Question

I don’t know if you know this situation, but sometimes I’m just browsing from one Wikipedia page to the next. So I also saw this one about illegal primes. I read the article and it sounds really interesting, but I didn’t really understand what it’s really about.

As far as I understand illegal primes are prime numbers that can be somehow use to generate malicious code? But how? Are there any other examples than the one in the article?

And what is the real life use of them?

Answer 1

The article uses the DeCSS program as an example. That program decrypts DVDs which, according to US Federal law and international treaties, is a crime. It is therefore illegal to posses or distribute that specific source code.

However, the source code can be expressed as a series of binary numbers like…

11100101 10001000 00001000 00000000 01001010 11110010

Which is 252372412549874 in decimal. If the binary code above were illegal, then the decimal number 252372412549874 would be an “illegal number”. An illegal prime number is one in a subset of illegal numbers that happens to be prime.

The fact that something like DeCSS code is also an ordinal value that represents an integer conflicts with the notion of it being illegal. After all, how can the abstract concept of a specific integer be illegal? The term “illegal number” is an oxymoron designed to point out that laws overreach when they attempt to control human artifacts that happen to coincide with abstract concepts. It is the act of decrypting DVDs that can be enforced, not the possession or knowledge of an integer on the number line.