非认证公共信道上密钥生成的可模拟性条件
On the Simulatability Condition in Key Generation Over a Non-authenticated Public Channel
摘要：
可模拟性条件是研究非认证公共信道上密钥生成的一个基本概念，其中Eve是活跃的，可以截获、修改和伪造非认证公共信道上的消息。利用这个条件，Maurer和Wolf给出了一个显著的“全有或全无”的结果：如果可模拟性条件不成立，则非认证公共信道上的密钥容量将与被动Eve的情况相同，而如果可模拟性条件成立，则非认证信道上的密钥容量将为零。然而，目前仍有两个问题有待解决：1）对于给定的联合概率质量函数（PMF），是否存在有效的算法（多项式复杂度算法）来检验可模拟性条件是否成立？2）如果可模拟性条件成立，是否有有效的算法来寻找相应的攻击策略？在本文中，我们肯定地回答了这两个开放性问题。特别是，对于一个给定的联合保偏滤波器，我们构造了一个线性规划（LP）问题，并证明了可模拟性条件保持\textit{if and only if}的最优值从构造的LP是零。此外，我们构造了另一个LP，并证明了新构造的LP的最小值是一个有效的攻击策略。两个LP都可以用多项式复杂度来求解。
英文摘要：
Simulatability condition is a fundamental concept in studying key generation over a non-authenticated public channel, in which Eve is active and can intercept, modify and falsify messages exchanged over the non-authenticated public channel. Using this condition, Maurer and Wolf showed a remarkable "all or nothing" result: if the simulatability condition does not hold, the key capacity over the non-authenticated public channel will be the same as that of the case with a passive Eve, while the key capacity over the non-authenticated channel will be zero if the simulatability condition holds. However, two questions remain open so far: 1) For a given joint probability mass function (PMF), are there efficient algorithms (polynomial complexity algorithms) for checking whether the simulatability condition holds or not?; and 2) If the simulatability condition holds, are there efficient algorithms for finding the corresponding attack strategy? In this paper, we answer these two open questions affirmatively. In particular, for a given joint PMF, we construct a linear programming (LP) problem and show that the simulatability condition holds \textit{if and only if} the optimal value obtained from the constructed LP is zero. Furthermore, we construct another LP and show that the minimizer of the newly constructed LP is a valid attack strategy. Both LPs can be solved with a polynomial complexity.
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。
