High Power Computing for Crypto Research Obviously, much of cryptography requires the assumption that adversaries have bounded computing power. 

So, I was wondering, are there any fields in cryptographic research for which high power computing would aid researchers? Obviously, even the most advanced computers today will not give them an asymptotic advantage, but my question is:

Does crypto research require high computing power and if so specifically which field?
Insofar as cryptanalysis is considered a part of crypto research, certainly.  More computing power is always helpful for breaking ciphers, and indeed, some of the more notable massive distributed computing efforts of recent decades have involved the brute force breaking of cipher challenges such as the RSA Factoring, DES and Secret-Key Challenges.  Even with more "analytical" attacks, such as the recent MD5 collision attacks, the final stage of the attack typically still requires testing a large number of candidate values by brute force, a task made considerably easier by the availability of high computing power.

In other parts of crypto research, not so much, although some recent crypto primitives have made use of computationally intensive (pseudo-) Monte Carlo methods for choosing constants or combinations of operations to maximize desired cryptographic properties.  For example, the rotation constants of the Threefish block cipher used in the SHA-3 finalist hash function Skein were selected using a genetic algorithm.