Non-adaptive Universal One-Way Hash Functions from Arbitrary One-Way Functions

In this work we give the first non-adaptive construction of universal one-way hash functions (UOWHFs) from arbitrary functions. Our uses $$O(n^9)$$ calls to function, has a key length $$O(n^{10})$$ , and can be implemented in NC1 assuming underlying function is NC1. Prior work, best UOWHF used $$O(n^{13})$$ adaptive size $$O(n^5)$$ (Haitner, Holenstein, Reingold, Vadhan Wee [Eurocrypt ’10]). By result Applebaum, Ishai Kushilevitz [FOCS ’04], above implies existence UOWHFs NC0, given We also show that PRG Haitner, Reingold (HRV, [STOC ’10]), with small modifications, yields relaxed notion UOWHFs, which family (inefficiently) converted by changing on negligible fraction inputs. order analyze construction, introduce next-bit unreachable entropy, replaces pseudoentropy HRV.