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194 Bibliography[42] Claude Carlet, Xiangyong Zeng, Chunlei Li, and Lei Hu. Further properties of severalclasses of Boolean functions with optimum algebraic immunity. Des. Codes Cryptography,52(3):303–338, 2009. (Cited on page 11.)[43] Robert Carls, David Russell Kohel, and David Lubicz. Higher-dimensional 3-adic CMconstruction. J. Algebra, 319(3):971–1006, 2008. (Cited on page 184.)[44] John William Scott Cassels. Lectures on elliptic curves, volume 24 of London MathematicalSociety Student Texts. Cambridge University Press, Cambridge, 1991. (Cited on page 99.)[45] Jinhui Chao, Osamu Nakamura, Kohji Sobataka, and Shigeo Tsujii. Construction of secureelliptic cryptosystems using CM tests and liftings. In Kazuo Ohta and Dingyi Pei, editors,ASIACRYPT, volume 1514 of Lecture Notes in Computer Science, pages 95–109. Springer,1998. (Cited on page 153.)[46] Pascale Charpin and Guang Gong. Hyperbent functions, Kloosterman sums, and Dicksonpolynomials. IEEE Transactions on Information Theory, 54(9):4230–4238, 2008. (Cited onpages 96, 110, 111, 113, and 232.)[47] Pascale Charpin, Tor Helleseth, and Victor Zinoviev. Divisibility properties of Kloostermansums over finite fields of characteristic two. In Information Theory, 2008. ISIT 2008. IEEEInternational Symposium on, pages 2608 –2612, july 2008. (Cited on pages 118 and 234.)[48] Pascale Charpin, Tor Helleseth, and Victor Zinoviev. Divisibility properties of classicalbinary Kloosterman sums. Discrete Mathematics, 309(12):3975–3984, 2009. (Cited onpage 120.)[49] Wei-Liang Chow. On compact complex analytic varieties. Amer. J. Math., 71:893–914,1949. (Cited on page 167.)[50] Marcus Tullius Cicero, Jules Martha, and Carlos Lévy. Des termes extrêmes des biens etdes maux: Livres I-II. Collection des universités de France. Série latine. Les Belles Lettres,1990. (Cited on page 1.)[51] Alfred Clebsch. Zur Theorie der binären algebraischen Formen. Math. Ann., 3(2):265–267,1870. (Cited on page 181.)[52] Clifford Cocks. An identity based encryption scheme based on quadratic residues. InBahram Honary, editor, IMA Int. Conf., volume 2260 of Lecture Notes in Computer Science,pages 360–363. Springer, 2001. (Cited on page 156.)[53] Gérard Denis Cohen and Jean-Pierre Flori. On a generalized combinatorial conjectureinvolving addition mod 2 k − 1. Cryptology ePrint Archive, Report 2011/400, 2011.http://eprint.iacr.org/. (Cited on page 20.)[54] Henri Cohen. A course in computational algebraic number theory, volume 138 of GraduateTexts in Mathematics. Springer-Verlag, Berlin, 1993. (Cited on pages 105 and 170.)[55] Henri Cohen. Advanced topics in computational number theory, volume 193 of GraduateTexts in Mathematics. Springer-Verlag, New York, 2000. (Cited on page 170.)[56] Henri Cohen, Gerhard Frey, Roberto Avanzi, Christophe Doche, Tanja Lange, Kim Nguyen,and Frederik Vercauteren, editors. Handbook of elliptic and hyperelliptic curve cryptography.Discrete Mathematics and its Applications (Boca Raton). Chapman & Hall/CRC, BocaRaton, FL, 2006. (Cited on pages 99, 105, 154, and 181.)
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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
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Page 209 and 210: 6.4. Class polynomials for genus 2
Page 211: Appendices
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Page 216 and 217: Table A.8: Coefficients for d = 8,
Page 218 and 219: 192 Bibliography[13] Elwyn Ralph Be
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
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Page 267: 3. Multiplication complexe et polyn
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