In his seminal work on recording quantum queries [Crypto 2019], Zhandry studied interactions between quantum query algorithms and the quantum oracle corresponding to random functions. Zhandry presented a framework for interpreting various states in the quantum space of the oracle as databases of the knowledge acquired by the algorithm and used that interpretation to provide security proofs in post-quantum cryptography.
In this paper, we introduce a similar interpretation for the case when the oracle corresponds to random permutations instead of random functions. Because both random functions and random permutations are highly significant in security proofs, we hope that the present framework will find applications in quantum cryptography. Additionally, we show how this framework can be used to prove that the success probability for a k-query quantum algorithm that attempts to invert a random N-element permutation is at most O(k^2/N).
We revisit the so-called compressed oracle technique, introduced by Zhandry for analyzing quantum algorithms in the quantum random oracle model (QROM). To start off with, we offer a concise exposition of the technique, which easily extends to the parallel-query QROM, where in each query-round the considered algorithm may make several queries to the QROM in parallel. This variant of the QROM allows for a more fine-grained query-complexity analysis. Our main technical contribution is a framework that simplifies the use of (the parallel-query generalization of) the compressed oracle technique for…
Quantum Simulation of Random Unitaries from Clebsch-Gordan Transforms
QuSoft, Amsterdam, The Netherlands（QuSoft）；Institute for Logic, Language and Computation, University of Amsterdam, The Netherlands（阿姆斯特丹大学逻辑、语言与计算研究所）；Korteweg-de Vries Institute for Mathematics, University of Amsterdam, The Netherlands（阿姆斯特丹大学科特韦格-德弗里斯数学研究所）；Department of Physics, Graduate School of Science, The University of Tokyo, Japan（东京大学理学研究科物理学系）
本文提出基于克莱布施-戈尔丹变换的精确压缩 oracle 构造方法，用于任意有限维紧群的 Haar 随机群作用，展示了其在量子算法和密码学中的应用。
We show the following generic result. Whenever a quantum query algorithm in the quantum random-oracle model outputs a classical value $t$ that is promised to be in some tight relation with $H(x)$ for some $x$, then $x$ can be efficiently extracted with almost certainty. The extraction is by means of a suitable simulation of the random oracle and works online, meaning that it is straightline, i.e., without rewinding, and on-the-fly, i.e., during the protocol execution and without disturbing it. The technical core of our result is a new commutator bound that bounds the operator norm of the commu…
Columbia University（哥伦比亚大学）；Saarland University（萨尔兰大学）；Harvard University（哈佛大学）；University of Washington（华盛顿大学）；Stanford University（斯坦福大学）；NTT Research, Inc（NTT研究所）
We construct a classically verifiable succinct interactive argument for quantum computation (BQP) with communication complexity and verifier runtime that are poly-logarithmic in the runtime of the BQP computation (and polynomial in the security parameter). Our protocol is secure assuming the post-quantum security of indistinguishability obfuscation (iO) and Learning with Errors (LWE). This is the first succinct argument for quantum computation in the plain model; prior work (Chia-Chung-Yamakawa, TCC '20) requires both a long common reference string and non-black-box use of a hash function mode…
Public-key quantum money is a cryptographic proposal for using highly entangled quantum states as currency that is publicly verifiable yet resistant to counterfeiting due to the laws of physics. Despite significant interest, constructing provably-secure public-key quantum money schemes based on standard cryptographic assumptions has remained an elusive goal. Even proposing plausibly-secure candidate schemes has been a challenge. These difficulties call for a deeper and systematic study of the structure of public-key quantum money schemes and the assumptions they can be based on. Motivated by t…
Query-Optimal and Gate-Efficient Lindbladian Simulation
Tsinghua University（清华大学）；Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Center on Frontiers of Computing Studies, Peking University（北京大学前沿计算研究中心）；School of Computer Science, Peking University（北京大学计算机学院）
