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Input-trees of finite automata and application to cryptanalysis

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Abstract

In this paper, weights of output set and of input set for finite automata are discussed. For a weakly invertible finite automaton, we prove that for states with minimal output weight, the distribution of input sets is uniform. Then for a kind of compound finite automata, we give weights of output set and of input set explicitly, and a characterization of their input-trees. For finite automaton public key cryptosystems, of which automata in public keys belong to such a kind of compound finite automata, we evaluate search amounts of exhaust search algorithms in average case and in worse case for both encryption and signature, and successful probabilities of stochastic search algorithms for both encryption and signature. In addition, a result on mutual invertibility of finite automata is also given.

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References

  1. Diffie W, Hellman M. New directions in cryptography.IEEE Trans. Information Theory, 1976, IT-22: 644–654.

    Article  MATH  MathSciNet  Google Scholar 

  2. Rivest R, Shamir A, Adleman L. A method for obtaining digital signatures and public-key cryptosystems.Communications of the ACM, 1978, 21: 120–126.

    Article  MATH  MathSciNet  Google Scholar 

  3. Merkle R C, Hellman M E. Hiding information and signatures in trapdoor knapsacks.IEEE Trans. Information Theory, 1978, 24: 525–530.

    Article  Google Scholar 

  4. McEliece R J. A public-key cryptosystem based on algebraic coding theory. DSN Progress Report, 1978, pp. 42–44.

  5. ElGamal T. A public key cryptosystem and a signature scheme based on discrete logarithms.IEEE Trans. Information Theory, 1985, IT-31: 469–472.

    Article  MATH  MathSciNet  Google Scholar 

  6. Koblitz N. Elliptic curve cryptosystems.Mathematics of Computation, 1987, 48: 203–209.

    Article  MATH  MathSciNet  Google Scholar 

  7. Salomaa A. Public-Key Cryptography. Springer-Verlag, Berlin, 1990.

    MATH  Google Scholar 

  8. Smith P. LUC public-key encryption.Dr. Dobb’s Journal, 1993, 18: 44–49.

    Google Scholar 

  9. Tao R, Chen S. A finite automaton public key cryptosystem and digital signatures.Chinese J. of Computers, 1985, 8: 401–409 (in Chinese).

    MathSciNet  Google Scholar 

  10. Tao R, Chen S. Two varieties of finite automaton public key cryptosystem and digital signatures.J. of Computer Science and Technology, 1986, 1: 9–18.

    Article  MATH  MathSciNet  Google Scholar 

  11. Tao R, Chen S, Chen X. FAPKC3: A new finite automaton public key cryptosystem.J. of Computer Science and Technology, 1997, 12: 289–305.

    Article  MathSciNet  Google Scholar 

  12. Tao R, Chen S. A variant of the public key cryptosystem FAPKC3.J. of Network and Computer Applications, 1997, 20: 283–303.

    Article  Google Scholar 

  13. Tao R, Chen S. A note on the public key cryptosystem FAPKC3. InAdvances in Cryptology—CHI-NACRYPT’98, Science Press, Beijing, 1998.

    Google Scholar 

  14. Tao R, Chen S. The generalization of public key cryptosystem FAPKC4.Chinese Science Bulletin, 1999, 44: 784–790.

    Article  MATH  MathSciNet  Google Scholar 

  15. Tao R, Chen S. On finite automaton public key cryptosystem.Theoretical Computer Science, 1999, 226: 143–172.

    Article  MATH  MathSciNet  Google Scholar 

  16. Dai D, Wu K, Zhang H. Cryptanalysis on a finite automaton public key cryptosystem.Science in China, Ser. A, 1996, 39: 27–36.

    MATH  MathSciNet  Google Scholar 

  17. Tao R. On invertibility of some compound finite automata. Technical Report No. ISCAS-LCS-95-06, Laboratory for Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, June 1995.

