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210 Bibliography[286] Chia-Fu Yu. The isomorphism classes of abelian varieties of CM-type. J. Pure Appl. Algebra,187(1-3):305–319, 2004. (Cited on page 174.)
IndexAAbelian variety . . . . . . . . . . . . . 161Divisor . . . . . . . . . . . . . . . 164Dual variety . . . . . . . . . . . . 164Endomorphism algebra . . . . . . 166Endomorphism ring . . . . . . . . 166Isotypic . . . . . . . . . . . . . . . 174Picard group . . . . . . . . . . . . 164Picard variety . . . . see Dual varietyPolarization . . . . . . . . . . . . 164Simple . . . . . . . . . . . . . . . 163Tate module . . . . . . . . . . . . 167with complex multiplication . see CMabelian varietyAdèle . . . . . . . . . . . . . . . . . . 172Algebraic curveAffine . . . . . . . . . . . . . . 99, 106Divisor . . . . . . . . . . . . . . . 134Elliptic . . . . . . . see Elliptic curveFunction field . . . . . . . . . . . 133Genus . . . . . . . . . . . . . 99, 105Hyperelliptic . see Hyperelliptic curveJacobian variety . . . . . . . . 135, 180Non-singular . . . . . . . . see SmoothPicard group . . . . . . . . . . . . 135Projective . . . . . . . . 99, 105, 106Singular . . . . . . . . . . . . . . 139Smooth . . . . . . . . . . 99, 105, 139with complex multiplication . . . 181Algebraic varietyAbelian . . . . . . see Abelian varietyComplete . . . . . . . . . . . . . . 132Projective . . . . . . . . . . . . . 132Artin–Schreier curve . . . . . 106, 117, 118Asymmetric cryptosystemDiscrete logarithm problem . 153, 155Identity-based cryptography . . . 156BBent function . . . . . . . . . . . 11, 96, 97Bernoulli number . . . . . . . . . . . 48, 54Binary quadratic form . . . . . . . . . 146Definite . . . . . . . . . . . . . . . 146Discriminant . . . . . . . . . . . . 146Primitive . . . . . . . . . . . . . . 146Reduced . . . . . . . . . . . . . . 146Boolean function . . . . . . . . . . . . . . 8Algebraic normal form . . . . . . . 10Annihilator . . . . . . . . . . . . . 10Fast algebraic attack . . . . . . . . 10Hamming distance . . . . . . . . . 11Hamming weight . . . . . . . . 9, 96Polynomial form . . . . . . . . . . . 97Sign function . . . . . . . . . . . . 97Support . . . . . . . . . . . . . 9, 96Trace representation . see PolynomialformWalsh–Hadamard transform . . . . 97Borchardt sequence . . . . . . . . . . . 184CCatalan number . . . . . . . . . . . . . 25Charpin–Gong criterion . . . . . . . . 113using hyperelliptic curves . . . . . 116Chebotarev density theorem . . . . . . 151Chinese Remainder Theorem . . . 107, 153Chu–Vandermonde identity . . . . . . . 76Class field theoryArtin reciprocity . . . . . . . . . 151Artin symbol . . . . . . . . . . . 151Congruence subgroup . . . . . . . 149Generalized ideal class group . . . 149Ring class field . . . . . . . . . . 149Class group . . . . . . . . . . . . . . . 144Class group . . . . 144, 149, 169, 170Class semigroup . . . . . . . . 144, 169
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2012-ENST-003EDITE de ParisDoctorat
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Jean-Pierre Flori: Boolean function
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AbstractThe core of this thesis is
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AcknowledgmentsVladimir. — Quand
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ContentsList of symbols and notatio
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Contentsxv4 Efficient characterizat
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List of figures1.1 The filter model
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List of symbols and notationGeneral
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List of symbols and notationxxil(t)
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List of symbols and notationxxiiidi
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List of symbols and notationxxvu
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2 Introduction1 Mathematics and cry
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4 Introductiongiving more general b
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Chapter 1Boolean functions incrypto
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1.1. Cryptographic criteria for Boo
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1.2. Families of Boolean functions
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20 Chapter 2. On a conjecture about
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Part IIBent functions and pointcoun
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96 Chapter 3. Bent functions and al
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98 Chapter 3. Bent functions and al
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100 Chapter 3. Bent functions and a
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110 Chapter 4. Efficient characteri
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Part IIIComplex multiplication and
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132 Chapter 5. Complex multiplicati
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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
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Page 205 and 206: 6.3. Complex multiplication 179pola
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Page 209 and 210: 6.4. Class polynomials for genus 2
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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 238 and 239: 212 IndexForm class group . . . . .
Page 240 and 241: 214 IndexKKloosterman sum . . . . .
Page 243 and 244: Résumé longFauĆ.Werd’ iĚ beru
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