  Pseudorandom states, introduced by Ji, Liu and Song (Crypto'18), are
efficiently-computable quantum states that are computationally
indistinguishable from Haar-random states. One-way functions imply the
existence of pseudorandom states, but Kretschmer (TQC'20) recently constructed
an oracle relative to which there are no one-way functions but pseudorandom
states still exist. Motivated by this, we study the intriguing possibility of
basing interesting cryptographic tasks on pseudorandom states.
  We construct, assuming the existence of pseudorandom state generators that
map a $\lambda$-bit seed to a $\omega(\log\lambda)$-qubit state, (a)
statistically binding and computationally hiding commitments and (b) pseudo
one-time encryption schemes. A consequence of (a) is that pseudorandom states
are sufficient to construct maliciously secure multiparty computation protocols
in the dishonest majority setting.
  Our constructions are derived via a new notion called pseudorandom
function-like states (PRFS), a generalization of pseudorandom states that
parallels the classical notion of pseudorandom functions. Beyond the above two
applications, we believe our notion can effectively replace pseudorandom
functions in many other cryptographic applications.
