All known constructions of classical or quantum commitments require at least one-way functions. Are one-way functions really necessary for commitments? In this paper, we show that non-interactive quantum commitments (for classical messages) with computational hiding and statistical binding exist if pseudorandom quantum states exist. Pseudorandom quantum states are set of quantum states that are efficiently generated but computationally indistinguishable from Haar random states [Z. Ji, Y.-K. Liu, and F. Song, CRYPTO 2018]. It is known that pseudorandom quantum states exist even if BQP=QMA (relative to a quantum oracle) [W. Kretschmer, TQC 2021], which means that pseudorandom quantum states can exist even if no quantum-secure classical cryptographic primitive exists. Our result therefore shows that quantum commitments can exist even if no quantum-secure classical cryptographic primitive exists. In particular, quantum commitments can exist even if no quantum-secure one-way function exists.
翻译：传统承诺或量子承诺的所有已知构建都至少需要单向函数。 单向函数对于承诺是否真正必要? 在本文中, 我们显示, 如果存在假冒的量子国家, 则存在计算隐藏和统计约束的非互动量子承诺( 对于古典信息 ) 。 普塞多兰多姆量子国家是一组量子状态, 这些量子状态是高效生成的, 但是在计算上无法与豪尔随机状态[Z. Ji, Y.- K. Liu, 和 F. Song, CRYPTO 2018] 区分。 已知假冒量子状态存在, 即使 BQP ⁇ MA( 与量子体相对) [W. Kretschmer, TQC 2021] 也存在。 这意味着即使没有量子安全古典加密原始存在, 也存在伪量子状态。 因此, 我们的结果显示即使不存在量子安全古典加密原始原始状态, 量子承诺也可以存在。 具体地说, 即使不存在量子安全的单向函数, 量子承诺也可以存在。
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