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For a given elliptic curve $$\\mathbf {E}$$E over a finite field of odd characteristic and a rational function f on $$\\mathbf {E}$$E we first study the linear complexity profiles of the sequences f(nG), $$n=1,2,\\dots $$n=1,2,ź which complements earlier results of Hess and Shparlinski. We use Edwards coordinates to be able to deal with many f where Hess and Shparlinski's result does not apply. Moreover, we study the linear complexities of the (generalized) elliptic curve power generators $$f(e^nG)$$f(enG), $$n=1,2,\\dots $$n=1,2,ź We present large families of functions f such that the linear complexity profiles of these sequences are large.

On the linear complexity profile of some sequences derived from elliptic curves