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In this paper, cryptanalysis is performed on the GST stream cipher, a cipher which uses cascaded 2-bit s-boxes. The results indicate that the output probabilities for single outputs, digraphs, and trigraphs asymptotically approach those of a random sequence generator. The cipher output was also subjected to a number of statistical tests for random sequences, including the Chi-square test, Lempel-Ziv test, and Maurer's Universal test. The output keystream passed all these randomness tests. A cryptographic attack was also mounted against the cipher, but results show that it requires more work than exhaustive key search. All of these results increase our confidence in the security of the cipher.