| In this paper the Bluetooth key stream generator is analyzed based on a reasonable probabilistic model. And the output sequence of this generator proved to be uniformly distributed. We analyze the correlation-immunity of this stream cipher, and point out that it is any grade, 3-order correlation immune and 3-grade, 4-order correlation immune. And it is proved out that given a block of output sequence before time /, the correlation property and conditional correlation property between the output and input after time t are same. The formulas for computing two kinds of conditional correlation coefficients and an iterative fomula for computing the integral correlation coefficient of general combiners with memory are presented, with which the changing trend of integral correlation property and maximal correlation property of the Bluetooth generator are analyzed.And a Fast Correlation Attack Algorithm is introduced in this paper. With this algorithm and the results of correlation properties analysis mentioned above we make an attack on Bluetooth key stream generator. And this attacking method can reconstructs the 128-bit secret key with complexity about 2~64.2 given an output key stream segment of length 2~34.311 and 2~31.311 memory. |
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