On the discrete logarithm problem in elliptic curves
نویسندگان
چکیده
We study the elliptic curve discrete logarithm problem over finite extension fields. We show that for any sequences of prime powers (qi)i∈N and natural numbers (ni)i∈N with ni −→ ∞ and ni log(qi) −→ 0 for i −→ ∞, the elliptic curve discrete logarithm problem restricted to curves over the fields Fqi i can be solved in subexponential expected time (qi i ) . We also show that there exists a sequence of prime powers (qi)i∈N such that the problem restricted to curves over Fqi can be solved in an expected time of ei 2/3).
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