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For a Sidelnikov sequence of period p m − 1 we obtain tight lower bounds on its linear complexity L over F p. In particular, these bounds imply that, uniformly over all p and m, L is close to its largest possible value p m − 1.

We consider the problem of recovering a hidden element s of a finite field F q of q elements from queries to an oracle that for a given x ∈ F q returns (x + s) e for a given divisor e | q − 1. We use some techniques from additive combinatorics and analytic number theory that lead to more efficient algorithms than the naive interpolation algorithm, for… (More)

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