    Google Scholar 

  18. Bao F, Igarashi Y. Break finite automata public key cryptosystem. InICALP’95, Automata, Languages and Programming, LNCS 944, Springer-Verlag, Berlin, 1995, pp. 147–158.

    Google Scholar 

  19. Tao R. OnR a R b transformation and inversion of compound finite automata. Technical Report No. ISCAS-LCS-95-10, Laboratory for Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, Sept. 1995.

    Google Scholar 

  20. Wang H. TheR a R b representation of a class of the reduced echelon matrices.J. of Software, 1997, 8: 772–780. (in Chinese)

    Google Scholar 

  21. Tao R, Feng P. On relations betweenR a R b transformation and canonical diagonal form of λ-matrix.Science in China, Ser. E, 1997, 40: 258–268.

    Article  MATH  MathSciNet  Google Scholar 

  22. Tao R. Several specific factorizations of matrix polynomials.Chinese J. of Computers, 1999, 22: 1–10. (in Chinese)

    Google Scholar 

  23. Qin Z, Zhang H. Cryptanalysis of finite automaton public key cryptosystems. InAdvances in Cryptology— CHINACRYPT’96, Science Press, Beijing, 1996, pp. 75–86. (in Chinese)

    Google Scholar 

  24. Dai Z. A class of separable nonlinear finite automata—and an analysis of a certain typed FA based public key encryption and signature scheme. InAdvances in Cryptology—CHINACRYPT’96, Science Press, Beijing, 1996, pp. 87–94. (in Chinese)

    Google Scholar 

  25. Bao F. Increasing ranks of linear finite automata and complexity of FA public key cryptosystem.Science in China, Ser. A, 1994, 37: 504–512.

    MATH  Google Scholar 

  26. Bao F, Igarashi Y. A randomized algorithm to finite automata public key cryptosystem. InProc. ISACC’94, LNCS 834, Springer-Verlag, Berlin, 1994, pp. 678–686.

    Google Scholar 

  27. Tao R. Analyzing several search attacks on FAPKC1. Unpublished Manuscript, 1994. (in Chinese)

  28. Qin Z, Zhang H. Enumeration of sequences in finite automata with application to cryptanalysis. InAdvances in Cryptology—CHINACRYPT’94, Science Press, Beijing, 1994, pp. 112–119. (in Chinese)

    Google Scholar 

  29. Qin Z, Zhang H. The attack algorithmAtM to finite automation public key cryptosystems.Chinese J. of Computers, 1995, 18: 199–204. (in Chinese)

    Google Scholar 

  30. Tao R, Chen S. On input-trees of finite automata. InAdvances in Cryptology—CHINACRYPT’94, Science Press, Beijing, 1994, pp.65–74. (in Chinese)

    Google Scholar 

  31. Bao F. Limited error-propagation, self-synchronization and finite input memory FSMa as weak invverses. InAdvances in Chinese Computer Science, World Scientific, Singapore, 1991, 3: 1–24.

    Google Scholar 

  32. Bao F. Composition and decomposition of weakly invertible finite automata.Science in China, Chinese Edition, 1993, 23: 759–766.

    Google Scholar 

  33. Raney G N. Sequential functions.J. of the Association for Computing Machinery, 1958, 5: 177–180.

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Laboratory for Computer Science, Institute of Software, Chinese Academy of Sciences, 100080, Beijing, P.R. China

    Tao Renji & Chen Shihua

Authors
  1. Tao Renji
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  2. Chen Shihua
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Corresponding author

Correspondence to Tao Renji.

Additional information

Supported by the National Natural Science Foundation of China under grant No. 69773022 and the NKBRSF of China.

For the biographies ofTAO Renji andCHEN Shihua, please refer to p.26 of No.1, Vol.15 of this journal.

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Tao, R., Chen, S. Input-trees of finite automata and application to cryptanalysis. J. Comput. Sci. & Technol. 15, 305–325 (2000). https://doi.org/10.1007/BF02948867

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  • DOI: https://doi.org/10.1007/BF02948867

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