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An Algebraic Cryptanalysis of Nonlinear Filter Generators using Gröbner bases

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(1)An Algebraic Cryptanalysis of Nonlinear Filter Generators using Gröbner bases Jean-Charles Faugère, Gwénolé Ars. To cite this version: Jean-Charles Faugère, Gwénolé Ars. An Algebraic Cryptanalysis of Nonlinear Filter Generators using Gröbner bases. [Research Report] RR-4739, INRIA. 2003. �inria-00071848�. HAL Id: inria-00071848 https://hal.inria.fr/inria-00071848 Submitted on 23 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. An Algebraic Cryptanalysis of Nonlinear Filter Generators using Gröbner bases Jean-Charles Faugère — Gwénolé Ars. N° 4739 Février 2003. ISSN 0249-6399. ISRN INRIA/RR--4739--FR+ENG. THÈME 2. apport de recherche.

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(74) 0y†ccgbY

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(81) B   

(82) B

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(84) B

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(88) B 

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(104)   LT

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(112) ›

(113) Æð ON "$L  %$EQ 8dd

(114)  :  L

(115) B '

(116)  c  

(117) bL

(118)   c ^ayzÂivYbq[y$vqmArucor

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(123) 4 [ k L

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(127) ›

(128) Æð T  %GkcL

(129)  V

(130) U 

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(132) B (D

(133) BX  P  k

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(136) B g E 

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(142) =.  C

(143)  c V  S œ ð & ð š

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(146)       

(147) B    k     Cc  6; = <   c 

(148)  !  N   %[  L ,[ : =  C L

(149) % =L

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(152) ±`q 1GJMKLKMKLJq : O Ô ³

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(156) bL  (,

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(161)  P#

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(165)  

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(171)   bÔ

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(183) ›

(184) Æ ð  "$L  %$Eg 8(  ([L

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(187) BcP kT"$# % '

(188)  kL

(189)  

(190)  >&

(191) B 3 :CL

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(193) B L 1 ± [ 1 JLKMKLKMJ [ : O Ô ³ P% )' )' O Ô  "$    k

(194)  L · 1  2ƒHN> 5 · N@@ 9  N  N ÓÔ 7  # = B ê:Ð · "· 1   N*!  N ÓÔ  %

(195) Bc  N  N ÓÔ  + N  Tß«)d± ] K L 1 ³ A  N :%  4%P bk d

(196)    C   k , +N  Tß«)d± ] N  L 1K³ vPı +1TÌ«)`± L 1K ³ JLKLKMKLJ +N  O Ô Tß«)d± ] N O Ô L 1K ³ J [ 1Õ â [ 1JMKLKLKLJ [ Õ: O Ô â [ : O Ô ³ O /3

(197) B   k  C    !

(198) 

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(200) B   N Ó Õ   N ÓÔ  N  - 

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(203) .% / 

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(237) B d

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(249)   k    F 

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(258) 

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(262)   GFc  « -   Ð   GFc  ° g    ° gd

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(268) ° cA C D

(269) B k 

(270)  L 

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(273) c

(274) % .C

(275) BD BQ$ k ?F4LA 

(276) A C  °  « -  'â VYVXVâ"« -  >&

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(289) B F (&

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(291)  Q

(292)   k    C

(293) B,

(294)  gG

(295) 

Références

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