On the discrete logarithm problem in elliptic curves II
Claus Diem · Algebra & Number Theory · 2013
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 .qi / i2ގ and natural numbers .ni / i2ގ with n i ! 1 and n i =log.qi / 2 !0 for i ! 1, the discrete logarithm problem in the groups of rational points of elliptic curves over the fields ކ q n i i can be solved in subexponential expected time .qLet a, b > 0 be fixed.Then the problem over fields ކ q n , where q is a prime power and n a natural number with a log.q/ 1=3 Ä n Ä b log.q/, can be solved in an expected time of e ᏻ.log.qn / 3=4 / .