Simplified isogeny formulas on twisted Jacobi quartic curves (Q2066406)

The authors introduce a \(w\)-coordinate system on Jacobi quartic curves and prove Montgomery-like group law formulas on such curves. Also, they give the connection between such \(w\)-coordinate and the projection map to some Kummer line. Explicit formulas for 2-isogenies and odd degree isogenies between Jacobi quartic curves are presented in the paper, too. The new derived formulas, especially those of curve parameters in odd degree isogenies, are simple to express in low algebraic complexity. The author also give the simple isogeny formulas based on the \(w\)-coordinate on Jacobi quartic curve, which share the similar forms as those on Montgomery curves (with only \(x\)-coordinate).