Linear Statistical Weakness of Alleged RC4 Keystream Generator

A keystream generator known as RC4 is analyzed by the linear model approach. It is shown that the second binary derivative of the least significant bit output sequence is correlated to 1 with the correlation coefficient close to 15 · 2−3n where n is the variable word size of RC4. The output sequence length required for the linear statistical weakness detection may be realistic in high speed applications if n ≤ 8. The result can be used to distinguish RC4 from other keystream generators and to determine the unknown parameter n, as well as for the plaintext uncertainty reduction if n is small.