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MOV attack in various subgroups on elliptic curves
 Illinois J. Math
"... Abstract. We estimate the probabilities that the MenezesOkamotoVanstone reduction of the discrete logarithm problem on an elliptic curve E to the discrete logarithm problem in a certain finite field succeeds for various groups on points on E. Our bounds imply that in all interesting cases these pr ..."
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Cited by 4 (1 self)
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Abstract. We estimate the probabilities that the MenezesOkamotoVanstone reduction of the discrete logarithm problem on an elliptic curve E to the discrete logarithm problem in a certain finite field succeeds for various groups on points on E. Our bounds imply that in all interesting cases these probabilities are exponentially small. This extends results of Balasubramanian and Koblitz who have treated the instance in which the order of the group of points on E is prime. 1.
Arbitrarily Tight Bounds On The Distribution Of Smooth Integers
 Proceedings of the Millennial Conference on Number Theory
, 2002
"... This paper presents lower bounds and upper bounds on the distribution of smooth integers; builds an algebraic framework for the bounds; shows how the bounds can be computed at extremely high speed using FFTbased powerseries exponentiation; explains how one can choose the parameters to achieve ..."
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Cited by 3 (1 self)
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This paper presents lower bounds and upper bounds on the distribution of smooth integers; builds an algebraic framework for the bounds; shows how the bounds can be computed at extremely high speed using FFTbased powerseries exponentiation; explains how one can choose the parameters to achieve any desired level of accuracy; and discusses several generalizations.