# PGP Attack FAQ: What if...

This section of the PGP Attack FAQ discusses answers to frequently-asked "but what if" type of questions.

## What if... my secret key was compromised?

A PGP secret key is kept conventionally encrypted with IDEA. Assuming your passphrase is secure enough the best method of attack will be a brute force key-search. If an attacker could test 1,000,000,000,000 keys per second, it would take 1x1017 years before the odds will be in the attacker's favor...

## What if... PGP ran out of primes?

There are an infinite amount of prime numbers. The approximate density of primes lesser than or equal to n is n/ln(n). For a 1024-bit key, this yields:

1.8*10308/ln(1.8*10308) = 2.5*10305

There are about 2.5*10228 times more prime numbers smaller than 21024 than there are atoms in the universe...

## What if... someone just listed all the prime numbers?

If you could store 1,000,000 terabytes of information in a device that weighs 1 gram, (and we figure each number fits in a space of 128 bytes or less) we would need a device that weighs 3.2*10289 grams or 7*10286 pounds. This is 1.6*10 256 times more massive than our sun. Nevermind the fact that we don't have enough matter to even concieve of building such a device, and if we could, it would collapse into a black-hole...

Even worse, to do a brute force attack with all these numbers, the attacker needs to try out every pair of prime numbers. There are 2.5E305(2.5E305-1)/2 possible pairs. This is 3.12*10610 combinations. Absurd, isn't it?

## What if... PGP chose composite numbers instead of primes?

The likelyhood of the Fermat Tests of passing a composite off as a prime is 1 in 1052. If PGP could generate 1,000,000,000,000 primes per second, It would take about 1032 years until odds are better than even for that to happen.