# One-way function with combination sets as output / image

One-way functions generally operate on bit strings, for the input and the output.

Are there any examples of one-way functions that produce a combination set in output? Let's call this function $$f$$. The function would take one bit string in input, of size $$p$$, and would produce a combination ($$k$$ elements among $$n$$). $$n$$ is a power of $$2$$.

Concrete example of combinations set: 64 elements among 256. The size of this set is 1.9E+61 (204 bits)

I have an algorithm to generate a combination through a hash function: the hash function is used to generate a pseudo random bit string, then the bit string is split into sub-strings of size $$\log_2(n)$$ whose value represents the position of the element in the set of size $$n$$. If the value was already selected, to check the next value. If the hash function has good properties the loop will stop after some iterations.

I would like to know whether there are constructions considered as primitives for this problem.

• A bitstring can encode any object, so just take any OWF and parse its output as whatever you want – fkraiem Jan 18 at 1:12