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Codes, Bent Functions and Permutations Suitable For DES-like Cryptosystems

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References

  1. 1.

    L.A. Bassalygo, G.V. Zaitsev, and V.A. Zinoviev, Uniformly packed codes, Problems of Information Transmission, Vol. 10, No1 (1974) pp. 9–14.

    Google Scholar 

  2. 2.

    L.A. Bassalygo and V.A. Zinoviev, Remark on uniformly packed codes, Problems of Information Transmission, Vol. 13, No3 (1977) pp. 22–25.

    Google Scholar 

  3. 3.

    E. Biham and A. Shamir, Differential cryptanalysis of DES-like cryptosystems, Journal of Cryptology, Vol. 4, No.1 (1991) pp. 3–72.

    Google Scholar 

  4. 4.

    A.E. Brouwer and L.M.G.M. Tolhuizen, A Sharpening of the Johnson Bound for Binary Linear Codes, Designs, Codes and Cryptography, Vol. 3, No.1 (1993) pp. 95–98.

    Google Scholar 

  5. 5.

    A.R. Calderbank, G. McGuire, B. Poonen and M. Rubinstein, On a conjecture of Helleseth regarding pairs of binary m-sequences, IEEE Transactions on Information Theory, Vol. 42 (1996) pp. 988–990.

    Article  Google Scholar 

  6. 6.

    P. Camion and A. Canteaut, Construction of t-resilient functions over a finite alphabet, Advances in Cryptology, EUROCRYPT'96, Lecture Notes in Computer Science, Springer-Verlag, New York, 1070 (1996) pp 283–293.

    Google Scholar 

  7. 7.

    C. Carlet, Partially-bent functions, Designs Codes and Cryptography, Vol. 3 (1993) pp. 135–145.

    Google Scholar 

  8. 8.

    C. Carlet, Two new classes of bent functions, Advances in Cryptology, EUROCRYPT'93, Lecture Notes in Computer Science, Springer-Verlag, New York, 765 (1994) pp. 77–101.

    Google Scholar 

  9. 9.

    T. Cusick and H. Dobbertin, Some new 3-valued crosscorrelation functions of binary m-sequences, IEEE Transactions on Information Theory, Vol. 42 (1996) pp. 1238–1240.

    Article  Google Scholar 

  10. 10.

    F. Chabaud and S. Vaudenay, Links between differential and linear cryptanalysis, Advances in Cryptology, EUROCRYPT'94, Lecture Notes in Computer Science, Springer-Verlag, NewYork, 950 (1995) pp. 356–365.

    Google Scholar 

  11. 11.

    P. Charpin, A. Tietäväinen and V. Zinoviev, On binary cyclic codes with d = 3, Problems of Information Transmission, Vol. 33, No.3 (1997).

  12. 12.

    P. Delsarte, Four Fundamental parameters of a code and their combinatorial significance, Inf. and Contr. Vol. 23 (1973) pp. 407–438.

    Google Scholar 

  13. 13.

    J.F. Dillon, Elementary Hadamard Difference Sets, Ph. D. Thesis, Univ. of Maryland (1974).

  14. 14.

    H. Dobbertin, Construction of bent functions and balanced Boolean functions with high nonlinearity, Fast Software Encryption: Proceedings of the 1994 Leuven Workshop on Cryptographic Algorithms, Lecture Notes in Computer Science, Springer-Verlag, New York, 1008 (1995) pp. 61–74.

    Google Scholar 

  15. 15.

    H. Dobbertin, One to one highly nonlinear power functions on GF(2n), preprint.

  16. 16.

    H. Dobbertin, Almost perfect nonlinear power functions on GF(2n), preprint.

  17. 17.

    H. Dobbertin, Another proof of Kasami's theorem, preprint.

  18. 18.

    S.M. Dodunekov and V.A. Zinoviev, V.A. A note on Preparata Codes, Proceedings of Sixth Intern. Symp. on Information Theory, Moscow-Tashkent Part 2 (1984) pp. 78–80.

  19. 19.

