Originally posted by AndyChow
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A natural construction to build large hash values is to concatenate several smaller hashes. For example, given two hash functions F and G, it seams reasonable given a message M to form the large hash value (F(M)||G(M)). In this construction, F and G can either be two completely different hash functions or two slightly different instances of the same hash function. If F and G are good iterated hash functions with no attack better than the generic birthday paradox attack, we claim that the hash function F||G obtained by concatenating F and G is not really more secure than F or G by itself. Moreover this result applies both to collision restistance, preimage resistance and second preimage resistance.
So having both a MD5 and a SHA1 hash does not make it any stronger than having only the SHA1 hash. Exactly why this is would take up far to much space here and I must therefore refer you to the linked paper.
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