of the Colorado Plateau and the western edge of the ...
banned the wearing of
jersey Jersey ( , ; nrf, Jèrri, label=Jèrriais ), officially the Bailiwick of Jersey (french: Bailliage de Jersey, links=no; Jèrriais: ), is an island country and self-governing Crown Dependency near the coast of north-west France. It is the la ...
s that bore the numbers 18, 14, or 13 (or the reverse, 81, 41, or 31). * In 2017, far-right Slovak politician
Marian Kotleba Marian Kotleba (; born 7 April 1977) is a Slovak politician and leader of the far-right, neo-Nazicriminally charged for donating 1,488 euros to a charity. The number is a reference to a white supremacist slogan and the
Nazi salute The Nazi salute, also known as the Hitler salute (german: link=no, Hitlergruß, , Hitler greeting, ; also called by the Nazi Party , 'German greeting', ), or the ''Sieg Heil'' salute, is a gesture that was used as a greeting in Nazi Germany. ...
.


See also

* HDCP master key release * Texas Instruments signing key controversy *
Normal number In mathematics, a real number is said to be simply normal in an integer base b if its infinite sequence of digits is distributed uniformly in the sense that each of the b digit values has the same natural density 1/b. A number is said to ...
*
Infinite monkey theorem The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type any given text, such as the complete works of William Shakespeare. In fact, the monkey would ...
*
The Library of Babel "The Library of Babel" ( es, La biblioteca de Babel) is a short story by Argentine author and librarian Jorge Luis Borges (1899–1986), conceiving of a universe in the form of a vast library containing all possible 410-page books of a certain f ...
*
Prior art Prior art (also known as state of the art or background art) is a concept in patent law used to determine the patentability of an invention, in particular whether an invention meets the novelty and the inventive step or non-obviousness criteria ...
*
Streisand effect Attempts to hide, remove, or censor information often have the unintended consequence of increasing awareness of that information via the Internet. This is called the Streisand effect. It is named after American singer and actress Barbra Streis ...


References


External links

* * * * * * * * * * {{cite web , last=Haran , first=Brady , author-link=Brady Haran , title=Illegal Numbers- feat. James Grime , url=http://www.numberphile.com/videos/illegal_numbers.html , work=Numberphile , url-status=dead , archive-url=https://web.archive.org/web/20180724183635/http://www.numberphile.com/videos/illegal_numbers.html , archive-date=July 24, 2018 , access-date=December 30, 2018 Cryptography law Numbers Trade secrets File sharing Numerals