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

More documents

Recommendations

Info

208 Bibliography[254] Marco Streng. Smaller class invariants for constructing curves of genus 2. Talk given atGeoCrypt 2011, slides available at http://iml.univ-mrs.fr/ati/GeoCrypt2011, June2011. (Cited on page 184.)[255] Marco Streng. Smaller class invariants for constructing curves of genus 2. Talk given atECC 2011, slides available at http://ecc2011.loria.fr/program.html, September 2011.(Cited on page 184.)[256] Stupeflip. Stupeflip, January 2003. (Cited on page 1.)[257] Andrew Victor Sutherland. Accelerating the CM method. 1009.1082, September 2010.(Cited on page 153.)[258] Andrew Victor Sutherland. Computing Hilbert class polynomials with the Chinese remaindertheorem. Math. Comput., 80(273):501–538, 2011. (Cited on page 153.)[259] Deng Tang, Claude Carlet, and Xiaohu Tang. Highly nonlinear Boolean functions withoptimal algebraic immunity and good behavior against fast algebraic attacks. CryptologyePrint Archive, Report 2011/366, 2011. http://eprint.iacr.org/. (Cited on pages 3, 8,12, 15, 16, 17, 21, 23, 24, 25, 221, and 222.)[260] Xiaohu Tang, Deng Tang, Xiangyong Zeng, and Lei Hu. Balanced Boolean functions with(almost) optimal algebraic immunity and very high nonlinearity. Cryptology ePrint Archive,Report 2010/443, 2010. http://eprint.iacr.org/. (Cited on pages 14 and 16.)[261] John Tate. Endomorphisms of abelian varieties over finite fields. Invent. Math., 2:134–144,1966. (Cited on page 174.)[262] Ziran Tu and Yingpu Deng. Boolean functions with all main cryptographic properties.Cryptology ePrint Archive, Report 2010/518, 2010. http://eprint.iacr.org/. (Cited onpages 14 and 17.)[263] Ziran Tu and Yingpu Deng. A class of 1-resilient function with high nonlinearity and algebraicimmunity. Cryptology ePrint Archive, Report 2010/179, 2010. http://eprint.iacr.org/.(Cited on page 14.)[264] Ziran Tu and Yingpu Deng. A conjecture about binary strings and its applications onconstructing Boolean functions with optimal algebraic immunity. Des. Codes Cryptography,60(1):1–14, 2011. (Cited on pages 3, 8, 12, 13, 14, 15, 16, 21, 29, 86, 90, 221, and 222.)[265] http://gcc.gnu.org. GCC, the GNU Compiler Collection – Version 4.6.1, 2011. http://gcc.gnu.org. (Cited on page 89.)[266] http://python.org. Python Programming Language – Version 2.6, 2011. http://python.org. (Cited on page 2.)[267] Maxima.sourceforge.net. Maxima, a Computer Algebra System (Version 5.23.2), 2011.http://maxima.sourceforge.net. (Cited on pages 48, 49, and 187.)[268] Pynac.sagemath.net. Pynac, symbolic computation with Python objects (Version 0.2.2),2011. http://pynac.sagemath.org. (Cited on pages 48, 49, and 187.)[269] Osmanbey Uzunkol. Über die Konstruktion algebraischer Kurven mittels komplexer Multiplikation.PhD thesis, Technischen Universität Berlin, 2010. (Cited on pages 153 and 184.)
Bibliography 209[270] Gerard van der Geer and Ben Moonen. Abelian Varieties. None, 2011. http://staff.science.uva.nl/~bmoonen/boek/BookAV.html. (Cited on pages 163 and 168.)[271] Alfred Jacobus van der Poorten and Andreas Stein, editors. Algorithmic Number Theory,8th International Symposium, ANTS-VIII, Banff, Canada, May 17-22, 2008, Proceedings,volume 5011 of Lecture Notes in Computer Science. Springer, 2008. (Cited on pages 191,192, and 198.)[272] Jacobus Hendrikus van Lint. Introduction to coding theory, volume 86 of Graduate Texts inMathematics. Springer-Verlag, Berlin, third edition, 1999. (Cited on page 13.)[273] Paul Bastiaan van Wamelen. Examples of genus two CM curves defined over the rationals.Math. Comput., 68(225):307–320, 1999. (Cited on pages 160, 178, and 240.)[274] Frederik Vercauteren. Advances in point counting. In Advances in elliptic curve cryptography,volume 317 of London Math. Soc. Lecture Note Ser., pages 103–132. Cambridge Univ. Press,Cambridge, 2005. (Cited on pages 107 and 121.)[275] Frederik Vercauteren. Computing zeta functions of curves over finite fields. PhD thesis,Katholieke Universiteit Leuven, 2007. (Cited on pages 107, 108, 121, 123, and 230.)[276] Frederik Vercauteren, Bart Preneel, and Joos Vandewalle. A memory efficient version ofSatoh’s algorithm. In Pfitzmann [219], pages 1–13. (Cited on page 107.)[277] Qichun Wang and Thomas Johansson. A note on fast algebraic attacks and higher ordernonlinearities. In Xuejia Lai, Moti Yung, and Dongdai Lin, editors, Information Securityand Cryptology, volume 6584 of Lecture Notes in Computer Science, pages 404–414. SpringerBerlin / Heidelberg, 2011. 10.1007/978-3-642-21518-6-28. (Cited on page 15.)[278] Qichun Wang, Jie Peng, Haibin Kan, and Xiangyang Xue. Constructions of cryptographicallysignificant Boolean functions using primitive polynomials. IEEE Transactions onInformation Theory, 56(6):3048–3053, 2010. (Cited on page 12.)[279] Lawrence Clinton Washington. Elliptic curves. Discrete Mathematics and its Applications(Boca Raton). Chapman & Hall/CRC, Boca Raton, FL, second edition, 2008. Numbertheory and cryptography. (Cited on page 99.)[280] William Charles Waterhouse. Abelian varieties over finite fields. Ann. Sci. École Norm.Sup. (4), 2:521–560, 1969. (Cited on pages 104, 160, 163, 167, and 179.)[281] Heinrich Weber. Lehrbuch der Algebra. Chelsea Pub Co, 3rd reprint edition, July 1979.(Cited on page 153.)[282] André Weil. On the theory of complex multiplication. In Proceedings of the internationalsymposium on algebraic number theory, Tokyo & Nikko, 1955, pages 9–22, Tokyo, 1956.Science Council of Japan. (Cited on page 166.)[283] Annegret Weng. Konstruktion kryptographisch geeigneter Kurven mit komplexer Multiplikation.PhD thesis, Universität GH Essen, 2001. (Cited on pages 160 and 182.)[284] Kim-Ee Yeoh. GP/Pari implementation of point counting in characteristic 2. http://pages.cs.wisc.edu/~yeoh/nt/satoh-fgh.gp. (Cited on page 123.)[285] Amr Mohamed Youssef and Guang Gong. Hyper-bent functions. In Pfitzmann [219], pages406–419. (Cited on page 96.)
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:
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 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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?