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126 Chapter 4. Efficient characterizations for bentnessThe implementation 11 was ma<strong>de</strong> using Sage [250] and Cython [24], performing direct calls toGivaro [74], NTL [241] and gf2x [26] libraries for efficient manipulation of finite field elementsand construction of Boolean functions.In Table 4.4 we give the results of the computations we conducted along with different piecesof information about them. One should remark that all the Boolean functions which couldbe tested are bent. Evi<strong>de</strong>nce that our computations were correct is given by the fact thatTable 4.4: Test of bentness for m evenm Nb. of cyclotomic classes Time All bent?4 1
4.5. Experimental results for m even 127Table 4.5: The fourteen cyclotomic classes such that K 16 (a) = 4 as elements of F 2 [x]/(x 16 + x 5 +x 3 + x 2 + 1)x 14 + x 11 + x 8 + x 6 + x 3 + xx 15 + x 13 + x 10 + x 8 + x 7 + x 6 + x 5 + x 4 + x 3 + 1x 14 + x 13 + x 12 + x 10 + x 8 + x 2 + xx 14 + x 12 + x 11 + x 9 + x 6 + xx 15 + x 11 + x 9 + x 7 + x 6 + x 3 + x 2 + 1x 13 + x 6 + x 4 + x 2 + x + 1x 12 + x 11 + x 10 + x 9 + x 5 + x 3 + x 2 + xx 15 + x 11 + x 7 + x 6 + x 5 + x 4 + x 3 + x 2x 15 + x 13 + x 9 + x 8 + x 5 + x 4 + x 3 + xx 15 + x 11 + x 10 + x 3x 13 + x 10 + x 9 + x 7 + x 6 + x 5 + x 3 + x 2 + xx 13 + x 10 + x 9 + x 7 + x 6 + x 5 + x 4 + x 3 + x 2 + xx 15 + x 13 + x 10 + x 9 + x 8 + x 7 + x 5 + xx 15 + x 11 + x 10 + x 3 + x + 1
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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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Page 119: Part IIBent functions and pointcoun
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Page 155: Part IIIComplex multiplication and
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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 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
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6.3. Complex multiplication 177We h
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6.3. Complex multiplication 179pola
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6.4. Class polynomials for genus 2
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6.4. Class polynomials for genus 2
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Appendices
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Table A.3: Coefficients for d = 3,
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Table A.8: Coefficients for d = 8,
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192 Bibliography[13] Elwyn Ralph Be
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194 Bibliography[42] Claude Carlet,
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196 Bibliography[72] Cunsheng Ding,
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198 Bibliography[102] David Freeman
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200 Bibliography[132] Marc Hindry a
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202 Bibliography[161] Philippe Lang
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204 Bibliography[191] Willi Meier a
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206 Bibliography[222] Oscar Seymour
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208 Bibliography[254] Marco Streng.
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210 Bibliography[286] Chia-Fu Yu. T
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212 IndexForm class group . . . . .
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214 IndexKKloosterman sum . . . . .
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Résumé longFauĆ.Werd’ iĚ beru
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1. Des fonctions booléennes et d
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2. Fonctions courbes et comptage de
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3. Multiplication complexe et polyn
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