TWL #7: This Number is Illegal

Lehan Edirisinghe and Elle Trump May 3, 2016

Watch Facts Elle's

Key takeaways

  • A prime number can encode computer software, including code that defeats DVD copyright protection. The video examines a large prime beginning with 8565078 that represents instructions associated with decrypting protected DVDs, demonstrating how an ordinary mathematical number can carry legally controversial information.

  • The 1998 Digital Millennium Copyright Act restricted bypassing copyright protections and distributing tools designed to defeat them. The narrator claims that merely possessing the prime number could lead to arrest in the United States, but possession of a mathematical number alone is not automatically a criminal offense.

“just the possession of this number is enough to get you arrested in the US.”

  • DVD-decryption software made it possible to bypass encryption and produce unauthorized movie copies. Programs such as DeCSS could defeat the Content Scramble System protecting commercial DVDs, creating a conflict between copyright enforcement and the distribution of computer code.

  • RSA-style encryption exploits the difficulty of factoring the product of two sufficiently large prime numbers. The narrator demonstrates with 11 × 13 = 143, explaining that multiplication is straightforward while recovering the original factors becomes computationally expensive at cryptographic scale.

  • The Electronic Frontier Foundation offered rewards reaching $250,000 for discovering exceptionally large prime numbers. The video cites these prizes to illustrate interest in prime-number research, although finding record-breaking primes differs from generating secure encryption keys.

All points

16 gathered points · 660 words

  • A prime number became controversial because it encoded software capable of bypassing DVD copyright protection. The narrator introduces a large prime number beginning with 8565078, explaining that it represents computer code associated with decrypting protected DVDs. He deliberately changes several digits when presenting it.

  • Prime numbers are whole numbers greater than one that are divisible only by one and themselves. The video uses 7 and 29 as examples and explains why primes are important to cryptography.

  • Testing whether a number is prime becomes more demanding as numbers grow. The narrator estimates that checking whether 43,721 is prime would require 21,861 divisions using a basic trial-and-error method. More efficient mathematical methods can substantially reduce this work.

  • There are infinitely many prime numbers, but discovering exceptionally large primes can require substantial computing resources. The video identifies (2^{74,207,281}-1) as the largest known prime at the time of production. This was a historical record, not a permanent mathematical limit.

  • Multiplying two prime numbers is much easier than recovering them from their product when the numbers are sufficiently large. The narrator illustrates this with 11 × 13 = 143. While multiplication is straightforward, factoring products of very large primes can be computationally difficult.

  • Public-key cryptography can exploit the difficulty of factoring large numbers. The video uses 143 as a simplified public-key example, with 11 and 13 representing secret factors. Real RSA cryptography uses a more elaborate mathematical process rather than simply checking whether two private numbers multiply to a public number.

  • Online banking is presented as an example of cryptography protecting sensitive communications. The narrator describes a bank and a customer's computer using public and private key information. The essential principle is that publicly available encryption information should not allow an attacker to recover the secret information needed to defeat the protection.

  • Cryptographic security depends partly on the computational cost of breaking an encryption system. The narrator argues that sufficiently large keys can make attacks economically impractical because factoring the relevant numbers could require enormous computing resources and time.

  • The Electronic Frontier Foundation offered prizes reaching $250,000 for discovering exceptionally large prime numbers. The video cites these rewards to illustrate interest in advancing computational mathematics. Discovering record-breaking primes is distinct from generating the secret primes used in ordinary encryption.

  • The Digital Millennium Copyright Act became US law in 1998. Its anti-circumvention provisions restrict bypassing certain technological copyright protections and manufacturing or distributing tools designed to circumvent them.

  • DVDs used a copyright-protection system intended to restrict unauthorized copying. The Content Scramble System (CSS) encrypted commercial DVDs to control access to their contents. Circumventing that protection could enable copying DVDs without authorization.

  • The controversial prime number represented source code capable of defeating DVD encryption. The number was associated with DeCSS, software developed to decrypt DVDs protected by CSS. Its significance came from the computer program encoded within the number, not from any inherently unlawful mathematical property.

  • Encoding software as a prime number exposed a difficult boundary between mathematics and copyright enforcement. A prime number is an abstract mathematical object, but its digits can also represent executable instructions. The controversy arose because the represented instructions could be used to circumvent technological copyright protection.

  • DeCSS made it possible for programmers to develop tools that decrypted protected DVDs. Such software could facilitate unauthorized duplication and distribution of films, undermining restrictions imposed by DVD copyright holders.

  • The narrator claims that possessing the controversial number alone could lead to arrest in the United States. This overstates the legal position: the DMCA's anti-circumvention provisions do not make mere possession of a mathematical number automatically criminal. Legal consequences depend on the conduct involved and the applicable provisions.

  • The central controversy was whether copyright law could restrict the distribution of information expressed as an ordinary number. The example illustrates how computer code can be represented mathematically while still raising legal questions when that code enables circumvention of copyright protections.