Ruttor Andreas, Kinzel Wolfgang, Kanter Ido
Institut für Theoretische Physik, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 May;75(5 Pt 2):056104. doi: 10.1103/PhysRevE.75.056104. Epub 2007 May 9.
Synchronization of neural networks has been used for public channel protocols in cryptography. In the case of tree parity machines the dynamics of both bidirectional synchronization and unidirectional learning is driven by attractive and repulsive stochastic forces. Thus it can be described well by a random walk model for the overlap between participating neural networks. For that purpose transition probabilities and scaling laws for the step sizes are derived analytically. Both these calculations as well as numerical simulations show that bidirectional interaction leads to full synchronization on average. In contrast, successful learning is only possible by means of fluctuations. Consequently, synchronization is much faster than learning, which is essential for the security of the neural key-exchange protocol. However, this qualitative difference between bidirectional and unidirectional interaction vanishes if tree parity machines with more than three hidden units are used, so that those neural networks are not suitable for neural cryptography. In addition, the effective number of keys which can be generated by the neural key-exchange protocol is calculated using the entropy of the weight distribution. As this quantity increases exponentially with the system size, brute-force attacks on neural cryptography can easily be made unfeasible.
神经网络同步已被用于密码学中的公共信道协议。对于树奇偶校验机，双向同步和单向学习的动态过程都由吸引和排斥随机力驱动。因此，它可以通过参与神经网络之间重叠的随机游走模型很好地描述。为此，通过解析推导了步长的转移概率和缩放定律。这些计算以及数值模拟都表明，双向交互平均会导致完全同步。相比之下，只有通过波动才能成功学习。因此，同步比学习快得多，这对于神经密钥交换协议的安全性至关重要。然而，如果使用具有三个以上隐藏单元的树奇偶校验机，双向和单向交互之间的这种定性差异就会消失，因此这些神经网络不适用于神经密码学。此外，使用权重分布的熵来计算神经密钥交换协议可以生成的有效密钥数量。由于这个量随系统大小呈指数增长，对神经密码学的暴力攻击很容易变得不可行。
