What is a dirty byte?

Cryptography: What is the probability of getting hash collisions in two different hash algorithms (like MD5 and SHA-256) for two different byte sequences?

• In practice, if I found two different files that have the exact same MD5 hash, what is the probability of also having the same SHA-256 hash for both files? I used MD5 and SHA-256 only as examples. The question is open to all hashing algorithms.

• Answer:

  As stated, the answer to the question is 2^-256, assuming the messages are randomly chosen and SHA-256 is a good hash function. However, if you ask a slightly different question, you get a more interesting answer.  Antoine Joux showed that you can't use a combined hash and expect a combined security result. In this case, the hash function hash(x) defined as md5(x) || SHA-256(x) can be broken in an expected 128 * 2^64 hashes, well below the theoretical bound expected for a hash of that size (2^192). The paper is written well and the algorithm is easy to understand http://www.iacr.org/cryptodb/archive/2004/CRYPTO/1472/1472.pdf