Quick: When you hear the phrase “computer geek,” how do you imagine that person spending his Saturday nights? Is he playing complex online games until dawn? Is he developing new software for music programs, hoping to become more famous than the one man band, Owl City? Is he searching for large prime numbers? If the third possibility didn’t occur to you, than perhaps you’ve never been told that using technology to find and publish certain prime numbers, like using technology to steal money from an ATM or affect the outcome of a presidential election, can be a form of law breaking. In short, some prime numbers are illegal.
To understand why, we’ll have to do a little math. An integer is any whole number. A prime number is any integer that’s divisible by only two numbers, either one or itself. With the exception of the number two, all prime numbers are odd numbers. However, not all odd numbers are prime numbers. Nine, for example, is an odd number. Since nine is divisible by three, though, it isn’t a prime number. Seven, on the other hand, is a prime number. Seven can only be divided by either seven or one. When working with relatively low numbers, it’s fairly simple to determine whether a number is prime. The higher the number is, the more difficult it is to determine whether or not that number is prime. High prime numbers are useful encryption keys, because whether a certain high number is prime may be difficult to determine. A computer code is always a series of numbers, and a prime number has fewer possible integers for hackers to find.
To see why prime numbers are useful for securing data, imagine signing onto your online bank account. Imagine that the public key, the number that’s sent from your computer to the bank to signal you’re a secure user, is one hundred forty three. [Actually, any public key would be a much higher number. We’re using smaller numbers to make this thought exercise easier.] One hundred forty-three factors into two prime numbers, eleven and thirteen. Those two numbers, then, would be the private keys, numbers held only by the bank. If the number that was sent from your computer when you tried to sign in to your online bank account were a number that didn’t factor into eleven and thirteen, you would be flagged as an unverified user of the site, and the bank data you were never entitled to access would remain secure. The reason this security measure works: Computers are designed to be much better at multiplying numbers than factoring them. The same encryption process can be used for any data a person or an organization wishes to secure.
For example, a very large prime number was used to encrypt the data on DVDs, in order to prevent DVD pirating. In March of 2001, an American, Phil Carmody, guessed that number. Carmody guessed the encryption code, called DeCSS, by using a theorem, Dirichlet’s Thorem, to find prime numbers that met the qualifications for the algorithm that would open DeCSS. Using the open source program Open PFGW, Carmody identified probable prime numbers. Using Titanix software’s Elliptical Curve Primality Proving algorithm, he determined which prime numbers were large enough to unzip the encrypted files for DeCSS. Essentially, he found the information that would allow people to efficiently violate copyright laws by copying DVDs.
The United States federal government takes copyright violations very seriously. In The Digital Millennium Copyright Act of 1998, Congress acknowledged that the methods needed for protecting copyrights would need to change as technology changed if it were to remain effective. In The Digital Millennium Copyright Act, Congress says those who commit copyright violations, such as the illegal copying of DVDs, may face fines. Someone who violates copyright law may owe fines in the amount of seven hundred fifty U.S. dollars to thirty thousand U.S. dollars for each work for which a copyright was infringed. At her discretion, a federal judge may award additional damages of two hundred dollars for unknowing copyright infringement, or up to one hundred thousand U.S. dollars for knowing copyright infringement. The Electronic Frontier Foundation is so dedicated to finding secure public keys that it will pay up to two hundred fifty thousand U.S. dollars for new prime numbers. Phil Carmody definitely made copyright infringement and security breaches possible by releasing an illegal prime number, but he hasn’t broken the law himself.
Carmody showed his intelligence by discovering the illegal prime number, and how he chose to release the number is further proof of that intelligence. Carmody didn’t release the first viable prime number he found. At one thousand four hundred one digits, it was too small to be archived. The next viable prime number he discovered that would unzip a DeCSS file was one thousand nine hundred five digits long. At this length, it was the tenth largest prime number to be proven using the Elliptical Curve Primality Proving algorithm. His feat was honored by the website, The Prime Pages, an archive of the twenty highest prime numbers (so far), along with the names of the people who discovered them. Carmody’s number was intrinsically archivable and publishable, as he had always planned for it to be. [The first idea he considered was printing it on a tee shirt.] The Prime Pages published the number for a reason (honoring Carmody’s achievement of finding the tenth largest prime number) completely unrelated to the number’s primary function (unzipping DeCSS files). Therefore, he has evaded legal responsibility for the publication of the number and any copyright violations resulting from its use. Carmody has learned his lesson from the experience, although perhaps not the lesson The United States’ federal government might have hoped he would learn. Carmody has discovered another illegal prime number that will unzip DeCSS files if it’s compressed using Linux software. This number is one thousand eight hundred eleven digits long. He plans to legally publish it.