@article{MVK_2019_10_2_a11,
author = {A. Yu. Nesterenko},
title = {Construction of strong elliptic curves suitable for cryptographic applications},
journal = {Matemati\v{c}eskie voprosy kriptografii},
pages = {135--144},
year = {2019},
volume = {10},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/MVK_2019_10_2_a11/}
}
A. Yu. Nesterenko. Construction of strong elliptic curves suitable for cryptographic applications. Matematičeskie voprosy kriptografii, Tome 10 (2019) no. 2, pp. 135-144. http://geodesic.mathdoc.fr/item/MVK_2019_10_2_a11/
[1] D. Aranha, P. Barreto, G. Pereira, J. Ricardini, A note on high-security general-purpose elliptic curves, , 2013 http://eprint.iacr.org/2013/647
[2] H. Baier, J. Buchmann, “Efficient construction of cryptographically strong elliptic curves”, INDOCRYPT 2000, Lect. Notes Comput. Sci., 1977, 2000, 191–202 | DOI | MR | Zbl
[3] D. Bernstein, “Curve25519: New Diffie-Hellman speed records”, PKC 2006, Lect. Notes Comput. Sci., 3958, 2006, 207–228 | DOI | MR
[4] D. Bernstein, T. Lange, “Faster addition and doubling on elliptic curves”, ASIACRYPT 2007, Lect. Notes Comput. Sci., 4833, 2007, 29–50 | DOI | MR | Zbl
[5] I. Blake, G. Seroussi, N. Smart, Elliptic Curves in Cryptography, London Math. Soc. Lecture Notes, 265, Cambridge Univ. Press, Cambridge, 1999, 204 pp. | MR | Zbl
[6] D. Chudnovsky, G. Chudnovsky, “Sequences of numbers generated by addition in formal groups and new primality and factorization tests”, Adv. Appl. Math., 7 (1986), 385–434 | DOI | MR | Zbl
[7] D. Cox, Primes of the Form $x^2 + ny^2$: Fermat, Class Field Theory and Complex Multiplication, J. Wiley and Sons, N.Y., etc., 1989, 363 pp. | MR | Zbl
[8] R. Crandal, C. Pomerance, Prime Numbers: A Computational Perspective, 2nd ed., Springer, 2005 | MR | Zbl
[9] D. Husemöller, Elliptic Curves, 2nd ed., Springer, Heidelberg etc., 2004 | Zbl
[10] GOST R 34.10-2012. Information technology. Cryptographic data security. Signature and verification processes of [electronic] digital signature, Standardinform, M., 2012
[11] W. Bosma, J. Cannon (eds.), Discovering Mathematics with Magma, Algor. and Comput. in Math., 19, Springer, Heidelberg etc., 2006, 364 pp. | MR | Zbl
[12] A. Menezes, S. Vanstone, T. Okamoto, “Reducing elliptic curve logarithms to logarithms in a finite field”, 23rd ACM Symp. Theory of Computing (1991), 80–89 | MR
[13] P. L. Montgomery, “Speeding the Pollard and elliptic curve methods of factorization”, Math. Comp., 48:177 (1987), 243–267 | DOI | MR
[14] A. Yu. Nesterenko, “Construction of elliptic curves endomorphisms”, Matematicheskie Voprosy Kriptografii, 5:2 (2014), 99–102 | DOI
[15] A. Yu. Nesterenko, “Some remarks on the elliptic curve discrete logarithm problem”, Matematicheskie Voprosy Kriptografii, 7:2 (2016), 115–120 | DOI | MR
[16] P. C. van Oorschot, M. J. Wiener, “Parallel collision search with cryptanalytic applications”, J. Cryptology, 12:1 (1999), 1–28 | DOI | MR | Zbl
[17] C. Petit, M. Kosters, A. Messeng, “Algebraic approaches for the elliptic curve discrete logarithm problem over prime fields”, PKC 2016, Lect. Notes Comput. Sci., 9615, 2016, 3–18 | DOI | MR | Zbl
[18] V. Popov, I. Kurepkin, S. Leontiev, RFC4357. Additional cryptographic algorithms for use with GOST 28147-89, GOST R 34.10-94, GOST R 34.10-2001, and GOST R 34.11-94 algorithms, 2006 https://www.rfc-editor.org/info/rfc4357
[19] J. M. Pollard, “Monte Carlo methods for index computation $\pmod p$”, Math. Comp., 32:143 (1978), 918–924 | MR | Zbl
[20] M. O. Rabin, “Probabilistic algorithm for testing primality”, J. Number Theory, 12:1 (1980), 128–138 | DOI | MR | Zbl
[21] R. L. Rivest, R. D. Silverman, Are “strong” primes needed for RSA?, , 1999, 23 pp. https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.310.4183&rep=rep1&type=pdf
[22] T. Satoh, K. Araki, “Fermat quotients and the polynomial time discrete log algorithm for anomalous curves”, Comm. Math. Univ. Sancti Pauli, 47 (1998), 81–92 | MR | Zbl
[23] R. Schoof, “Counting points on elliptic curves over finite fields”, J. Theorie des Nombres de Bordeaux, 7:1 (1995), 219–254 | DOI | MR | Zbl
[24] I. Semaev, “Evaluation of discrete logarithms in a group of ptorsion points of an elliptic curve in characteristic $p$”, Math. Comp., 67:221 (1998), 353–356 | DOI | MR | Zbl
[25] J. H. Silverman, The Arithmetic of Elliptic Curves, Springer, Heidelberg etc., 1986, 400 pp. | MR | Zbl
[26] N. Smart, “The discrete logarithm problem on elliptic curves of trace one”, J. Cryptology, 12 (1999), 193–196 | DOI | MR | Zbl
[27] Technical Guideline TR-03111. Elliptic curve cryptography, German Federal Office for Inform. Secur., 2007
[28] E. Teske, “Square-root algorithms for the discrete logarithm problem (a survey)”, Publickey cryptography and computational number theory (Warsaw, 2000), de Gruyter, Berlin, 2001, 283–301 | MR | Zbl