On the complexity of some cryptographic problems based on the general decoding problem

A new probabilistic algorithm for decoding one received word from a set of many given received words, into a codeword such that the Hamming distance between the received word and the codeword is at most t, is proposed. The new algorithm is applicable to several cryptographic problems, such as the Stern (1989, 1994) identification scheme, the McEliece (1978) public-key cryptosystem, and in correlation attacks on stream ciphers. When applicable, it runs significantly faster than previous algorithms used for attacks on these cryptosystems.