Geodesic
Some Remarks on Arithmetical Properties of Recursive Sequences on Elliptic Curves over a Finite Field
Matematičeskie zametki, Tome 82 (2007) no. 6, pp. 926-933

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In connection with problems of information theory, we study arithmetical progressions constructed at the points of elliptic curves over a finite field. For certain types of such curves, we establish the distribution of the quadratic residues at the $x$-coordinates of the sequence of points corresponding to progressions if the elliptic curves is defined over a simple field. A description of the set of all progressions on elliptic curves over a finite field is also given.
Keywords: Weierstrass normal form, elliptic curve, arithmetical progression, finite field, generator of pseudorandom numbers, Sylow subgroup. 
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     author = {V. E. Tarakanov},
     title = {Some {Remarks} on {Arithmetical} {Properties} of {Recursive} {Sequences} on {Elliptic} {Curves} over a {Finite} {Field}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {926--933},
     publisher = {mathdoc},
     volume = {82},
     number = {6},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_6_a12/}
}
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V. E. Tarakanov. Some Remarks on Arithmetical Properties of Recursive Sequences on Elliptic Curves over a Finite Field. Matematičeskie zametki, Tome 82 (2007) no. 6, pp. 926-933. http://geodesic.mathdoc.fr/item/MZM_2007_82_6_a12/