We continue our study on the elliptic curve discrete logarithm problem over finite extension fields. We show, among others, the following results:
For sequences of prime powers and natural numbers with and for , the discrete logarithm problem in the groups of rational points of elliptic curves over the fields can be solved in subexponential expected time .
Let , be fixed. Then the problem over fields , where is a prime power and a natural number with , can be solved in an expected time of .
"On the discrete logarithm problem in elliptic curves II." Algebra Number Theory 7 (6) 1281 - 1323, 2013. https://doi.org/10.2140/ant.2013.7.1281