Year: 2024
Type: conference-paper
Abstract: One-way state generators (OWSG) [1] are natural quantum analogs to classical one-way functions. We consider statistically-verifiable OWSGs (sv-OWSG), which are potentially weaker objects than OWSGs. We show that$O\left(\frac{n}{\log (n)}\right)$-copy sv-OWSGs ($n$represents the input length) are equivalent to$poly (n)$-copy sv-OWSGs and to quantum commitments. Since known results show that$o\left(\frac{n}{\log (n)}\right)$-copy OWSGs cannot imply commitments [2], this shows that$O\left(\frac{n}{\log(n)}\right)$-copy sv-OWSGs are the weakest OWSGs from which we can get commitments (and hence much of quantum cryptography). Our construction follows along the lines of Hastad, Impagliazzo, Levin and Luby [3], who obtained classical pseudorandom generators (PRG) from classical one-way functions (OWF), however with crucial modifications. Our construction, when applied to the classical case, provides an alternative to the construction provided by [3] to obtain a classical mildly non-uniform PRG from any classical OWF. Since we do not argue conditioned on the output$f(x)$, our construction and analysis is arguably simpler and may be of independent interest. For converting a mildly non-uniform PRG to a uniform PRG, we can use the same construction as [3].
Authors: Rishabh Batra, Rahul Jain
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4404848049