Names for big numbers

Cryptographic keys don't sound that big because we usually talk about how many bits they have, which is really just the logarithm of a number. The numbers that we're dealing with in cryptography are big. Really big. They're so big that most people probably haven't heard of the names for them.

A 128-bit key, for example, represents a number that's roughly 10³⁹, or about a hundred undecillion. A 256-bit key represents a number that's roughly 10⁷⁷, or about a hundred quattuorvigintillion. The numbers that are used in public-key algorithms are even bigger. A 1,024-bit key represents a number that's about 10³⁰⁸, or a hundred thousand centillion.

If you're using a 15,360-bit RSA key, like you need to do to get the same strength as a 256-bit AES key, you have a number that's roughly 10^4,623, or a trecentillion trecentillion trecentillion trecentillion trecentillion quintrigintillion. At that point, the words don't seem to work very well and it's probably better to just think of the number as having 15,360 bits.