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. 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.
翻译:由 Ji、 Liu 和 Song ( Crypto' 18) 介绍的普塞多兰多姆州是高效的可计算数量国家,在计算上无法与哈阿兰地国家区分。 单向函数意味着存在伪兰国, 但Kretschmer (TQC'20) 近期建造了一个神器, 相对而言, 没有单向函数, 但伪兰地国家仍然存在。 受此动机的驱动, 我们研究在伪兰地国家建立有趣的加密任务的可能性。 我们建构, 假设伪兰地国家发电机的存在, 将美元/ 拉姆巴元- 比特种子映射成 $\ omga (\ log\lambda) $- quit state 国家, (a) 在统计上约束和计算上隐藏承诺, 以及 (b) 假冒的一次性加密计划。 (a) 伪兰地国家足以在不诚实的多数国家环境中建立恶意安全的多价计算协议。 我们的构造是通过一个名为伪兰地函数(PRFS) 这样的新概念产生, 超越了我们假冒冒版应用概念, 。