edited by: Dan Boneh
We introduce the concept of torus-based cryptography, give a new public key system called CEILIDH, and compare it to other discrete log based systems including Lucas-based systems and XTR. Like those systems, we obtain small key sizes. While Lucas-based systems and XTR are essentially restricted to exponentiation, we are able to perform multiplication as well. We also disprove the open conjectures from , and give a new algebro-geometric interpretation of the approach in that paper and of LUC and XTR.