论文标题
Koopman对公共密码系统的解释和分析：Diffie-Hellman密钥交换
Koopman interpretation and analysis of a public-key cryptosystem: Diffie-Hellman key exchange
论文作者
论文摘要
公用密钥系统的安全性依赖于计算困难问题，这些问题是通过数字理论方法对经典进行分析的。在本文中，我们通过将Diffie-Hellman密钥交换解释为非线性动力学系统来介绍有关密码系统的新观点。利用库普曼理论，我们将此动态系统转移到一个高维空间中，以分析性地得出纯线性系统，该系统等效地描述了基础的密码系统。在这种形式中，线性系统的分析工具使我们能够通过简单的操作重建密钥交换的秘密整数。此外，我们在最小必需的提升尺寸上提供了上限，以获得完美的准确性。为了证明我们方法的潜力，我们将发现与算法复杂性的现有结果联系起来。最后，我们将此方法转移到数据驱动的设置中，其中从密码系统的数据样本中学到了Koopman表示。
The security of public-key cryptosystems relies on computationally hard problems, that are classically analyzed by number theoretic methods. In this paper, we introduce a new perspective on cryptosystems by interpreting the Diffie-Hellman key exchange as a nonlinear dynamical system. Employing Koopman theory, we transfer this dynamical system into a higher-dimensional space to analytically derive a purely linear system that equivalently describes the underlying cryptosystem. In this form, analytic tools for linear systems allow us to reconstruct the secret integers of the key exchange by simple manipulations. Moreover, we provide an upper bound on the minimal required lifting dimension to obtain perfect accuracy. To demonstrate the potential of our method, we relate our findings to existing results on algorithmic complexity. Finally, we transfer this approach to a data-driven setting where the Koopman representation is learned from data samples of the cryptosystem.
