How to compute an isogeny on the extended Jacobi quartic curves?
Abstract
Computing isogenies between elliptic curves is a significant
part of post-quantum cryptography with many practical
applications (for example, in SIDH, SIKE, B-SIDH, or CSIDH
algorithms). Comparing to other post-quantum algorithms, the
main advantages of these protocols are smaller keys, the similar
idea as in the ECDH, and a large basis of expertise about
elliptic curves. The main disadvantage of the isogeny-based
cryptosystems is their computational efficiency - they are slower
than other post-quantum algorithms (e.g., lattice-based). That is
why so much effort has been put into improving the hitherto
known methods of computing isogenies between elliptic curves.
In this paper, we present new formulas for computing isogenies
between elliptic curves in the extended Jacobi quartic form
with two methods: by transforming such curves into the short
Weierstrass model, computing an isogeny in this form and then
transforming back into an initial model or by computing an
isogeny directly between two extended Jacobi quartics.
References
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