Since the first implementation of elliptic curves over finite fields for the GnuPG and the implementation on OpenSSL of the curves over finite and binary fields, back in the 2000s, many things have happened over this mathematical construction. We've witnessed instances like the birth and death of certain isogenies or searching for algorithms that resist quantum computing, which are only a few to mention.

We moved from the NIST curves on the P1363 to use Edwards variety, and there is a recent proposal with Double-odd curves. So the assortment is increasing, but we need to squeeze them more. For each new curve, all users always share the same group. This talk will review the path walked and evaluate the progress in implementing the Double-odd Jacobi Quartic in Libgcrypt and GnuPG.