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Partitioning CCZ classes into EA classes
1. | RMIT University, G.P.O. Box 2476, Melbourne, VIC 3001, Australia, Australia |
References:
[1] |
B. Aslan, M. T. Sakalli and E. Bulus, Classifying 8-bit to 8-bit S-boxes based on power mappings from the point of DDT and LAT distributions, in "Proc. WAIFI 2008'' (eds. J. von zur Gathen), Springer, Berlin, (2008), 123-133. |
[2] |
C. Bracken, E. Byrne, G. McGuire and G. Nebe, On the equivalence of quadratic APN functions, Des. Codes Cryptogr., 61 (2011), 261-272.
doi: 10.1007/s10623-010-9475-8. |
[3] |
M. Brinkmann and G. Leander, On the classification of APN functions up to dimension 5, Des. Codes Cryptogr., 49 (2008), 273-288.
doi: 10.1007/s10623-008-9194-6. |
[4] |
K. A. Browning, J. F. Dillon, R. E. Kibler and M. T. McQuistan, APN polynomials and related codes, J. Comb. Inf. Syst. Sci., 34 (2009), 135-159. |
[5] |
L. Budaghyan, C. Carlet and A. Pott, New classes of almost bent and almost perfect nonlinear polynomials, IEEE Trans. Inform. Theory, 52 (2006), 1141-1152.
doi: 10.1109/TIT.2005.864481. |
[6] |
C. Carlet, P. Charpin and V. Zinoviev, Codes, bent functions and permutations suitable for DES-like cryptosystems, Des. Codes Cryptogr., 15 (1998), 125-156.
doi: 10.1023/A:1008344232130. |
[7] |
R. East, "Nonlinear Functions over Finite Fields,'' Honours thesis, RMIT University, 2008, (unpublished). |
[8] |
Y. Edel, APN functions and dual hyperovals, in "NATO Advanced Research Workshop,'' Veliko Tarnovo, Bulgaria, (2008). |
[9] | |
[10] |
Y. Edel, G. Kyureghyan and A. Pott, A new APN function which is not equivalent to a power mapping, IEEE Trans. Inform. Theory, 52 (2006), 744-747.
doi: 10.1109/TIT.2005.862128. |
[11] |
Y. Edel and A. Pott, A new almost perfect nonlinear function which is not quadratic, Adv. Math. Commun., 3 (2009), 59-81.
doi: 10.3934/amc.2009.3.59. |
[12] |
K. J. Horadam, "Hadamard Matrices and their Applications,'' Princeton University Press, Princeton, 2007. |
[13] |
K. J. Horadam, Relative difference sets, graphs and inequivalence of functions between groups, J. Combin. Des., 18 (2010), 260-273. |
[14] |
K. J. Horadam, Equivalence classes of functions between finite groups, J. Algebr. Comb., (2012), to appear, DOI 10.1007/s10801-011-0310-8.
doi: 10.1007/s10801-011-0310-8. |
[15] |
K. J. Horadam and D. G. Farmer, Bundles, presemifields and nonlinear functions, Des. Codes Cryptogr., 49 (2008), 79-94.
doi: 10.1007/s10623-008-9172-z. |
[16] |
G. M. Kyureghyan and A. Pott, Some theorems on planar mappings, in "Proc. WAIFI 2008'' (eds. J. von zur Gathen et al), Springer, Berlin, (2008), 117-122. |
[17] |
K. Nyberg, Differentially uniform mappings for cryptography, in "EUROCRYPT-93,'' Springer, New York, (1994), 55-64. |
show all references
References:
[1] |
B. Aslan, M. T. Sakalli and E. Bulus, Classifying 8-bit to 8-bit S-boxes based on power mappings from the point of DDT and LAT distributions, in "Proc. WAIFI 2008'' (eds. J. von zur Gathen), Springer, Berlin, (2008), 123-133. |
[2] |
C. Bracken, E. Byrne, G. McGuire and G. Nebe, On the equivalence of quadratic APN functions, Des. Codes Cryptogr., 61 (2011), 261-272.
doi: 10.1007/s10623-010-9475-8. |
[3] |
M. Brinkmann and G. Leander, On the classification of APN functions up to dimension 5, Des. Codes Cryptogr., 49 (2008), 273-288.
doi: 10.1007/s10623-008-9194-6. |
[4] |
K. A. Browning, J. F. Dillon, R. E. Kibler and M. T. McQuistan, APN polynomials and related codes, J. Comb. Inf. Syst. Sci., 34 (2009), 135-159. |
[5] |
L. Budaghyan, C. Carlet and A. Pott, New classes of almost bent and almost perfect nonlinear polynomials, IEEE Trans. Inform. Theory, 52 (2006), 1141-1152.
doi: 10.1109/TIT.2005.864481. |
[6] |
C. Carlet, P. Charpin and V. Zinoviev, Codes, bent functions and permutations suitable for DES-like cryptosystems, Des. Codes Cryptogr., 15 (1998), 125-156.
doi: 10.1023/A:1008344232130. |
[7] |
R. East, "Nonlinear Functions over Finite Fields,'' Honours thesis, RMIT University, 2008, (unpublished). |
[8] |
Y. Edel, APN functions and dual hyperovals, in "NATO Advanced Research Workshop,'' Veliko Tarnovo, Bulgaria, (2008). |
[9] | |
[10] |
Y. Edel, G. Kyureghyan and A. Pott, A new APN function which is not equivalent to a power mapping, IEEE Trans. Inform. Theory, 52 (2006), 744-747.
doi: 10.1109/TIT.2005.862128. |
[11] |
Y. Edel and A. Pott, A new almost perfect nonlinear function which is not quadratic, Adv. Math. Commun., 3 (2009), 59-81.
doi: 10.3934/amc.2009.3.59. |
[12] |
K. J. Horadam, "Hadamard Matrices and their Applications,'' Princeton University Press, Princeton, 2007. |
[13] |
K. J. Horadam, Relative difference sets, graphs and inequivalence of functions between groups, J. Combin. Des., 18 (2010), 260-273. |
[14] |
K. J. Horadam, Equivalence classes of functions between finite groups, J. Algebr. Comb., (2012), to appear, DOI 10.1007/s10801-011-0310-8.
doi: 10.1007/s10801-011-0310-8. |
[15] |
K. J. Horadam and D. G. Farmer, Bundles, presemifields and nonlinear functions, Des. Codes Cryptogr., 49 (2008), 79-94.
doi: 10.1007/s10623-008-9172-z. |
[16] |
G. M. Kyureghyan and A. Pott, Some theorems on planar mappings, in "Proc. WAIFI 2008'' (eds. J. von zur Gathen et al), Springer, Berlin, (2008), 117-122. |
[17] |
K. Nyberg, Differentially uniform mappings for cryptography, in "EUROCRYPT-93,'' Springer, New York, (1994), 55-64. |
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