In this paper, we consider the Frobenius endomorphism on twisted Edwards curve and give the characteristic polynomial of the map. Applying the Frobenius endomorphism on twisted Edwards curve, we construct a skew-Frobenius map defined on the quadratic twist of an twisted Edwards curve. Our results show that the Frobenius endomorphism on twisted Edwards curve and the skew-Frobenius endomorphism o...

Edwards curves have attracted great interest for several reasons. When curve parameters are chosen properly, the addition formulas use only 10M+1S. The formulas are strongly unified, i.e., work without change for doublings; even better, they are complete, i.e., work without change for all inputs. Dedicated doubling formulas use only 3M + 4S, and dedicated tripling formulas use only 9M + 4S. Thi...