Commitments are equivalent to one-way state generators

arXiv:2404.03220v1 Announce Type: cross
Abstract: One-way state generators (OWSG) are natural quantum analogs to classical one-way functions. We show that $O\left(\frac{n}{\log(n)}\right)$-copy OWSGs ($n$ represents the input length) are equivalent to $poly(n)$-copy OWSG and to quantum commitments. Since known results show that $o\left(\frac{n}{\log(n)}\right)$-copy OWSG cannot imply commitments, this shows that $O\left(\frac{n}{\log(n)}\right)$-copy OWSGs are the weakest OWSGs from which we can get commitments (and hence much of quantum cryptography).
Our construction follows along the lines of H\r{a}stad, Impagliazzo, Levin and Luby [HILL], …

arxiv copy cs.cr functions imply input length log natural poly quant-ph quantum results state