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26
A class of quadratic APN binomials inequivalent to power functions
, 2006
"... We exhibit an infinite class of almost perfect nonlinear quadratic binomials from F2n to F2n (n ≥ 12, n divisible by 3 but not by 9). We prove that these functions are EAinequivalent to any power function and that they are CCZinequivalent to any Gold function and to any Kasami function. It means t ..."
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Cited by 27 (7 self)
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We exhibit an infinite class of almost perfect nonlinear quadratic binomials from F2n to F2n (n ≥ 12, n divisible by 3 but not by 9). We prove that these functions are EAinequivalent to any power function and that they are CCZinequivalent to any Gold function and to any Kasami function. It means that for n even they are CCZinequivalent to any known APN function, and in particular for n = 12,24, they are therefore CCZinequivalent to any power function. It is also proven that, except in particular cases, the Gold mappings are CCZinequivalent to the Kasami and Welch functions.
New Classes of Almost Bent and Almost Perfect Nonlinear Polynomials
 Proceedings of the Workshop on Coding and Cryptography 2005
, 2005
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An infinite class of quadratic APN functions which are Not Equivalent To power mappings
 PROCEEDINGS OF THE IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY 2006
, 2005
"... We exhibit an infinite class of almost perfect nonlinear quadratic polynomials from F 2 n to F 2 n (n 12, n divisible by 3 but not by 9). We prove that these functions are EAinequivalent to any power function. In the forthcoming version of the present paper we will proof that these function ..."
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Cited by 25 (7 self)
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We exhibit an infinite class of almost perfect nonlinear quadratic polynomials from F 2 n to F 2 n (n 12, n divisible by 3 but not by 9). We prove that these functions are EAinequivalent to any power function. In the forthcoming version of the present paper we will proof that these functions are CCZinequivalent to any Gold function and to any Kasami function, in particular for n = 12, they are therefore CCZinequivalent to power functions.
Another class of quadratic APN binomials over $\F_{2^n}$: the case $n$ divisible by 4
 IACR EPRINT
, 2006
"... We exhibit an infinite class of almost perfect nonlinear quadratic binomials from $\mathbb{F}_{2^{n}}$ to $\mathbb{F}_{2^{n}}$ with $n=4k$ and $k$ odd. We prove that these functions are CCZinequivalent to known APN power functions when $k\ne 1$. In particular it means that for $n=12,20,28$, they ar ..."
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Cited by 13 (4 self)
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We exhibit an infinite class of almost perfect nonlinear quadratic binomials from $\mathbb{F}_{2^{n}}$ to $\mathbb{F}_{2^{n}}$ with $n=4k$ and $k$ odd. We prove that these functions are CCZinequivalent to known APN power functions when $k\ne 1$. In particular it means that for $n=12,20,28$, they are CCZinequivalent to any power function.
Classes of Quadratic APN Trinomials and Hexanomials and Related Structures
 IEEE Trans. Inform. Theory
, 2007
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On Plateaued Functions and Their Constructions
 in Fast Software Encryption FSE ′ 2003, 10th International Workshop (Lund, Sweden. February 24–26, 2003). Proceedings (Springer
, 2003
"... Abstract. We use the notion of covering sequence, introduced by C. Carlet and Y. Tarannikov, to give a simple characterization of bent functions. We extend it into a characterization of plateaued functions (that is bent and threevalued functions). After recalling why the class of plateaued function ..."
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Cited by 6 (0 self)
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Abstract. We use the notion of covering sequence, introduced by C. Carlet and Y. Tarannikov, to give a simple characterization of bent functions. We extend it into a characterization of plateaued functions (that is bent and threevalued functions). After recalling why the class of plateaued functions provides good candidates to be used in cryptosystems, we study the known families of plateaued functions and their drawbacks. We show in particular that the class given as new by Zhang and Zheng is in fact a subclass of MaioranaMcFarland’s class. We introduce a new class of plateaued functions and prove its good cryptographic properties.
Determining the Nonlinearity of a New Family of APN Functions
"... Abstract. We compute the Walsh spectrum and hence the nonlinearity of a new family of quadratic multiterm APN functions. We show that the distribution of values in the Walsh spectrum of these functions is the same as the Gold function. ..."
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Cited by 5 (2 self)
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Abstract. We compute the Walsh spectrum and hence the nonlinearity of a new family of quadratic multiterm APN functions. We show that the distribution of values in the Walsh spectrum of these functions is the same as the Gold function.
On Certain 3Weight Cyclic Codes Having Symmetric Weights and a Conjecture of Helleseth
 Sequences and their Applications  Proceedings of SETA'01
, 2001
"... When the binary cyclic code of length 2 m 1 with check polynomial m 1 (x)m t (x) has exactly three nonzero weights, we discuss the symmetry of the two outer weights about the middle weight. This question is connected to a conjecture of Helleseth, that the crosscorrelation function of two msequen ..."
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Cited by 2 (1 self)
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When the binary cyclic code of length 2 m 1 with check polynomial m 1 (x)m t (x) has exactly three nonzero weights, we discuss the symmetry of the two outer weights about the middle weight. This question is connected to a conjecture of Helleseth, that the crosscorrelation function of two msequences of length 2 m 1 must take at least four values when m is a power of 2. We present partial results on this problem, and some equivalent conditions to the symmetry of the weights. 1