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

L Mérai, A Winterhof - Designs, Codes and Cryptography, 2016 - Springer
Designs, Codes and Cryptography, 2016Springer
For a given elliptic curve EE over a finite field of odd characteristic and a rational function f
on EE we first study the linear complexity profiles of the sequences f (nG), n= 1, 2,\dots n= 1,
2,⋯ 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 (en G), n= 1, 2,\dots n= 1, 2,⋯ We present large families of functions f …
Abstract
For a given elliptic curve over a finite field of odd characteristic and a rational function f on we first study the linear complexity profiles of the sequences f(nG), 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 , We present large families of functions f such that the linear complexity profiles of these sequences are large.
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