Abstract
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 [2], and give a new algebro-geometric interpretation of the approach in that paper and of LUC and XTR.
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Rubin, K., Silverberg, A. (2003). Torus-Based Cryptography. In: Boneh, D. (eds) Advances in Cryptology - CRYPTO 2003. CRYPTO 2003. Lecture Notes in Computer Science, vol 2729. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45146-4_21
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DOI: https://doi.org/10.1007/978-3-540-45146-4_21
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