1. There might be a misunderstanding with terminology. Asking for a k-independent/k-wise independent family of hash function doesn’t mean “k hash functions.” It

1. There might be a misunderstanding with terminology. Asking for a k-independent/k-wise independent family of hash function doesn’t mean “k hash functions.” It is a technical term that means: a set H of functions having the property that, if you pick a random function h: X -> Y from that set, hashing any k items with h results in “no correlation” in the output. (Formally, over the randomness of h in H, for all x1, x2, … xk in X; y1, y2, … yk in Y, P[h(x1) = y1 and h(x2) = y2 and … h(xk) = yk] = 1/(|Y|^k).) (Although, granted, most Bloom filter papers do draw m functions from a k-wise independent family. That brings me to 2…) 2. The target audience is different. CS theory papers often limit their scope to a smaller result. In a bloom filter context, they don’t want to concern themselves with whether a particular hash function like SHA256 behaves k-wise independently when random characters are appended to the input. They only care that a k-wise independent hash family is needed. A different paper can analyze SHA256 or whatever other hash function.