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It has been shown that simple substitution ciphers can be solved using statistical methods such as probabilistic relaxation. However, the utility of such solutions has been limited by their inability to cope with noise encountered in practical applications. We propose a new solution to substitution deciphering based on hidden Markov models. We show that our algorithm is more accurate than relaxation and much more robust in the presence of noise, making it useful for applications in compressed document processing. Recovering character interpretations from the sequence of cluster identifiers in a symbolically compressed document can be treated as a cipher problem. Although a significant amount of noise is present in the cluster sequence, enough information can be recovered with a robust deciphering algorithm to accomplish certain document analysis tasks. The feasibility of this approach is demonstrated in a multilingual document duplicate detection system.