承诺等价于统计可验证的单向态生成器
Commitments are equivalent to statistically-verifiable one-way state generators
AI总结：
本文证明 O(n/log n) 份统计可验证单向态生成器等价于量子承诺，并给出受经典 OWF 到 PRG 构造启发但更简单的新构造。
摘要：
单向态生成器（OWSG）是经典单向函数的自然量子对应物。我们考虑统计可验证的 OWSG（sv-OWSG），它们可能是比 OWSG 更弱的对象。我们证明，O(n/log(n)) 份拷贝的 sv-OWSG（n 表示输入长度）等价于 poly(n) 份拷贝的 sv-OWSG，也等价于量子承诺。由于已知结果表明 o(n/log(n)) 份拷贝的 OWSG 不能推出承诺，这表明 O(n/log(n)) 份拷贝的 sv-OWSG 是我们能够从中获得承诺（并由此获得量子密码学的许多内容）的最弱 OWSG。我们的构造遵循 Hastad、Impagliazzo、Levin 和 Luby 的思路，他们从经典单向函数（OWF）获得经典伪随机生成器（PRG），但我们作出了关键修改。将我们的构造应用于经典情形时，它提供了经典构造的一种替代方案，可从任意经典 OWF 获得经典轻度非均匀 PRG。由于我们不以输出 $f(x)$ 为条件进行论证，我们的构造和分析可以说更简单，并且可能具有独立价值。为了将轻度非均匀 PRG 转换为均匀 PRG，我们可以使用经典构造。
英文摘要：
One-way state generators (OWSG) are natural quantum analogs to classical one-way functions. We consider statistically-verifiable OWSGs (sv-OWSG), which are potentially weaker objects than OWSGs. We show that O(n/log(n))-copy sv-OWSGs (n represents the input length) are equivalent to poly(n)-copy sv-OWSGs and to quantum commitments. Since known results show that o(n/log(n))-copy OWSGs cannot imply commitments, this shows that O(n/log(n))-copy sv-OWSGs are the weakest OWSGs from which we can get commitments (and hence much of quantum cryptography). Our construction follows along the lines of Hastad, Impagliazzo, Levin and Luby, who obtained classical pseudorandom generators (PRG) from classical one-way functions (OWF), however with crucial modifications. Our construction, when applied to the classical case, provides an alternative to the classical construction to obtain a classical mildly non-uniform PRG from any classical OWF. Since we do not argue conditioned on the output $f(x)$, our construction and analysis is arguably simpler and may be of independent interest. For converting a mildly non-uniform PRG to a uniform PRG, we can use the classical construction.
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