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Lower bounds on the linear complexity of the discrete logarithm in finite fields

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2 Author(s)
Meidl, W. ; Inst. of Discrete Math., Austrian Acad. of Sci., Vienna, Austria ; Winterhof, A.

Let p be a prime, r a positive integer, q=pr, and d a divisor of p(q-1). We derive lower bounds on the linear complexity over the residue class ring Zd of a (q-periodic) sequence representing the residues modulo d of the discrete logarithm in Fq . Moreover, we investigate a sequence over Fq representing the values of a certain polynomial over Fq introduced by Mullen and White (1986) which can be identified with the discrete logarithm in Fq via p-adic expansions and representations of the elements of Fq with respect to some fixed basis

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Information Theory, IEEE Transactions on  (Volume:47 ,  Issue: 7 )