[Resource Topic] 2003/039: Torus-based cryptography

Welcome to the resource topic for 2003/039

Torus-based cryptography

Authors: Karl Rubin, Alice Silverberg


We introduce cryptography based on algebraic tori, give a new public key system called CEILIDH, and compare it to other discrete log based systems including LUC and XTR. Like those systems, we obtain small key sizes. While LUC and XTR are essentially restricted to exponentiation,
we are able to perform multiplication as well. We also disprove the open conjectures from the paper “Looking beyond XTR”, and give a new algebro-geometric interpretation of the approach in that paper and of LUC and XTR.

ePrint: https://eprint.iacr.org/2003/039

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