Results 1 
7 of
7
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 ..."
Abstract

Cited by 25 (6 self)
 Add to MetaCart
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.
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 ..."
Abstract

Cited by 24 (6 self)
 Add to MetaCart
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.
New Classes of Almost Bent and Almost Perfect Nonlinear Functions
 IEEE Trans. Inform. Theory
, 2006
"... We construct infinite classes of almost bent and almost perfect nonlinear polynomials, which are affinely inequivalent to any sum of a power function and an affine function. ..."
Abstract

Cited by 24 (10 self)
 Add to MetaCart
We construct infinite classes of almost bent and almost perfect nonlinear polynomials, which are affinely inequivalent to any sum of a power function and an affine function.
Degree of composition of highly nonlinear functions and applications to higher order differential cryptanalysis
 EUROCRYPT 2002
, 2002
"... To improve the security of iterated block ciphers, the resistance against linear cryptanalysis has been formulated in terms of provable security which suggests the use of highly nonlinear functions as round functions. Here, we show that some properties of such functions enable to find a new upper bo ..."
Abstract

Cited by 21 (6 self)
 Add to MetaCart
To improve the security of iterated block ciphers, the resistance against linear cryptanalysis has been formulated in terms of provable security which suggests the use of highly nonlinear functions as round functions. Here, we show that some properties of such functions enable to find a new upper bound for the degree of the product of its Boolean components. Such an improvement holds when all values occurring in the Walsh spectrum of the round function are divisible by a high power of 2. This result leads to a higher order differential attack on any 5round Feistel ciphers using an almost bent substitution function. We also show that the use of such a function is precisely the origin of the weakness of a reduced version of MISTY1 reported in [23, 1].
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 ..."
Abstract

Cited by 12 (3 self)
 Add to MetaCart
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. Submitted, available at http://eprint.iacr.org/2007/098
"... A method for constructing differentially 4uniform quadratic hexanomials has been recently introduced by J. Dillon. We give various generalizations of this method and we deduce the constructions of new infinite classes of almost perfect nonlinear quadratic trinomials and hexanomials from F 2 2m to F ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
A method for constructing differentially 4uniform quadratic hexanomials has been recently introduced by J. Dillon. We give various generalizations of this method and we deduce the constructions of new infinite classes of almost perfect nonlinear quadratic trinomials and hexanomials from F 2 2m to F 2 2m. We check for m = 3 that some of these functions are CCZinequivalent to power functions.
Cryptographic Functions and Design Criteria for Block Ciphers
"... Abstract. Most lastround attacks on iterated block ciphers provide some design criteria for the round function. Here, we focus on the links between the underlying properties. Most notably, we investigate the relations between the functions which oppose a high resistance to linear cryptanalysis and ..."
Abstract
 Add to MetaCart
Abstract. Most lastround attacks on iterated block ciphers provide some design criteria for the round function. Here, we focus on the links between the underlying properties. Most notably, we investigate the relations between the functions which oppose a high resistance to linear cryptanalysis and to differential cryptanalysis. 1