here - Sites personnels de TELECOM ParisTech - TÃ©lÃ©com ParisTech

More documents

Recommendations

Info

50 Chapter 2. On a conjecture about addition modulo 2 k − 1Figure 2.5: Graph of f d (β i ) for β i = 10, i ≠ 1we prove this in Proposition 2.5.19. There is a recursion relation between coefficients with differentd’s:a d,n+1(i + 1,...,i n,0) ad,n (i = 1,...,i n) 3ad−1,n (i ;1,...,i n)this is Corollary 2.5.18. There is a relation between coefficients with a given d:this is Proposition 2.5.3.a d,n(i,j,...) = i + 1 a d,nj(i+1,j−1,...) ;2.5.2 Splitting the sum into atomic partsWe consider a general d ≥ 1. From Proposition 2.4.10, we havef d (β 1 , . . . , β d ) =B−1∑E=0∑∑d ei=E0≤e i∏P (e i ) ,where P (e i ) has three different expressions according to the value of e i :⎧⎪⎨ 2 −βi if e i = 0 ,2P (e i ) =−β i3⎪⎩(2ei − 2 −ei ) if 0 < e i < β i ,2 β i −2 −β i32 −ei if β i ≤ e i .Let us denote for a vector X ∈ {0, 1, 2} d :• the i-th coordinate by X i with 1 ≤ i ≤ d;• j k = # {i | X i = k} for 0 ≤ k ≤ 2;• B 0,1 = ∑ {i|X i≠2} β i;d
2.5. A closed-form expression for f d 51• E 1 = ∑ {i|X i=1} e i.We can now define subsets S d X of the sum in Proposition 2.4.10 where each P (e i) has a specificbehavior given by the value of the i-th coordinate of such a vector X.S d X ==B−1∑∑∑E=0d e i=1i=Ee i =0 if X i =00
Page 1:
2012-ENST-003EDITE de ParisDoctorat
Page 4 and 5:
Jean-Pierre Flori: Boolean function
Page 7:
AbstractThe core of this thesis is
Page 11 and 12:
AcknowledgmentsVladimir. — Quand
Page 13 and 14:
ContentsList of symbols and notatio
Page 15 and 16:
Contentsxv4 Efficient characterizat
Page 17 and 18:
List of figures1.1 The filter model
Page 19 and 20:
List of symbols and notationGeneral
Page 21 and 22:
List of symbols and notationxxil(t)
Page 23 and 24:
List of symbols and notationxxiiidi
Page 25: List of symbols and notationxxvu
Page 28 and 29: 2 Introduction1 Mathematics and cry
Page 30 and 31: 4 Introductiongiving more general b
Page 33 and 34: Chapter 1Boolean functions incrypto
Page 35 and 36: 1.1. Cryptographic criteria for Boo
Page 37 and 38: 1.2. Families of Boolean functions
Page 43: 1.2. Families of Boolean functions
Page 46 and 47: 20 Chapter 2. On a conjecture about
Page 119: Part IIBent functions and pointcoun
Page 122 and 123: 96 Chapter 3. Bent functions and al
Page 124 and 125: 98 Chapter 3. Bent functions and al
Page 126 and 127:
100 Chapter 3. Bent functions and a
Page 128 and 129:
Page 130 and 131:
Page 132 and 133:
Page 134 and 135:
Page 136 and 137:
110 Chapter 4. Efficient characteri
Page 138 and 139:
Page 140 and 141:
Page 142 and 143:
Page 144 and 145:
Page 146 and 147:
Page 148 and 149:
Page 150 and 151:
Page 152 and 153:
Page 155:
Part IIIComplex multiplication and
Page 158 and 159:
132 Chapter 5. Complex multiplicati
Page 160 and 161:
Page 162 and 163:
Page 164 and 165:
Page 166 and 167:
Page 168 and 169:
Page 170 and 171:
Page 172 and 173:
Page 174 and 175:
Page 176 and 177:
Page 178 and 179:
Page 180 and 181:
Page 182 and 183:
Page 185 and 186:
Chapter 6Complex multiplication in
Page 187 and 188:
6.1. Abelian varieties 1616.1 Abeli
Page 189 and 190:
6.1. Abelian varieties 163Theorem 6
Page 191 and 192:
6.1. Abelian varieties 165A homomor
Page 193 and 194:
6.1. Abelian varieties 1676.1.5 Hom
Page 195 and 196:
6.2. Class groups and units 169The
Page 197 and 198:
6.2. Class groups and units 171in [
Page 199 and 200:
6.3. Complex multiplication 173If t
Page 201 and 202:
6.3. Complex multiplication 175•
Page 203 and 204:
6.3. Complex multiplication 177We h
Page 205 and 206:
6.3. Complex multiplication 179pola
Page 207 and 208:
6.4. Class polynomials for genus 2
Page 209 and 210:
6.4. Class polynomials for genus 2
Page 211:
Appendices
Page 214 and 215:
Table A.3: Coefficients for d = 3,
Page 216 and 217:
Table A.8: Coefficients for d = 8,
Page 218 and 219:
192 Bibliography[13] Elwyn Ralph Be
Page 220 and 221:
194 Bibliography[42] Claude Carlet,
Page 222 and 223:
196 Bibliography[72] Cunsheng Ding,
Page 224 and 225:
198 Bibliography[102] David Freeman
Page 226 and 227:
200 Bibliography[132] Marc Hindry a
Page 228 and 229:
202 Bibliography[161] Philippe Lang
Page 230 and 231:
204 Bibliography[191] Willi Meier a
Page 232 and 233:
206 Bibliography[222] Oscar Seymour
Page 234 and 235:
208 Bibliography[254] Marco Streng.
Page 236 and 237:
210 Bibliography[286] Chia-Fu Yu. T
Page 238 and 239:
212 IndexForm class group . . . . .
Page 240 and 241:
214 IndexKKloosterman sum . . . . .
Page 243 and 244:
Résumé longFauĆ.Werd’ iĚ beru
Page 245 and 246:
1. Des fonctions booléennes et d
Page 247 and 248:
Page 249 and 250:
Page 251 and 252:
Page 253 and 254:
2. Fonctions courbes et comptage de
Page 255 and 256:
Page 257 and 258:
Page 259 and 260:
Page 261 and 262:
3. Multiplication complexe et polyn
Page 263 and 264:
Page 265 and 266:
Page 267:
show all

here - Sites personnels de TELECOM ParisTech - TÃ©lÃ©com ParisTech

Create successful ePaper yourself

Delete template?

Save as template?