kryptoanalysis for sha(sha(sha.....))) and CPU error rate.

[blub]

Im thinking about making a Brainwallet with following technique:

take a rememberable passphrase and hash it about 100 billion times. This should take a few days on a decent cpu, and efectly render bruteforcing impossible for some years to come.

Has there been any serious analysis of the sha2 hash under this conditions? Worst case would be the chained hashing converging against some constant value...

Second problem: How high is the probability of a cpu not making a single mistake in the process?

[Geremia]

Worst case would be the chained hashing converging against some constant value...

Would that really happen?

[grue]

see: https://en.wikipedia.org/wiki/Key_stretching