Why do big corporations use such large encryption keys?

[SW VandeCarr]

Simple question. I understand that the product of two "large" primes is a nearly unbreakable code. How large is "large" and if it's that easy, why aren't big corporations using this?

 

[jedishrfu]

This article discusses the problem of factorization and has some tables that estimate how long given a number of n bits as the key

http://en.m.wikipedia.org/wiki/RSA_(cryptosystem)

 

[Mark44]

Simple question. I understand that the product of two "large" primes is a nearly unbreakable code. How large is "large" and if it's that easy, why aren't big corporations using this?

In essence, they are. One technique that's used is public key encryption, which relies on two keys -- a public key and a private key.

"Unbreakable" is a relative term. Encryptions that were unbreakable by a single computer ten or twenty years ago were able to be broken using large networks of computers, each working in parallel to search for a factorization of a large composite number with two prime factors. As a result we've seen the keys get larger in size. See http://en.wikipedia.org/wiki/Key_size and http://en.wikipedia.org/wiki/Key_(cryptography).