A statistical estimation algorithm of the weight distribution of a linear code is shown, based on using its generator matrix as a compression function on random bit strings.
@cite_3: The best known cryptanalytic attack on McEliece's public-key cryptosystem based on algebraic coding theory is to repeatedly select k bits at random from an n-bit ciphertext vector, which is corrupted by at most t errors, in hope that none of the selected k bits are in error until the cryptanalyst recovers the correct message. The method of determining whether the recovered message is the correct one has not been throughly investigated. In this paper, we suggest a systematic method of checking, and describe a generalized version of the cryptanalytic attack which reduces the work factor sigdicantly (factor of 211 for the commonly used example of n=1024 Goppa code case). Some more improvements are also given. We also note that these cryptanalytic algorithms can be viewed as generalized probabilistic decoding algorithms for any linear error correcting codes.
Lee and Brickell observed @cite_3 that the best cryptanalytic attack consisted in choosing a set @math of @math random elements of @math , selecting the corresponding columns of @math as a @math matrix @math , and computing @math . If @math , this procedure returns the correct @math . They also observe that not only is it costly to invert a random @math matrix, there is also a cost associated with checking that the result is correct: if @math , then @math . One would therefore also have to compute @math to be able to claim that @math .