论文标题
部分可观测时空混沌系统的无模型预测
An algebraic attack to the Bluetooth stream cipher E0
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
In this paper we study the security of the Bluetooth stream cipher E0 from the viewpoint it is a "difference stream cipher", that is, it is defined by a system of explicit difference equations over the finite field GF(2). This approach highlights some issues of the Bluetooth encryption such as the invertibility of its state transition map, a special set of 14 bits of its 132-bit state which when guessed implies linear equations among the other bits and finally a small number of spurious keys, with 83 guessed bits, which are compatible with a keystream of about 60 bits. Exploiting these issues, we implement an algebraic attack using Gröbner bases, SAT solvers and Binary Decision Diagrams. Testing activities suggest that the version based on Gröbner bases is the best one and it is able to attack E0 in about 2^79 seconds on an Intel i9 CPU. To the best of our knowledge, this work improves any previous attack based on a short keystream, hence fitting with Bluetooth specifications.
