From the preface:

The Algorithmic Number Theory Symposium (ANTS), held biennially since 1994, is the premier international forum for research in computational number theory. ANTS is devoted to algorithmic aspects of number theory, including elementary, algebraic, and analytic number theory, the geometry of numbers, arithmetic algebraic geometry, the theory of finite fields, and cryptography.

This volume is the proceedings of the tenth ANTS meeting, held 9–13 July 2012 at the University of California, San Diego. The scientific program of ANTS X consisted of 5 invited lectures, 25 contributed talks, a poster session, and a rump session. The invited speakers were Manjul Bhargava (Princeton University), Nils Bruin (Simon Fraser University), Wen-Ching Winnie Li (Pennsylvania State University), Nils-Peter Skoruppa (Universität Siegen), and Andrew Sutherland (Massachusetts Institute of Technology). Extended abstracts of the presentations of Bruin and Sutherland are included in this volume.

The contributed talks were presentations of papers chosen through a competitive review process. Each of the 55 papers submitted for consideration was reviewed by at least three members of the program committee, often with input from one or more external reviewers as well. Revised and edited versions of the 25 accepted papers are included in this volume.

At each ANTS since 2006, the Number Theory Foundation has sponsored the
Selfridge Prize, an award for the best contributed paper, as judged by
the program committee. The Selfridge Prize for ANTS X was awarded to
Andrew Sutherland for his paper *On the evaluation of modular polynomials*.

Abstracts of all presentations (including invited presentations and posters), PDF slides of many presentations, and the versions of the contributed papers that were presented at the conference can be found on the conference web site.

For each of the previous ANTS conferences, the proceedings volume was
produced before the meeting and was available at the meeting. This
publication timeline allowed for very little editing and did not permit
authors to revise their papers to incorporate insights gained from
discussions during the conference. Following a suggestion that had been
raised in previous years, the ANTS X organizing committee decided to
produce the proceedings volume *after* the conference. The
committee also decided to switch publishers; we are proud to note that
this volume is the inaugural volume of the Open Book Series of
Mathematical Sciences Publishers.

The editors are grateful to the authors of the papers in this volume for
their flexibility and graciousness during the editing process. The
editors are equally grateful to Silvio Levy and Alex Scorpan, our
contacts at Mathematical Sciences Publishers, for *their*
flexibility and graciousness. We hope that the reader will find the
value added by the editing to be sufficient recompense for the extra
year's wait for the volume to appear.

Alina Bucur | University of California, San Diego |

Joe Buhler | Center for Communications Research, La Jolla |

Dan Gordon | Center for Communications Research, La Jolla |

Everett Howe | Center for Communications Research, La Jolla |

Kiran Kedlaya | University of California, San Diego |

Kristin Lauter | Microsoft Research |

Dan Bernstein | University of Illinois, Chicago |

Alina Bucur | University of California, San Diego |

Joe Buhler | Center for Communications Research, La Jolla |

Henri Cohen | Université de Bordeaux 1 |

Chantal David | Concordia University |

Steven Galbraith | University of Auckland |

Dan Gordon | Center for Communications Research, La Jolla |

Everett Howe (cochair) | Center for Communications Research, La Jolla |

Kiran Kedlaya (cochair) | University of California, San Diego |

Jürgen Klüners | Universität Paderborn |

Kristin Lauter | Microsoft Research |

Fernando Rodriguez Villegas | University of Texas, Austin |

Peter Stevenhagen | Universiteit Leiden |

Michael Stoll | Universität Bayreuth |

Bianca Viray | Brown University |

Microsoft Research |

National Science Foundation |

National Security Agency |

Number Theory Foundation |

University of California, San Diego |

No. | Year | Location | Proceedings | |

I | 1994 | Cornell University | (Ithaca, NY, USA) | LNCS 877 |

II | 1996 | Université Bordeaux 1 | (Talence, France) | LNCS 1122 |

III | 1998 | Reed College | (Portland, OR, USA) | LNCS 1423 |

IV | 2000 | Universiteit Leiden | (The Netherlands) | LNCS 1838 |

V | 2002 | University of Sydney | (Australia) | LNCS 2369 |

VI | 2004 | University of Vermont | (Burlington, VT, USA) | LNCS 3076 |

VII | 2006 | Technische Universität Berlin | (Germany) | LNCS 4076 |

VIII | 2008 | Banff Centre | (Banff, Alberta, Canada) | LNCS 5011 |

IX | 2010 | INRIA | (Nancy, France) | LNCS 6197 |

X | 2012 | University of California | (San Diego, CA, USA) | OBS 1 |

Proceedings of the previous ANTS meetings have been published in the Springer Lecture Notes in Computer Science series (LNCS). This volume is the first volume of the Mathematical Sciences Publishers's Open Book Series (OBS).

ANTS XI is planned to be held in August 2014 in Gyeongju, Korea. The organizing committee includes Jung Hee Cheon (Seoul National University), Soonhak Kwon (Sungkyunkwan University), Hyang-Sook Lee (Ewha Womans University), and Hyungju Park (POSTECH).