[PDF] Top 20 Terapia génica mediante sistemas CRISPR-Cas
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Dickson polynomials, hyperelliptic curves and hyper-bent functions
... Hyper-bent functions were defined by Youssef and Gong [26] in 2001 and are both of theoretical and practical ...such functions are rare, and so interesting from a combinatorial point of view: ... See full document
67
A new class of hyper-bent functions and Kloosterman sums
... [12] J. Flori and S. Mesnager. Dickson polynomials, hyperelliptic curves and hyper-bent functions. To be published in the proceedings of SETA 2012, 2012. [13] J. Flori, S. ... See full document
6
Constructing hyper-bent functions from Boolean functions with the Walsh spectrum taking the same value twice
... Gong’s hyper-bent functions in terms of the number of rational points on certain hyperelliptic ...such hyper-bent functions with time complexity and space complexity O(r ... See full document
81
A note on hyper-bent functions via Dillon-like exponents
... In Section 2, we provide some background on the different objects we manipulate in the following sections, namely Boolean functions, Walsh-Hadamard transform, Dickson polynomials, exponential ... See full document
73
The graph of minimal distances of bent functions and its properties
... [15] Logachev O.A., Sal’nikov A.A., Yashenko V.V., Boolean functions in coding theory and cryptography, Moscow center of uninterrupted mathematical education, Moscow (2004). Translated in English by AMS in series ... See full document
26
Infinite-dimensional Lie algebras determined by the space of symmetric squares of hyperelliptic curves
... We construct Lie algebras of vector fields on universal bundles of symmetric squares of hyperelliptic curves of genus g = 1, 2, . . . . For each of these Lie algebras, the Lie subalge- bra of vertical ... See full document
251
An analysis of the $C$ class of bent functions
... x 2 li . For details we refer to [2, 13]. We show here that bent functions in the C class, corresponding to φ, can be constructed by adding indicator functions of subspaces of codimension 2. The ... See full document
6
Secondary constructions on generalized bent functions
... generalized bent Boolean functions, characterized generalized bent Boolean functions symmetric with respect to two ...of bent functions for any even posi- tive integer ...the ... See full document
30
Permutation polynomials in one and several variables
... Chapter 2 gives the fundamental concepts of a permutation polynomial and an orthogonal system.The cyclic and Dickson polynomials are defined and permutation properties of Chebyshev polyn[r] ... See full document
42
Several Classes of Permutation Polynomials over Finite Fields
... by Dickson [4] for arbitrary finite fields. Permutation polynomials have been studied extensively and have important applications in coding theory, cryp- tography, combinatorics, and design theory ... See full document
48
Néron Tate heights on the Jacobians of high genus hyperelliptic curves
... This thesis builds on the original results of N´ eron, combined with work of Arakelov [Ara74], Faltings [Fal84] and Hriljac [Hri83], who interpret ˆ h as an arith- metic intersection pairing on the N´ eron model of the ... See full document
54
A New Method for Decomposition in the Jacobian of Small Genus Hyperelliptic Curves
... In this work, we provide a new method for decomposition. The factor basis remains the same as in Gaudry’s method and also the linear algebra step remains unchanged. Our main contribution is to show an alternative method ... See full document
96
Recent progress on the elliptic curve discrete logarithm problem
... To maximise the benefit from these ideas one wishes to find large groups that act on the summation polynomials. Faug` ere, Gaudry, Huot and Renault [36] considered the action of [−1] (i.e., P 7→ −P ) and also the ... See full document
23
Complex Wave Solutions to Mathematical Biology Models I: Newell-Whitehead-Segel and Zeldovich Equations
... some hyper- bolic functions are determined by using some relations between the hyper- bolic functions and trigonometric functions based on Sine-Gordon equation and traveling wave ... See full document
7
A Simple Method for Obtaining Relations Among Factor Basis Elements for Special Hyperelliptic Curves
... relations among the factor basis elements. Both Nagao’s and the Joux-Vitse methods require solv- ing a multi-variate system of non-linear equations. In this work, we revisit Nagao’s approach with the idea of avoiding the ... See full document
15
Some results on $q$-ary bent functions
... generalized bent functions exist for every value of q and n, except when n is odd and q = 2 mod 4, whereas Boolean bent functions exist only for even ...of bent functions in the ... See full document
81
A note on generalized bent criteria for Boolean functions
... is a generalization of the connection between bent and negabent function proved by Parker and Pott [3]. It is observed that if the absolute value of an entry in the spectrum of a function with respect to a ... See full document
16
New results on nonexistence of generalized bent functions
... Rothaus proved that there exists a bent function of type [n, 2] if and only if n is even. Later, Kumar et al. constructed a GBF for all cases of even n or q ̸≡ 2 (mod 4). There are many materials about the ... See full document
8
Constructing Infinite Families of Low Differential Uniformity $(n,m)$-Functions with $m>n/2$
... those functions of the form F (x, z) = φ(z)G(x) with φ linear or affine, seems more or less the first framework to be ...Gold functions are the simplest to be handled, the inverse function behaves function ... See full document
6
Bent and Semi-bent Functions via Linear Translators
... Boolean functions to get Boolean functions with optimal or very high ...of bent and semi-bent functions from Boolean maps having linear structures or linear translator in Sections 3, 4 ... See full document
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