On some computational problems in finite abelian groups

  title={On some computational problems in finite abelian groups},
  author={Johannes A. Buchmann and Michael John Jacobson and Edlyn Teske},
  journal={Math. Comput.},
We present new algorithms for computing orders of elements, discrete logarithms, and structures of finite abelian groups. We estimate the computational complexity and storage requirements, and we explicitly determine the O-constants and Ω-constants. We implemented the algorithms for class groups of imaginary quadratic orders and present a selection of our experimental results. Our algorithms are based on a modification of Shanks' baby-step giant-step strategy, and have the advantage that their… 

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