zbMATH — the first resource for mathematics

New families of quadratic almost perfect nonlinear trinomials and multinomials. (English) Zbl 1153.11058
The authors present two families of APN functions on certain finite binary fields, one on fields of order \(2^{2k}\) for \(k\) not divisible by 2, and the other on fields of order \(2^{3k}\) for \(k\) not divisible by 3. The polynomials they present are specific in terms of their roots and number of terms. The polynomials in the first family have between three and \(k+2\) terms, the second family’s polynomials have three terms.

11T06 Polynomials over finite fields
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
94A60 Cryptography
Full Text: DOI
[1] Budaghyan, L.; Carlet, C., Classes of quadratic APN trinomials and hexanomials and related structures, preprint, available at · Zbl 1177.94134
[2] Budaghyan, L.; Carlet, C.; Felke, P.; Leander, G., An infinite class of quadratic APN functions which are not equivalent to power mappings, ()
[3] L. Budaghyan, C. Carlet, G. Leander, A class of quadratic APN binomials inequivalent to power functions, preprint · Zbl 1177.94135
[4] Budaghyan, L.; Carlet, C.; Pott, A., New constructions of almost bent and almost perfect nonlinear functions, IEEE trans. inform. theory, 52, 3, 1141-1152, (2006) · Zbl 1177.94136
[5] C. Carlet, Boolean functions for cryptography and error correcting codes, in: P. Hammer, Y. Crama (Eds.), Boolean Methods and Models, Cambridge Univ. Press, a chapter of the monography, in press · Zbl 1209.94035
[6] Carlet, C.; Charpin, P.; Zinoviev, V., Codes, bent functions and permutations suitable for DES-like cryptosystems, Des. codes cryptogr., 15, 2, 125-156, (1998) · Zbl 0938.94011
[7] J. Dillon, Slides from talk given at “Polynomials over Finite Fields and Applications,” held at Banff International Research station, November 2006
[8] Edel, Y.; Kyureghyan, G.; Pott, A., A new APN function which is not equivalent to a power mapping, IEEE trans. inform. theory, 52, 2, 744-747, (2006) · Zbl 1246.11185
[9] Nyberg, K., Differentially uniform mappings for cryptography, (), 55-64 · Zbl 0951.94510
[10] Rothaus, O., On bent functions, J. combin. theory ser. A, 20, 181-199, (1976) · Zbl 0336.12012
[11] J.F. Voloch, Symmetric cryptography and algebraic curves, preprint · Zbl 1151.14319
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.