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On the Bounded Sum-of-Digits Discrete Logarithm Problem in Finite Fields

2005
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SIAM journal on computing (Print)
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In this paper, we study the bounded sum-of-digits discrete logarithm problem in finite fields. Our results concern primarily with fields Fqn where n|q − 1. The fields are called Kummer extensions of Fq. It is known that we can efficiently construct an element g with order greater than 2 n in the fields. Let Sq(•) be the function from integers to the sum of digits in their q-ary expansions. We first present an algorithm that given g e (0 ≤ e < q n ) finds e in random polynomial time, provided

doi:10.1137/s0097539704446037
fatcat:wxmpgefqkbbg7nnxgxyfmdjeke