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Breaking Substitution Cyphers Using Stochastic Automata
February 1993 (vol. 15 no. 2)
pp. 185-192

Let Lambda be a finite plaintext alphabet and V be a cypher alphabet with the same cardinality as Lambda . In all one-to-one substitution cyphers, there exists the property that each element in V maps onto exactly one element in Lambda and vice versa. This mapping of V onto Lambda is represented by a function T*, which maps any v in V onto some lambda in Lambda (i.e., T*(v)= lambda ). The problem of learning the mapping of T* (or its inverse (T*)/sup -1/) by processing a sequence of cypher text is discussed. The fastest reported method to achieve this is a relaxation scheme that utilizes the statistical information contained in the unigrams and trigrams of the plaintext language. A new learning automaton solution to the problem called the cypher learning automaton (CLA) is given. The proposed scheme is fast, and the advantages of the scheme in terms of time and space requirements over the relaxation method have been listed. Simulation results comparing both cypher-breaking techniques are presented.

[1] G. Dewey,Relative Frequency of English Speech Sounds. Cambridge, MA: Harvard Univ. Press, 1923.
[2] P. A. V. Hall and G. R. Dowling, "Approximate string matching,"ACM Comput. Surveys, vol. 12, pp. 381-402, 1980.
[3] R. A. Kirby, "A product rule relaxation method,"Comput. Graphics Image Processing, vol. 13, no. 2, pp. 158-189, June 1980.
[4] S. Lakshmivarahan,Learning Algorithms Theory and Applications, New York: Springer-Verlag, 1981.
[5] K. S. Narendra, and M. A. L. Thathachar, "Learning automata--A survey,"IEEE Trans. Syst. Man Cybern., pp. 323-334, 1974.
[6] K. S. Narendra,Learning Automata: An Introduction. Englewood Cliffs, NJ: Prentice-Hall, 1989.
[7] B. J. Oommen and D. C. Y. Ma, "Deterministic learning automata solutions to the equipartitioning problem"IEEE Trans. Comput.vol. 37, no. 1, pp. 2-13, Jan. 1988.
[8] S. Peleg, "A new probabilistic relaxation scheme" inProc. IEEE Conf. Patt. Recogn. Image Processing(Chicago), Aug. 1979, pp. 337-343.
[9] S. Peleg and A. Rosenfeld, "Breaking substitution ciphers using a relaxation algorithm" inCommun. ACM, vol. 22, no. 11, pp. 598-605, Nov. 1979.
[10] M. L. Tsetlin,Automaton Theory and the Modeling of Biological Systems. New York and London, Academic, 1973.
[11] C. T. Yu, M. K. Siu, K. Lam, and F. Tai, "Adaptive clustering schemes: General framework," inProc. IEEE COMPSAC Conf., 1981, pp. 81-89.
[12] D.E. Denning,Cryptography and Data Security, Addison-Wesley Publishing Co., Reading, Mass., 1982.
[13] B. J. Oommen and J. Zgierski, "A learning automaton solution to breaking substitution cyphers," Tech. Rep. (SCS-TR-182), School Comput. Sci., Carleton Univ., Ottawa, Canada.

Index Terms:
substitution cyphers; stochastic automata; finite plaintext alphabet; cypher alphabet; cardinality; learning; relaxation scheme; statistical information; unigrams; trigrams; automaton solution; cypher learning automaton; cryptography; learning systems; relaxation theory; stochastic automata
Citation:
B.J. Oommen, J.R. Zgierski, "Breaking Substitution Cyphers Using Stochastic Automata," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 2, pp. 185-192, Feb. 1993, doi:10.1109/34.192492
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