Algorithms going under the name `complex multiplication' typically have a run time that is exponential in the size of the input data. We will show that nevertheless such algorithms may sometimes be profitably used in cryptographic settings.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/5044