Generating Random Factored Ideals in Number Fields

  title={Generating Random Factored Ideals in Number Fields},
  author={Zachary B. Charles},
  journal={Math. Comput.},
We present a randomized polynomial-time algorithm to generate a random integer according to the distribution of norms of ideals at most N in any given number field, along with the factorization of the integer. Using this algorithm, we can produce a random ideal in the ring of algebraic integers uniformly at random among ideals with norm up to N, in polynomial time. We also present a variant of this algorithm for generating ideals in function fields. 
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