Illegal prime is a prime number that represents legally protected information that is prohibited to be stored and distributed. One of the first illegal prime numbers was made public in 2001 . When correct [ clarify ] the interpretation of it is a computer program that circumvents the copyright protection scheme. The distribution of such programs in the United States is illegal under the DMCA , which transforms beyond the legal field not only direct copyright infringement by copying, but also the production and distribution of technologies that allow circumventing technical means of copyright protection . Illegal prime numbers are a subset of illegal numbers .
Content
Background
One of the first illegal prime numbers was built in May 2001 by Phil Carmody. Its binary representation is associated with a compressed version of a C program that performs a DeCSS decryption algorithm, which can be used to bypass DVD copy protection.
The protests against the official charge of DeCSS author Jon Lech Johansen ( eng. En: Jon Lech Johansen ) and the law prohibiting the publication of the DeCSS code took various forms. One of them was to present the illegal code in a form that has a certain property that makes it permitted for publication regardless of the legality of the code itself. Since the bits that make up the computer program are also a number, the plan was to pick a number with a special property that would make it interesting to publish (one way was to print the number on t-shirts, which is popular, for example, for Mersenne primes ) [ 1] [2] . The simplicity of a number is a fundamental property in number theory that does not depend on the legal definitions of any authority.
For example, The Prime Pages publishes the 20 largest known prime numbers in several categories. One of the categories is numbers whose simplicity is proved by the method of elliptic curves (ECPP). Thus, if the number is long enough, and its simplicity is proved by the ECPP method, then it is of theoretical interest for publication.
Build
Let the compressed program code be represented by the number k . According to Dirichlet's theorem on primes in an arithmetic progression , each arithmetic progression , the first term b and the difference a of which are natural mutually simple numbers , contains an infinite number of primes. Using the fact that the gzip compression program ignores the bytes after the terminating character (null terminated) of the compressed file, we can take a to equal some power of 256 to greater than b . Then by unzipping the number k · a + b we get our number k . This means that there is an infinite set of primes that, after unzipping, represent the same code. Thus, candidates for prime numbers were generated, each of which, when unzipping, gives the DeCSS code in the C programming language . In particular, Phil Carmody showed that such numbers are:
Some of these numbers were identified as probably simple using the open source program OpenPFGW, and the simplicity of one of them was confirmed by the ECPP algorithm, which was implemented using the Titanix software. However, even in 2001, the first number consisting of 1401 decimal digits was too small to publish, so Carmody created a second prime number consisting of 1,905 digits, which was the tenth prime number found using the ECPP. Carmody also built another prime number, which directly represents the executable machine code for Linux i386 , which does the same as the previous programs.
First illegal prime number
The Register indicates the number:
4,850,500;);) No. 9711.Chimes. 77176 02984 12552 44647 44505 58346 28144 88335 63190 27253 19590 43928 38737 64073 91689 12579 24055 01 562))))) 956653hhhhhhhf 71304 04321 18261 01035 91186 47666 29638 58495 08744 84973 73476 86142 08805 29443.
The first illegal executable prime
This prime number, containing 1811 decimal digits, can be interpreted as uncompressed executable code for the x86 processor for the Linux operating system, which performs the same task as the compressed program above:
493103809809809803_xxxxxxxxxxxxxxxxxxxxxfxxf 3211 Black and White. 6274601525301.jpg Unity 02795 61868 92925 38069 33052 04238 14996 99454 56945 77413 83356 89906 00587 08321 81270 48611 3368 2 0 5 5 5 5 5 6 8 1965 08558829808cccccccccccc0cccc0ncncncncncncccccccccccccccccccccccccccccccccccccccccccccqmccgcccccccccccccccccgmvgvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvtvtvpcpcp.html 14784 66791 55096 51543 10113 53858 62081 96875 83688 35955 77893 91454 53935 68199 60988 08540 47659 07 358 97289 89834 25047 12891 84162 65878 96821 85380 87956 27903 99786 29449 39760 54675 34821 25675 01215 17082 73710 76462 70712 46753 21024 83678 15940 00875 05452 54353 7.
See also
- AACS
- Content Scramble System
Notes
- ↑ Memorandum Order, in MPAA v. Reimerdes, Corley and Kazan (NY; Feb. 2, 2000) Archival copy of September 29, 2007 on the Wayback Machine .
- ↑ Prime glossary - Illegal prime .
Links
- The prime pages (eng.)
- Prime glossary - Illegal prime (English)
- Prime Curios - Illegal prime (English)
- The first illegal prime
- DVD descrambler encoded in 'illegal' prime number (Thomas C. Greene, The Register , Mon 19 March 2001 ) (eng.)
- Phil Carmody's page discussing executable primes. (eng.)