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1 results

  • On the discrete logarithm problem in elliptic curves

  • Part of
  • Claus Diem
  • Journal:
    Compositio Mathematica / Volume 147 / Issue 1 / January 2011
    Published online by Cambridge University Press:
    15 October 2010, pp. 75-104
    Print publication:
    January 2011
    • Article
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  • 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 𝔽qnii can be solved in subexponential expected time (qnii)o(1). 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 e𝒪(log (qi)2/3).