Isogeny Club - Season 4 - Talk #1: SCALLOP

This is the discussion thread for the first session of season four of The Isogeny Club, where Simon presents his talk titled: SCALLOP: a somewhat scalable effective group action from isogenies

In this talk, we motivate and present an effective group action based on isogenies of supersingular curves, called SCALLOP. Similar to CSIDH and OSIDH, an imaginary order’s class group acts on a set of oriented supersingular elliptic curves. Its main benefit compared to CSIDH is that the structure of the acting class group can be easily computed - it can even be partially controlled when choosing parameters. This data is required to uniquely represent and efficiently act by arbitrary group elements which is useful for example when constructing efficient signatures.

The class group structure for the smallest parameter set of CSIDH could be computed with a world record class group computation - leading to CSI-FiSh. However, for larger security levels computing the structure in CSIDH remains elusive with currently known methods. On the other hand, SCALLOP can be instantiated for security levels comparable to CSIDH-512 and CSIDH-1024 using only modest computational resources. We discuss several of our design choices with respect to security and computational efficiency. Asymptotically, some scaling issues remain and while evaluating the SCALLOP group action is feasible, its performance requires further improvement before it can be used for practical applications.


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