Geodesic
Some remarks on the elliptic curve discrete logarithm problem
Matematičeskie voprosy kriptografii, Tome 7 (2016) no. 2, pp. 115-120 
A. Yu. Nesterenko. Some remarks on the elliptic curve discrete logarithm problem. Matematičeskie voprosy kriptografii, Tome 7 (2016) no. 2, pp. 115-120. http://geodesic.mathdoc.fr/item/MVK_2016_7_2_a10/
@article{MVK_2016_7_2_a10,
     author = {A. Yu. Nesterenko},
     title = {Some remarks on the elliptic curve discrete logarithm problem},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {115--120},
     year = {2016},
     volume = {7},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MVK_2016_7_2_a10/}
}
TY  - JOUR
AU  - A. Yu. Nesterenko
TI  - Some remarks on the elliptic curve discrete logarithm problem
JO  - Matematičeskie voprosy kriptografii
PY  - 2016
SP  - 115
EP  - 120
VL  - 7
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MVK_2016_7_2_a10/
LA  - en
ID  - MVK_2016_7_2_a10
ER  - 
%0 Journal Article
%A A. Yu. Nesterenko
%T Some remarks on the elliptic curve discrete logarithm problem
%J Matematičeskie voprosy kriptografii
%D 2016
%P 115-120
%V 7
%N 2
%U http://geodesic.mathdoc.fr/item/MVK_2016_7_2_a10/
%G en
%F MVK_2016_7_2_a10

Voir la notice de l'article provenant de la source Math-Net.Ru

We propose an algorithm for solving the discrete logarithm problem on the elliptic curve. This algorithm uses additional information on the multiplicative order of the solution and may be realised in parallel.

[1] Blake I., Seroussi G., Smart N., Elliptic Curves in Cryptography, London Math. Soc. Lect. Notes, 265, Cambridge Univ. Press, Cambridge, 1999, 224 pp. | MR | Zbl

[2] van Oorschot P., Wiener M. J., “Parallel collision search with cryptanalytic applications”, J. Cryptology, 12:1 (1999), 1–28 | DOI | MR | Zbl

[3] Pollard J. M., “Theorems on factorization and primality testing”, Proc. Cambridge Phil. Soc., 76:3 (1974), 521–528 | DOI | MR | Zbl

[4] Pollard J. M., “Monte Carlo methods for index computation $\pmod p$”, Math. Comput., 32:143 (1978), 918–924 | MR | Zbl

[5] Shanks D., “Class number, a theory of factorization and genera”, 1969 Number Theory Institute, Proc. Symp. Pure Math., XX, 1971, 415–440 | DOI | MR | Zbl

[6] Teske E., “Square-root algorithms for the discrete logarithm problem (a survey)”, Publickey Cryptography and Computational Number Theory, Walter de Gruyter, Berlin etc., 2001, 283–301 | MR