# finding hash collisions for set of hashes

I am searching info on dependencies between different hash functions.

Let's say that we have a set of x hashes H1, H2 ... Hn (using different hashing functions) of the same string S. For every hash we can find collision in some time T1, T2 ... Tn

It seems logical that finding collision for every hash in set will take time T = T1+T2+..Tn

On the other hand, every hash exposes additional information on string, thus there is a possibility that some hashes could have properties which can speed up finding collision in another hash (to give a simplified example, something like "if md5 ends with 1111 then last bit of sha1 must be 0")

So, question is, if there exists any research on that subject (or maybe a proof or counter -proof that such dependencies exists for some hashing alghoritms) ?

• You are looking for the concatenation combiner $H_1(M )\mathbin\|H_2(M )$. See Generic Attacks on Hash Combiners by Bao et al.. But what is your aim? Do you want to get rid of collisions? Use SHA512 or SHA3-512, done! – kelalaka Oct 27 '20 at 15:05
• no particular aim, just curiosity – ts01 Oct 27 '20 at 15:12
• There is no dependencies and we don't expect. – kelalaka Oct 27 '20 at 15:14
• I do not see why adding the times "seems logical". By this "logic", finding a 7-letter password formed by concatenating a 3-letter password and a 4-letter password would only use the sum of the effort it takes to find each password. – fgrieu Oct 27 '20 at 16:35
• if you know that it is the structure of password, then yes.. What I am talking about it is set of different hashes of the same message – ts01 Oct 27 '20 at 16:59