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

More documents

Recommendations

Info

200 Bibliography[132] Marc Hindry and Joseph Hillel Silverman. Diophantine geometry, volume 201 of GraduateTexts in Mathematics. Springer-Verlag, New York, 2000. An introduction. (Cited onpages 161 and 162.)[133] Laura Hitt. On the minimal embedding field. In Tsuyoshi Takagi, Tatsuaki Okamoto,Eiji Okamoto, and Takeshi Okamoto, editors, Pairing, volume 4575 of Lecture Notes inComputer Science, pages 294–301. Springer, 2007. (Cited on page 155.)[134] Laura Hitt O’Connor, Gary McGuire, Michael Naehrig, and Marco Streng. A CM constructionfor curves of genus 2 with p-rank 1. J. Number Theory, 131(5):920–935, 2011. (Citedon page 183.)[135] Hendrik Hubrechts. Computing zeta functions of curves over finite fields. PhD thesis,Katholieke Universiteit Leuven, 2003. (Cited on page 107.)[136] Hendrik Hubrechts. Point counting in families of hyperelliptic curves in characteristic 2.LMS J. Comput. Math., 10:207–234, 2007. (Cited on page 107.)[137] Hendrik Hubrechts. Point counting in families of hyperelliptic curves. Foundations ofComputational Mathematics, 8(1):137–169, 2008. (Cited on page 107.)[138] Dale Husemöller. Elliptic curves, volume 111 of Graduate Texts in Mathematics. Springer-Verlag, New York, second edition, 2004. With appendices by Otto Forster, Ruth Lawrenceand Stefan Theisen. (Cited on page 99.)[139] Jun-ichi Igusa. Arithmetic variety of moduli for genus two. Ann. of Math. (2), 72:612–649,1960. (Cited on pages 159 and 181.)[140] The OEIS Foundation Inc. The On-Line Encyclopedia of Integer Sequences. http://oeis.org. (Cited on page 26.)[141] Michael Jacobson, Jr., Alfred John Menezes, and Andreas Stein. Hyperelliptic curves andcryptography. In High primes and misdemeanours: lectures in honour of the 60th birthdayof Hugh Cowie Williams, volume 41 of Fields Inst. Commun., pages 255–282. Amer. Math.Soc., Providence, RI, 2004. (Cited on page 105.)[142] Qingfang Jin, Zhuojun Liu, and Baofeng Wu. 1-resilient Boolean function with optimalalgebraic immunity. Cryptology ePrint Archive, Report 2011/549, 2011. http://eprint.iacr.org/. (Cited on pages 17 and 20.)[143] Qingfang Jin, Zhuojun Liu, Baofeng Wu, and Xiaoming Zhang. A general conjecturesimilar to T-D conjecture and its applications in constructing Boolean functions withoptimal algebraic immunity. Cryptology ePrint Archive, Report 2011/515, 2011. http://eprint.iacr.org/. (Cited on pages 8, 16, 17, 23, 221, and 222.)[144] Nicholas Katz and Ron Livné. Sommes de Kloosterman et courbes elliptiques universellesen caractéristiques 2 et 3. C. R. Acad. Sci. Paris Sér. I Math., 309(11):723–726, 1989.(Cited on pages 104, 105, 110, 114, and 230.)[145] Kiran Sridhara Kedlaya. Complex multiplication and explicit class field theory, April 1996.(Cited on pages 149, 151, and 237.)[146] Kiran Sridhara Kedlaya. Counting points on hyperelliptic curves using Monsky-Washnitzercohomology. J. Ramanujan Math. Soc., 16(4):323–338, 2001. (Cited on page 107.)
Bibliography 201[147] Kiran Sridhara Kedlaya. Errata for: “Counting points on hyperelliptic curves using Monsky-Washnitzer cohomology” [J. Ramanujan Math. Soc. 16 (2001), no. 4, 323–338; mr1877805].J. Ramanujan Math. Soc., 18(4):417–418, 2003. Dedicated to Professor KaraikurichiSrinivasan Padmanabhan. (Cited on page 107.)[148] Brian Wilson Kernighan and Dennis MacAlistair Ritchie. C Programming Language.Prentice Hall, 2 edition, April 1988. (Cited on pages 2, 89, and 227.)[149] Jean-Louis Kerouac. The Dharma Bums. Penguin classics. Penguin Books, 2000. (Cited onpage 131.)