Algorithmic number theory : 6th international symposium ANTS VI Burlington VT USA June 13 18 2004 ; proceedings This book constitutes the refereed proceedings of the 6th International Algorithmic Number Theory Symposium ANTS 2004 held in Burlington VT USA in June 2004. The 30 revised full papers presented together with 3 invited papers were carefully reviewed and selected for inclusion in the book. Among the topics addressed are zeta functions elliptic curves hyperelliptic curves GCD algorithms number field computations complexity primality testing Weil and Tate pairings cryptographic algorithms function field sieve algebraic function field mapping quartic fields cubic number fields lattices discrete logarithms and public key cryptosystems