# If multiple hashing algorithms are chained together, is the compound hash function more collision resistant? [duplicate]

The DASH cryptocurrency uses X11, which is a Proof of Work hashing algorithm composed of 11 separate hash functions which are run as a sequence.

Example: $$Digest = H_{11}...(H_3(H_2(H_1(Input))))$$

Questions:

1) Is this algorithm's collision resistance that of the weakest function in the sequence?

2) Can this algorithm tolerate a hashing collision found in one of the constituent parts and still produce output that is considered safe?

1) Just assume $$H_1(x)$$ is weak and you can generate two $$x_1,x_2$$ with the same hash. The other hashes then work on the same input, and hashes are deterministic, so the final output is the same. So on the first glance, it seems at best the collisions resistance is equal to the minimum of the functions. But it could also be worse. On the other hand, it depends on what kind of collisions you can create, because to find a collision for the original input would require finding preimages of the correct size in in the inner hashes.