    J.M. Goethals and S.L. Snover, Nearly perfect codes, Discrete Mathematics, Vol. 3 (1972) pp. 64–88.

    Article  Google Scholar 

  20. 20.

    J.M. Goethals and H.C.A. Van Tilborg, Uniformly packed codes, Philips Res. Repts Vol. 30 (1975) pp. 9–36.

    Google Scholar 

  21. 21.

    T. Helleseth and P.V. Kumar, Sequences with low correlation, Handbook of coding theory (V. S. Pless and W. C. Huffman, eds., R. A. Brualdi, asst. ed.), to appear.

  22. 22.

    H. Janwa, G. McGuire and R.M. Wilson Double-error-correcting codes and absolutely irreductible polynomials over GF(2), Journal of Algebra, Vol. 178 (1995) pp. 665–676.

    Article  Google Scholar 

  23. 23.

    T. Kasami, Weight distributions of Bose-Chaudhuri-Hocquenghem Codes, Combinatorial Math. and Applications (R.C. Bose and T.A. Dowlings, eds.), Univ. of North Carolina Press, Chapel Hill, NC (1969).

    Google Scholar 

  24. 24.

    T. Kasami, The weight enumerators for several classes of subcodes of the 2nd order binary Reed-Muller codes, Information and Control Vol. 18 (1971) pp. 369–394.

    Google Scholar 

  25. 25.

    G. Lachaud and J. Wolfmann, The weights of the orthogonals of the extended quadratic binary Goppa codes, IEEE Transactions on Information Theory, Vol. 36 (1990) pp. 686–692.

    Article  Google Scholar 

  26. 26.

    R. Lidl and H. Niederreiter, Finite Fields, Encyclopedia of Mathematics and its Applications, Vol. 20, Cambridge University Press, Cambridge (1983).

    Google Scholar 

  27. 27.

    Y. Niho, Multi-valued cross-correlation functions between two maximal linear recursive sequences, Ph. D. Thesis, USCEE Rep. 409 (1972).

  28. 28.

    V. Pless, Power moment identities on weight distributions in error-correcting codes, Info. and Control, Vol. 6 (1963) pp. 147–152.

    Google Scholar 

  29. 29.

    F.J. Mac Williams and N.J. Sloane, The theory of error-correcting codes, Amsterdam, The Netherlands: North Holland (1977).

    Google Scholar 

  30. 30.

    M. Matsui, Linear cryptanalysis method for DES cipher, Advances in Cryptography, EUROCRYPT'93, Lecture Notes in Computer Science, Springer-Verlag, New York, 765 (1994) pp. 386–397.

    Google Scholar 

  31. 31.

    K. Nyberg, Perfect non-linear S-boxes, Advances in Cryptology, EUROCRYPT' 91, Lecture Notes in Computer Science, Springer-Verlag, New York, 547 (1992) pp. 378–386.

    Google Scholar 

  32. 32.

    K. Nyberg, Differentially uniform mappings for cryptography, Advances in Cryptography, EUROCRYPT' 93, Lecture Notes in Computer Science, Springer-Verlag, New York, 765 (1994) pp. 55–64.

    Google Scholar 

  33. 33.

    O.S. Rothaus, On Bent Functions, J. Comb. Theory, Vol. 20A (1976) pp. 300–305.

    Google Scholar 

  34. 34.

    N.V. Semakov, V.A. Zinoviev and G.V. Zaitsev, Uniformly packed codes, Problems of Information Transmission, Vol. 7, No1 (1971) pp. 38–50.

    Google Scholar 

  35. 35.

    V.M. Sidel'nikov, On the mutual correlation of sequences, Soviet Math. Dokl., Vol. 12 (1971) pp. 197–201

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Carlet, C., Charpin, P. & Zinoviev, V. Codes, Bent Functions and Permutations Suitable For DES-like Cryptosystems. Designs, Codes and Cryptography 15, 125–156 (1998). https://doi.org/10.1023/A:1008344232130

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  • almost perfect nonlinear
  • almost bent
  • bent
  • Boolean function
  • sequence
  • linear code
  • cyclic code