On isogeny classes of Edwards curves over finite fields
We count the number of isogeny classes of Edwards curves over odd characteristic finite
fields, answering a question recently posed by Rezaeian and Shparlinski. We also show that
each isogeny class contains a complete Edwards curve, and that an Edwards curve is
isogenous to an original Edwards curve over Fq if and only if its group order is divisible by 8
if q≡− 1 (mod4), and 16 if q≡ 1 (mod4). Furthermore, we give formulae for the proportion of
d∈ Fq∖{0, 1} for which the Edwards curve Ed is complete or original, relative to the total …
fields, answering a question recently posed by Rezaeian and Shparlinski. We also show that
each isogeny class contains a complete Edwards curve, and that an Edwards curve is
isogenous to an original Edwards curve over Fq if and only if its group order is divisible by 8
if q≡− 1 (mod4), and 16 if q≡ 1 (mod4). Furthermore, we give formulae for the proportion of
d∈ Fq∖{0, 1} for which the Edwards curve Ed is complete or original, relative to the total …
We count the number of isogeny classes of Edwards curves over odd characteristic finite fields, answering a question recently posed by Rezaeian and Shparlinski. We also show that each isogeny class contains a complete Edwards curve, and that an Edwards curve is isogenous to an original Edwards curve over Fq if and only if its group order is divisible by 8 if q≡−1(mod4), and 16 if q≡1(mod4). Furthermore, we give formulae for the proportion of d∈Fq∖{0,1} for which the Edwards curve Ed is complete or original, relative to the total number of d in each isogeny class.
Elsevier