广义单向函数及其应用
Generalized one-way function and its application
AI总结：
本文扩展函数定义构造了广义单向函数，并基于此开发了一种仅依赖经典数据处理的无条件安全密钥分发协议，突显了概率论与随机性在对抗无限计算能力敌手中的有效性。
摘要：
单向函数是经典密码学的基础，其存在性仍是计算复杂性理论中的一个长期问题。最近，一种可证明的量子单向函数被提出，即使在无限计算资源下它仍保持单向性。在此，我们扩展了函数的数学定义，通过虚拟测量可证明量子单向函数的量子比特，并以相同概率随机分配相应的测量结果，从而构造出广义单向函数。值得注意的是，利用该广义单向函数，我们开发了一种仅基于经典数据处理的无条件安全密钥分发协议，可用于安全加密和签名。我们的工作突显了信息在表征量子系统及密度矩阵物理意义中的重要性。我们证明，概率论和随机性是对抗具有无限计算能力敌手的有效工具。
英文摘要：
One-way functions are fundamental to classical cryptography and their existence remains a longstanding problem in computational complexity theory. Recently, a provable quantum one-way function has been identified, which maintains its one-wayness even with unlimited computational resources. Here, we extend the mathematical definition of functions to construct a generalized one-way function by virtually measuring the qubit of provable quantum one-way function and randomly assigning the corresponding measurement outcomes with identical probability. Remarkably, using this generalized one-way function, we have developed an unconditionally secure key distribution protocol based solely on classical data processing, which can then utilized for secure encryption and signature. Our work highlights the importance of information in characterizing quantum systems and the physical significance of the density matrix. We demonstrate that probability theory and randomness are effective tools for countering adversaries with unlimited computational capabilities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
