Cryptography from Pseudorandom Quantum States

Understand

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.