A Study on Parity Checks in Stream Cipher Correlation Attacks

Abstract

The commonest stream cipher system uses a keystream generator which consists of several LFSRs combined by a combining function. If there exists a measure of correlation between the output sequence of the keystream generator and an arbitrary LFSR, the initial state of the LFSR can be reconstructed by a correlation attack, that is, the partial key in the LFSR is determined. W. Meier and O. Staffelbach proposed a correlation attack method using parity check equations. In this paper, we discuss the algorithm and its constraints, and then propose some improvements: computing more low-weight parity check equations, accounting the precise number of relations of each digit, and solving the system of linear independent equations from digits instead of calculating the whole output sequence and the initial state of the LFSR from the relations among the digits.