Cryptography from Pseudorandom Quantum States

Abstract

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 𝜆-bit seed to a 𝜔(log 𝜆)-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.

Complementarity and the unitarity of the black hole S-matrix

“…1 Second, while the internal dynamics of the black hole was modeled as a Haar-random unitary in ref. [1], we reach similar conclusions by modeling the dynamics more realistically as a computationally efficient pseudorandom unitary transformation [10,11]. Third, we show that, even in the presence of infalling agents, the non-isometric map of ref.…”

“…ensured when the black hole dynamics has polynomial complexity. This is achieved under the assumption that the internal black hole dynamics is pseudorandom [10] and also that the infaller performs an operation with complexity scaling polynomially in the entropy of the black hole. Moreover, under similar assumptions, we show that the complexity of the black hole S-matrix is polynomial in the black hole entropy.…”

“…The existence of such a unitary U would follow from the assumption that pseudorandom unitaries exist [10]. At a high level, this assumption means that there is a family of efficient unitary transformations such that an average over the family cannot be distinguished by computationally bounded observers from an average over Haar measure.…”

“…[1], we model the black hole dynamics by a Haar-random unitary transformation, and conclude that the deviations from unitarity induced by the infaller are negligible. Then, more realistically, we assume that the black hole dynamics is pseudorandom [10,11], and infer that deviations from unitarity are small if operations performed by the infaller have complexity polynomial in the black hole entropy. Moreover, under related assumptions, we show that the computational complexity of the black hole S-matrix remains polynomial in its entropy.…”

Estimating the randomness of quantum circuit ensembles up to 50 qubits

“…The frame potential is a user-friendly measure of how random a given ensemble is in terms of operator norms: the smaller the frame potential is, the more chaotic and more complicated the ensembles are, and the more easily we can achieve computational advantages [29,30]. In fact, in certain quantum cryptographic tools, concepts identical or similar to approximate k-designs are used, making use of the exponential separation of complexities between classical and quantum computations [31][32][33][34][35][36][37][38]. The efficient tensor network contraction algorithm is developed in the QTensor framework [39][40][41].…”