Unpredictable functions (UPFs) play essential roles in classical cryptography, including message authentication codes (MACs) and digital signatures. In this paper, we introduce a quantum analog of UPFs, which we call unpredictable state generators (UPSGs). UPSGs are implied by pseudorandom function-like states generators (PRFSs), which are a quantum analog of pseudorandom functions (PRFs), and therefore UPSGs could exist even if one-way functions do not exist, similar to other recently introduced primitives like pseudorandom state generators (PRSGs), one-way state generators (OWSGs), and EFIs. In classical cryptography, UPFs are equivalent to PRFs, but in the quantum case, the equivalence is not clear, and UPSGs could be weaker than PRFSs. Despite this, we demonstrate that all known applications of PRFSs are also achievable with UPSGs. They include IND-CPA-secure secret-key encryption and EUF-CMA-secure MACs with unclonable tags. Our findings suggest that, for many applications, quantum unpredictability, rather than quantum pseudorandomness, is sufficient.
Indefinite probabilities in quantum spacetime: A deepening of unpredictability
Università degli studi di Roma Tor Vergata（罗马托尔维加塔大学）；INFN, Sezione di Roma Tor Vergata（罗马托尔维加塔分部意大利国家核物理研究所）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Centro Ricerche Enrico Fermi—Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”（恩里科·费米研究中心——物理学史博物馆及恩里科·费米研究与教育中心）；Università di Napoli Federico II（那不勒斯费德里科二世大学）；INFN, Sezione di Napoli（那不勒斯分部意大利国家核物理研究所）；Institute for Quantum Optics and Quantum Information - Vienna, Austrian Academy of Sciences（奥地利科学院维也纳量子光学与量子信息研究所）
Traceable random numbers from a nonlocal quantum advantage
University of Colorado, Boulder（科罗拉多大学博尔德分校）；National Institute of Standards and Technology（美国国家标准与技术研究院）；Oak Ridge National Laboratory（橡树岭国家实验室）；Joint Quantum Institute（联合量子研究所）；University of Maryland（马里兰大学）；Center for Quantum Information and Control, University of New Mexico（新墨西哥大学量子信息与控制中心）；University of California, Berkeley（加州大学伯克利分校）；Quside Technologies（Quside 科技公司）
