量子密码的广义测不准原理
Generalized Uncertainty Principles for Quantum Cryptography
摘要：
我们知道经典的公钥密码算法都是基于某些NP难问题的，如RSA中的整数分解和Diffie-Hellman中的离散对数。他们将在容错量子计算机中变得脆弱。我们还知道，量子比特或量子比特的不确定性原理，如基于量子不确定性原理的量子密钥分配或QKD，提供了信息理论安全性。从经典计算到量子计算的范式转变的有趣含义是，用于经典密码学的NP-硬度可能会转移到量子密码学的不确定性原理，包括量子对称加密，后量子密码学，以及相干光通信的相空间中的量子加密。本文将探讨这些所谓的广义不确定性原理，并解释它们对量子安全的影响。我们确定了三个提供量子安全的广义不确定性原理：置换门之间的不可互换性，相干态的位移和相移算子之间的不可互换性，以及后量子密码学的一般线性代数中的模丢番图方程问题。
英文摘要：
We know the classical public cryptographic algorithms are based on certain NP-hard problems such as the integer factoring in RSA and the discrete logarithm in Diffie-Hellman. They are going to be vulnerable with fault-tolerant quantum computers. We also know that the uncertainty principle for quantum bits or qubits such as quantum key distribution or QKD based on the quantum uncertainty principle offers the information theoretical security. The interesting implication with the paradigm shifts from classical computing to quantum computing is that the NP-hardness used for classical cryptography may shift to the uncertainty principles for quantum cryptography including quantum symmetric encryption, post-quantum cryptography, as well as quantum encryption in phase space for coherent optical communications. This paper would like to explore those so-called generalized uncertainty principles and explain what their implications are for quantum security. We identified three generalized uncertainty principles offering quantum security: non-commutability between permutation gates, non-commutability between the displacement and phase shift operators for coherent states, and the modular Diophantine Equation Problem in general linear algebra for post-quantum cryptography.
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。
