Pseudorandom functions (PRFs) are one of the most fundamental primitives in classical cryptography. On the other hand, in quantum cryptography, it is possible that PRFs do not exist but their quantum analogues could exist, and still enabling many applications including SKE, MACs, commitments, multiparty computations, and more. Pseudorandom unitaries (PRUs) [Ji, Liu, Song, Crypto 2018], pseudorandom isometries (PRIs) [Ananth, Gulati, Kaleoglu, Lin, Eurocrypt 2024], and pseudorandom function-like state generators (PRFSGs) [Ananth, Qian, Yuen, Crypto 2022] are major quantum analogs of PRFs. PRUs imply PRIs, and PRIs imply PRFSGs, but the converse implications remain unknown. An important open question is whether these natural quantum analogues of PRFs are equivalent. In this paper, we partially resolve this question by ruling out black-box constructions of them:
1. There are no black-box constructions of $O(\logλ)$-ancilla PRUs from PRFSGs. 2. There are no black-box constructions of $O(\logλ)$-ancilla PRIs with $O(\logλ)$ stretch from PRFSGs. 3. There are no black-box constructions of $O(\logλ)$-ancilla PRIs with $O(\logλ)$ stretch from PRIs with $Ω(λ)$ stretch.
Here, $O(\logλ)$-ancilla means that the generation algorithm uses at most $O(\logλ)$ ancilla qubits. PRIs with $s(λ)$ stretch is PRIs mapping $λ$ qubits to $λ+s(λ)$ qubits. To rule out the above black-box constructions, we construct a unitary oracle that separates them. For the separations, we construct an adversary based on the quantum singular value transformation, which would be independent of interest and should be useful for other oracle separations in quantum cryptography.
University of Maryland, College Park（马里兰大学帕克分校）；University of Texas at Austin（德克萨斯大学奥斯汀分校）；IonQ Inc.（IonQ公司）；Technology Innovation Institute（技术创新研究所）；Singapore Institute of Technology（新加坡理工大学）；Agency for Science, Technology and Research (A*STAR)（科学技术研究局（A*STAR））；Singapore University of Technology and Design（新加坡科技设计大学）；California Institute of Technology（加州理工学院）；National University of Singapore（新加坡国立大学）；Nanyang Technological University（南洋理工大学）
This paper, for the first time, addresses the questions related to the connections between the quantum pseudorandomness and quantum hardware assumptions, specifically quantum physical unclonable functions (qPUFs). Our results show that the efficient pseudorandom quantum states (PRS) are sufficient to construct the challenge set for the universally unforgeable qPUF, improving the previous existing constructions that are based on the Haar-random states. We also show that both the qPUFs and the quantum pseudorandom unitaries (PRUs) can be constructed from each other, providing new ways to obtain …
Efficient High-Dimensional Quantum Circuit Synthesis: From Multi-Controlled Gates to Isometries and Quantum Channels
Institute for Advanced Study in Mathematics, Harbin Institute of Technology（哈尔滨工业大学高等研究院）；School of Mathematics, Harbin Institute of Technology（哈尔滨工业大学数学学院）
We consider the problem of efficiently simulating random quantum states and random unitary operators, in a manner which is convincing to unbounded adversaries with black-box oracle access. This problem has previously only been considered for restricted adversaries. Against adversaries with an a priori bound on the number of queries, it is well-known that $t$-designs suffice. Against polynomial-time adversaries, one can use pseudorandom states (PRS) and pseudorandom unitaries (PRU), as defined in a recent work of Ji, Liu, and Song; unfortunately, no provably secure construction is known for PRU…
We give three new algorithms for efficient in-place estimation, without using ancilla qubits, of average fidelity of a quantum logic gate acting on a d-dimensional system using much fewer random bits than what was known so far. Previous approaches for efficient estimation of average gate fidelity replaced Haar random unitaries in the naive estimation algorithm by approximate unitary 2-designs, and sampled them uniformly and independently. In contrast, in our first algorithm we sample the unitaries of the approximate unitary 2-design uniformly using a limited independence pseudorandom generator…
On Limits on the Provable Consequences of Quantum Pseudorandomness
Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）；KIAS, Korea（韩国高等研究院）；UT Austin, USA（美国德克萨斯大学奥斯汀分校）；KAIST, Daejeon, Korea（韩国科学技术院）；Surf, The Netherlands（荷兰SURF）；De Vinci Higher Education, De Vinci Research Center, Paris, France（法国巴黎德芬奇高等教育与研究中心）
It is a longstanding open problem to devise an oracle relative to which BQP does not lie in the Polynomial-Time Hierarchy (PH). We advance a natural conjecture about the capacity of the Nisan-Wigderson pseudorandom generator [NW94] to fool AC_0, with MAJORITY as its hard function. Our conjecture is essentially that the loss due to the hybrid argument (which is a component of the standard proof from [NW94]) can be avoided in this setting. This is a question that has been asked previously in the pseudorandomness literature [BSW03]. We then make three main contributions: (1) We show that our conj…
Rapid Mixing of Parallel Kac's Walk: From Spheres to Stiefel Manifolds
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；National University of Singapore（新加坡国立大学）；Portland State University（波特兰州立大学）；Nanjing University（南京大学）；Hefei National Laboratory（合肥国家实验室）
