On the discrete logarithm problem in elliptic curves
2010 ◽
Vol 147
(1)
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pp. 75-104
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Keyword(s):
AbstractWe study the elliptic curve discrete logarithm problem over finite extension fields. We show that for any sequences of prime powers (qi)i∈ℕand natural numbers (ni)i∈ℕwithni⟶∞andni/log (qi)⟶0 fori⟶∞, the elliptic curve discrete logarithm problem restricted to curves over the fields 𝔽qniican be solved in subexponential expected time (qnii)o(1). We also show that there exists a sequence of prime powers (qi)i∈ℕsuch that the problem restricted to curves over 𝔽qican be solved in an expected time ofe𝒪(log (qi)2/3).
2004 ◽
Vol 7
◽
pp. 167-192
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2002 ◽
Vol 5
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pp. 127-174
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2004 ◽
Vol 7
◽
pp. 50-72
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