Preface The 12th conference Arithmetic, Geometry, Cryptography and Coding The- ory (AGC2T 12) took place in Marseille at the Centre International de Recontres Math´ ematiques (CIRM) from 30 March to 3 April 2009. This biennial conference has been a major event in applied arithmetic geometry for nearly a quarter cen- tury, organized by the research group Arithm´ etique et Th´ eorie de l’Information of the Institut de Math´ ematiques de Luminy. There were more than 40 research talks and 80 participants from sixteen countries. This year the AGC2T was preceded by a three-day Exploratory Workshop funded by the European Science Foundation on Curves, Coding Theory, and Cryptography, which brought some 30 researchers together for expository lectures and discussions on the arithmetic of curves and ap- plications. We especially thank the speakers Dan Bernstein, Claus Diem, Ralf Gerk- mann, Hendrik Hubrechts, Ian Kimming, Tanja Lange, Gabriele Nebe, Christophe Ritzenthaler, Patrick Sol´ e, and Gabor Wiese for their lectures, and all participants of both events for creating a stimulating research environment. Less than one month later, on a different continent, the ATI group, together with the eRISCS laboratory of the Universit´ e de la Mediterran´ ee, Marseille and the AOC laboratory (Analyse, Optimisation, Contrˆ ole) of the Universit´ e des Antilles et de la Guyane, assembled 34 participants for the first Geocrypt conference from 27 April to 1 May 2009, in Pointe-` a-Pitre, Guadeloupe. We thank Yves Aubry, Stephane Ballet, Vicent Cossart, Noam Elkies, Everett Howe, Marc Girault, Marc Joye, Gilles Lachaud, Kristin Lauter, Heeralal Janwa, Gary McGuire, Christophe Ritzenthaler, Fran¸ cois Rodier, Karl Rubin, Ren´ e Schoof, Alice Silverberg, Peter Stevenhagen, and John Voight for their mathematical contributions, making this both an enjoyable and informative extension of the AGC2T conference. We also thank Microsoft Research for financial support as well as R´egis Blache for the occasion of his habilitation defense to make this possible. The 12 articles of this volume represent a selection of research presented at this trilogy of events in the spring of 2009. vii
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