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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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/

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