- Page 1: 2012-ENST-003EDITE de ParisDoctorat
- Page 5: To Choupi
- Page 9: RésuméLe cœur de cette thèse es
- Page 12 and 13: xiiAcknowledgmentsMadore, Bertrand
- Page 14 and 15: xivContents2.3.6 A combinatorial pr
- Page 16 and 17: xviContents6.2.2 Computation of the
- Page 18 and 19: xviiiLists of figures, tables and a
- Page 20 and 21: xxList of symbols and notationBoole
- Page 22 and 23: xxiiList of symbols and notation〈
- Page 24 and 25: xxivList of symbols and notationFra
- Page 27 and 28: IntroductionBeaucoup d’travail co
- Page 29 and 30: 3. Outline 33 OutlineThe main matte
- Page 31: Part IBoolean functions and acombin
- Page 34 and 35: 8 Chapter 1. Boolean functions in c
- Page 36 and 37: 10 Chapter 1. Boolean functions in
- Page 38 and 39: 12 Chapter 1. Boolean functions in
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- Page 42 and 43: 16 Chapter 1. Boolean functions in
- Page 45 and 46: Chapter 2On a conjecture about addi
- Page 47 and 48: 2.1. General properties 21Tang [259
- Page 49 and 50: 2.1. General properties 23Lemma 2.1
- Page 51 and 52: 2.2. The case ɛ = −1 25In the ca
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2.2. The case ɛ = −1 27Proof. We
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2.3. The case ɛ = +1 292.3 The cas
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2.3. The case ɛ = +1 31Proof. Inde
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2.3. The case ɛ = +1 33Theorem 2.3
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2.4. A block splitting pattern 352.
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2.4. A block splitting pattern 37Th
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2.4. A block splitting pattern 39Su
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2.4. A block splitting pattern 41Pr
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2.4. A block splitting pattern 43Ac
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2.4. A block splitting pattern 45Le
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2.5. A closed-form expression for f
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2.5. A closed-form expression for f
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2.5. A closed-form expression for f
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2.5. A closed-form expression for f
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2.5. A closed-form expression for f
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2.5. A closed-form expression for f
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2.5. A closed-form expression for f
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2.5. A closed-form expression for f
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2.5. A closed-form expression for f
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2.5. A closed-form expression for f
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2.6. Asymptotic behavior: β i →
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2.6. Asymptotic behavior: β i →
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2.6. Asymptotic behavior: β i →
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2.6. Asymptotic behavior: β i →
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2.6. Asymptotic behavior: β i →
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2.6. Asymptotic behavior: β i →
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2.6. Asymptotic behavior: β i →
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2.7. An inductive approach 81• O
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2.7. An inductive approach 83Propos
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2.8. Other works 852.8 Other worksW
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2.9. Efficient test of the Tu-Deng
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2.9. Efficient test of the Tu-Deng
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2.9. Efficient test of the Tu-Deng
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Chapter 3Bent functions and algebra
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3.1. Bent functions 97from F 2 k to
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3.2. Algebraic curves 993.1.4 Dicks
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3.2. Algebraic curves 101Figure 3.2
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3.2. Algebraic curves 103Propositio
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3.2. Algebraic curves 105It should
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3.2. Algebraic curves 107Let us beg
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Chapter 4Efficient characterization
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4.1. Hyper-bentness characterizatio
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4.1. Hyper-bentness characterizatio
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4.2. Reformulation in terms of card
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4.2. Reformulation in terms of card
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4.3. Divisibility of binary Klooste
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4.4. Finding specific values of bin
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4.4. Finding specific values of bin
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4.5. Experimental results for m eve
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4.5. Experimental results for m eve
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Chapter 5Complex multiplication and
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5.1. Further background on elliptic
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5.1. Further background on elliptic
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5.1. Further background on elliptic
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5.2. Elliptic curves over the compl
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5.2. Elliptic curves over the compl
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5.2. Elliptic curves over the compl
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5.2. Elliptic curves over the compl
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5.3. Elliptic curves with complex m
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5.3. Elliptic curves with complex m
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5.3. Elliptic curves with complex m
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5.4. Elliptic curves in cryptograph
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5.4. Elliptic curves in cryptograph
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5.4. Elliptic curves in cryptograph
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160 Chapter 6. Complex multiplicati
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162 Chapter 6. Complex multiplicati
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164 Chapter 6. Complex multiplicati
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166 Chapter 6. Complex multiplicati
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168 Chapter 6. Complex multiplicati
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170 Chapter 6. Complex multiplicati
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172 Chapter 6. Complex multiplicati
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174 Chapter 6. Complex multiplicati
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176 Chapter 6. Complex multiplicati
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178 Chapter 6. Complex multiplicati
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180 Chapter 6. Complex multiplicati
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182 Chapter 6. Complex multiplicati
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184 Chapter 6. Complex multiplicati
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Appendix ACoefficients of f dIn ano
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Table A.6: Coefficients for d = 6,
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Bibliography[1] Milton Abramowitz a
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Bibliography 193[28] Reinier Martij
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Bibliography 195[57] Brian Conrad.
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Bibliography 197[87] Andreas Enge a
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Bibliography 199[116] Alice Chia Pi
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Bibliography 201[147] Kiran Sridhar
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Bibliography 203[176] Reynald Lerci
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Bibliography 205[206] Richard Molon
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Bibliography 207[239] Goro Shimura
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Bibliography 209[270] Gerard van de
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IndexAAbelian variety . . . . . . .
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Index 213Division polynomial . . .
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Index 215SSemi-bent function . . .
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218 Résumé longEstragon. — Alor
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220 Résumé long⊕ ⊕ ⊕s i+L
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222 Résumé long1.2 D’une conjec
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224 Résumé longAfin d’utiliser
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226 Résumé longSon graphe est rep
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228 Résumé longLa caractérisatio
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230 Résumé longThéorème 2.4 (Th
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232 Résumé longprécédent. Dans
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234 Résumé longProposition 2.13.
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236 Résumé longFigure 8 - Un tore
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238 Résumé longAlgorithme 1 - Cal
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240 Résumé longThéorème 3.8 ([2