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A few more quadratic APN functions. (English) Zbl 1282.11162
Summary: We present an infinite family of quadrinomial APN functions on \(\mathrm{GF}(2^n)\) where \(n\) is divisible by 3 but not 9. The family contains inequivalent functions, obtained by setting some coefficients equal to 0. We also discuss the inequivalence proof (by computation) which shows that these functions are new.

11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
94A60 Cryptography
Full Text: DOI arXiv
[1] Bracken, C., Byrne, E., Markin, N., McGuire, G.: New families of quadratic almost perfect nonlinear trinomials and multinomials. Finite Fields Their Appl. 14(3), 703–714 (2008) · Zbl 1153.11058 · doi:10.1016/j.ffa.2007.11.002
[2] Bracken, C., Byrne, E., Markin, N., McGuire, G.: Determining the nonlinearity of a new family of APN functions. In: Boztas, S., Lu, H.-F. (eds.) Proc. AAECC-17 Conference. LNCS, vol. 4851, pp. 72–79 (2007) · Zbl 1195.94048
[3] Budaghyan, L., Carlet, C.: Classes of quadratic APN trinomials, hexanomials and related structures. IEEE Trans. Inf. Theory 54(5), 2354–2357 (2008) · Zbl 1177.94134 · doi:10.1109/TIT.2008.920246
[4] Budaghyan, L., Carlet, C., Felke, P., Leander, G.: An infinite class of quadratic APN functions which are not equivalent to power mappings. In: Proceedings of ISIT 2006, Seattle, USA (2006)
[5] Budaghyan, L., Carlet, C., Pott, A.: New constructions of almost bent and almost perfect nonlinear functions. IEEE Trans. Inf. Theory 52(3), 1141–1152 (2006) · Zbl 1177.94136 · doi:10.1109/TIT.2005.864481
[6] Budaghyan, L., Carlet, C., Leander, G.: Another class of quadratic APN binomials over $F_{2\^n}$ : the case n divisible by 4. In: Proceedings of WCC 07, pp. 49–58. Versailles, France (2007)
[7] Budaghyan, L., Carlet, C., Leander, G.: Two classes of quadratic APN binomials inequivalent to power functions. IEEE Trans. Inf. Theory 54(9), 4218–4229 (2008) · Zbl 1177.94135 · doi:10.1109/TIT.2008.928275
[8] Budaghyan, L., Carlet, C., Leander, G.: Constructing new APN functions from known ones. Finite Fields Their Appl. 15(2), 150–159 (2009) · Zbl 1184.94228 · doi:10.1016/j.ffa.2008.10.001
[9] Carlet, C., Charpin, P., Zinoviev, V.: Codes, bent functions and permutations suitable for DES-like cryptosystems. Designs Codes Cryptogr. 15(2), 125–156 (1998) · Zbl 0938.94011 · doi:10.1023/A:1008344232130
[10] Dillon, J.: Slides from talk given at Polynomials over Finite Fields and Applications. Held at Banff International Research Station (2006)
[11] Edel, Y., Kyureghyan, G., Pott, A.: A new APN function which is not equivalent to a power mapping. IEEE Trans. Inf. Theory 52(2), 744–747 (2006) · Zbl 1246.11185 · doi:10.1109/TIT.2005.862128
[12] Feulner, T.: APN functions, available online at http://www.algorithm.uni-bayreuth.de/en/research/Coding_Theory/APN_Functions/index.html
[13] Nyberg, K.: Differentially uniform mappings for cryptography. Advances in Cryptology-EUROCRYPT 93. Lecture Notes in Computer Science, pp. 55–64. Springer-Verlag (1994) · Zbl 0951.94510
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