New correlation attacks on stream ciphers

We introduce two new correlation attacks on stream ciphers that make use of non-linearly combined linear feedback shift-registers (LFSRs). The first attack utilises the well-known Lempel-Ziv complexity measure for binary sequences. The second attack is based on the binary derivative, applied in conjunction with the distribution of runs in a binary sequence. Both attacks make use of ciphertext only, and give very good results. They are able to recover the unknown (secret) initial state of an internal LFSR, even when only a very small correlation of q=0.52 occurs between the observed ciphertext and the output of an internal LFSR, and approximately 60000 ciphertext bits are required for attacks to succeed. The computational complexity and memory requirements of the binary derivative attack are substantially lower than for the Lempel-Ziv attack, making It feasible to attack stream ciphers with LFSR-lengths of approximately 40 to 50 bits.