Cryptanalysis of LU Decomposition-based Key Pre-distribution Scheme for Wireless Sensor Networks
S. J. Choi and H. Y. Youn proposed a key pre-distribution scheme for Wireless Sensor Networks based on LU decomposition of symmetric matrix, and later many researchers did works based on this scheme. Nevertheless, we find a mathematical relationship of L and U matrixes decomposed from symmetric matrix, by using which we can calculate one matrix from another regardless of their product -- the key matrix K. This relationship would profoundly harm the secure implementation of this decomposition scheme in the real world. In this paper, we first present and prove the mathematical theorem. Next we give samples to illustrate how to break the networks by using this theorem. Finally, we state the conclusion and some directions for improving the security of the key pre-distribution scheme.