Introduction Proof of the first conjecture
22 Pages
English
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Introduction Proof of the first conjecture

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22 Pages
English

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Introduction Proof of the first conjecture Proof of the third conjecture New families A proof of two conjectures on APN functions. Elodie Leducq Institut de Mathematiques de Jussieu Universite Paris 7 AGCT-13 17/03/11 Elodie Leducq A proof of two conjectures on APN functions.

  • satisfies ∆d

  • institut de mathematiques de jussieu universite

  • ∆d ≤

  • introduction proof

  • apn functions

  • fq ?


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AGCT-13 17/03/11
Institut de Math´ tiques de Jussieu ema Universite´Paris7
A proof of two conjectures on APN functions.
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Elodie Leducq
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n Let q = p , p being a prime number, n an odd integer.
p n d dp i I 3 5 134 (134,160,238,230,206) II 3 5 152 (152,214,158,232,212) III 3 7 40 (40,120,360,1080,1054,976,742) IV 3 7 224 (224,672,2016,1676,656,1968,1532) V 3 7 274 (274,822,280,840,334,1002,820) VI 5 3 14 (14,70,102) VII 5 5 843 (843,1091,2331,2283,2043)
Δ f = max( N f ( a , b ) , a , b F q , a 6 = 0) = 2 .
Definition If f : F q F q , for all a and b F q , we denote by N f ( a , b ) the number of solutions in F q of the equation f ( x + a ) f ( x ) = b . We say that f is APN if
sn.
We put m = n +21 .
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