Recently, Aaronson et al. (arXiv:2009.07450) showed that detecting interference between two orthogonal states is as hard as swapping these states. While their original motivation was from quantum gravity, we show its applications in quantum cryptography. 1. We construct the first public key encryption scheme from cryptographic \emph{non-abelian} group actions. Interestingly, the ciphertexts of our scheme are quantum even if messages are classical. This resolves an open question posed by Ji et al. (TCC '19). We construct the scheme through a new abstraction called swap-trapdoor function pairs, which may be of independent interest. 2. We give a simple and efficient compiler that converts the flavor of quantum bit commitments. More precisely, for any prefix X,Y $\in$ {computationally,statistically,perfectly}, if the base scheme is X-hiding and Y-binding, then the resulting scheme is Y-hiding and X-binding. Our compiler calls the base scheme only once. Previously, all known compilers call the base schemes polynomially many times (Cr\'epeau et al., Eurocrypt '01 and Yan, Asiacrypt '22). For the security proof of the conversion, we generalize the result of Aaronson et al. by considering quantum auxiliary inputs.

翻译：最近，阿伦森等人（arXiv:2009.07450）表明，检测两个正交态之间的干涉在难度上等同于交换这些态。虽然他们最初的动机来源于量子引力，但我们展示了这一发现在量子密码学中的应用。1. 我们构建了首个基于密码学非阿贝尔群作用的公钥加密方案。有趣的是，即使消息是经典的，我们方案中的密文也是量子态的。这解决了季等人（TCC '19）提出的一个开放问题。我们通过一种称为交换陷门函数对的新抽象来构建该方案，该抽象可能具有独立的研究价值。2. 我们给出了一种简单高效的编译器，用于转换量子比特承诺的语义类型。更精确地说，对于任意前缀X,Y ∈ {计算性、统计性、完美性}，若基础方案是X-隐藏且Y-绑定的，则所得方案是Y-隐藏且X-绑定的。我们的编译器仅调用基础方案一次。而此前所有已知的编译器都需要多项式次调用基础方案（克雷波等人，Eurocrypt '01和严，Asiacrypt '22）。为了证明该转换的安全性，我们考虑了量子辅助输入，从而推广了阿伦森等人的结果。