Modeling Block Decoding Approaches for the Fast Correlation Attack

In this paper, a general framework which enables to compare previously proposed block decoding approaches for the fast correlation attack is developed. All attacks are based on decoding using a set of parity check sums of an underlying linear code. The purpose of this paper is twofold: 1) to provide a simple close form estimate about the number of check sums of a particular structure necessary for the corresponding attack to succeed; 2) to illustrate how such estimates are useful in minimizing the computational complexity of each attack considered, and consequently, in establishing a unified framework for comparison.