[150] Hae Young Kim, Jung Youl Park, Jung Hee Cheon, Je Hong Park, Jae Heon Kim, andSang Geun Hahn. Fast elliptic curve point counting using Gaussian normal basis. In Fiekerand Kohel [90], pages 292–307. (Cited on page 107.)[151] Jürgen Klüners and Sebastian Pauli. Computing residue class rings and Picard groups oforders. J. Algebra, 292(1):47–64, 2005. (Cited on pages 160, 170, and 171.)[152] Anthony William Knapp. Elliptic curves, volume 40 of Mathematical Notes. PrincetonUniversity Press, Princeton, NJ, 1992. (Cited on page 99.)[153] Neal Koblitz. Elliptic curve cryptosystems. Math. Comp., 48(177):203–209, 1987. (Citedon page 153.)[154] Neal Koblitz. Constructing elliptic curve cryptosystems in characteristic 2. In Alfred JohnMenezes and Scott Alexander Vanstone, editors, CRYPTO, volume 537 of Lecture Notes inComputer Science, pages 156–167. Springer, 1990. (Cited on pages 99 and 105.)[155] Neal Koblitz. Algebraic aspects of cryptography, volume 3 of Algorithms and Computationin Mathematics. Springer-Verlag, Berlin, 1998. With an appendix by Alfred John Menezes,Yi-Hong Wu and Robert Joseph Zuccherato. (Cited on page 99.)[156] Gilles Lachaud and Jacques Wolfmann. Sommes de Kloosterman, courbes elliptiques etcodes cycliques en caractéristique 2. C. R. Acad. Sci. Paris Sér. I Math., 305(20):881–883,1987. (Cited on pages 110, 114, and 230.)[157] Gilles Lachaud and Jacques Wolfmann. The weights of the orthogonals of the extendedquadratic binary Goppa codes. IEEE Transactions on Information Theory, 36(3):686Ð692,1990. (Cited on pages 110, 111, and 119.)[158] Xuejia Lai and Kefei Chen, editors. Advances in Cryptology - ASIACRYPT 2006, 12thInternational Conference on the Theory and Application of Cryptology and InformationSecurity, Shanghai, China, December 3-7, 2006, Proceedings, volume 4284 of Lecture Notesin Computer Science. Springer, 2006. (Cited on pages 198 and 203.)[159] Serge Lang. Complex multiplication, volume 255 of Grundlehren der MathematischenWissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, NewYork, 1983. (Cited on pages 160, 162, 164, 165, 167, 168, 172, 173, 174, 175, 176, 177, 178,179, 180, 240, and 241.)[160] Serge Lang. Elliptic functions, volume 112 of Graduate Texts in Mathematics. Springer-Verlag, New York, second edition, 1987. With an appendix by J. Tate. (Cited on pages 105,139, 143, 144, 145, 149, 150, 151, 152, 153, 172, and 237.)
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 39 and 40:
Page 41 and 42:
Page 43:
Page 46 and 47:
20 Chapter 2. On a conjecture about
Page 48 and 49:
Page 50 and 51:
Page 52 and 53:
Page 54 and 55:
Page 56 and 57:
Page 58 and 59:
Page 60 and 61:
Page 62 and 63:
Page 64 and 65:
Page 66 and 67:
Page 68 and 69:
Page 70 and 71:
Page 72 and 73:
Page 74 and 75:
Page 76 and 77:
Page 78 and 79:
Page 80 and 81:
Page 82 and 83:
Page 84 and 85:
Page 86 and 87:
Page 88 and 89:
Page 90 and 91:
Page 92 and 93:
Page 94 and 95:
Page 96 and 97:
Page 98 and 99:
Page 100 and 101:
Page 102 and 103:
Page 104 and 105:
Page 106 and 107:
Page 108 and 109:
Page 110 and 111:
Page 112 and 113:
Page 114 and 115:
Page 116 and 117:
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: 150 Chapter 5. Complex multiplicati
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 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 253 and 254: 2. Fonctions courbes et comptage de
Page 261 and 262: 3. Multiplication complexe et polyn
Page 267: 3. Multiplication complexe et polyn
show all

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

Create successful ePaper yourself

Delete template?

Save as template?