[
1. Koblitz, N. A Course in Number Theory and Cryptography. Springer Science & Business Media, 2 September 1994.10.1007/978-1-4419-8592-7
]Search in Google Scholar
[
2. Caelli, W. J., E. P. Dawson, S. A. Rea. PKI, Elliptic Curve Cryptography, and Digital Signatures. – Computers & Security, Vol. 18, 1 January 1999, No 1, pp. 47-66.10.1016/S0167-4048(99)80008-X
]Search in Google Scholar
[
3. Valenta, L., N. Sullivan, A. Sanso, N. Heninger. In Search of CurveSwap: Measuring Elliptic Curve Implementations in the Wild. – In: Proc. of 2018 IEEE European Symposium on Security and Privacy (EuroS&P’18), 24 April 2018, IEEE, pp. 384-398.10.1109/EuroSP.2018.00034
]Search in Google Scholar
[
4. Koblitz, N., A. Menezes, S. Vanstone. The State of Elliptic Curve Cryptography. Designs, Codes and Cryptography. – Vol. 19, March 2000, No 2, pp. 173-193.10.1023/A:1008354106356
]Search in Google Scholar
[
5. Hankerson, D., A. Menezes, S. Vanstone. Guide to Elliptic Curve Cryptography. Springer, 2003. ISBN: 0-387-95273-X.
]Search in Google Scholar
[
6. Menezes, A. J., T. Okamoto, S. A. Vanstone. Reducing Elliptic Curve Logarithms to Logarithms in a Finite Field. – IEEE Transactions on Information Theory, Vol. 39, September 1993, No 5, pp. 1639-1646.10.1109/18.259647
]Search in Google Scholar
[
7. Koblitz, A. H., N. Koblitz, A. Menezes. Elliptic Curve Cryptography: The Serpentine Course of a Paradigm Shift. – Journal of Number Theory, Vol. 131, 1 May 2011, No 5, pp. 781-814. DOI:10.1016/j.jnt.2009.01.006.10.1016/j.jnt.2009.01.006
]Search in Google Scholar
[
8. Smart, N. P. The Discrete Logarithm Problem on Elliptic Curves of Trace One. – Journal of Cryptology, Vol. 12, 1 Jun 1999, No 3, pp. 193-196.10.1007/s001459900052
]Search in Google Scholar
[
9. Flori, J. P., J. Plût, J. R. Reinhard, M. Ekerå. Diversity and Transparency for ECC. – IACR Cryptol. ePrint Arch., 11 Jun 2015, 2015/659.
]Search in Google Scholar
[
10. Menezes, A. Evaluation of Security Level of Cryptography: The Elliptic Curve Discrete Logarithm Problem (ECDLP). University of Waterloo, 14 December 2001.
]Search in Google Scholar
[
11. Baier, H., J. Buchmann. Generation Methods of Elliptic Curves. An Evaluation Report for the Information-Technology Promotion Agency, Japan, 27 August 2002.
]Search in Google Scholar
[
12. Semaev, I. Evaluation of Discrete Logarithms in a Group of p-Torsion Points of an Elliptic Curve in Characteristic p. – Mathematics of Computation, Vol. 67, 1998, No 221, pp. 353-356.10.1090/S0025-5718-98-00887-4
]Search in Google Scholar
[
13. Washington, L. C. Elliptic Curves: Number Theory and Cryptography. CRC Press, 3 April 2008.
]Search in Google Scholar
[
14. Konstantinou, E., A. Kontogeorgis, Y. C. Stamatiou, et al. – J Cryptol., Vol. 23, 2010, 477. https://doi.org/10.1007/s00145-009-9037-210.1007/s00145-009-9037-2
]Search in Google Scholar
[
15. Konstantinou, E., A. Kontogeorgis, Y. C. Stamatiou, C. Zaroliagis. On the Efficient Generation of Prime-Order Elliptic Curves. – Journal of Cryptology, Vol. 23, 1 July 2010, No 3, pp. 477-503.10.1007/s00145-009-9037-2
]Search in Google Scholar
[
16. Savaş, E., T. A. Schmidt, C. K. Koç. Generating Elliptic Curves of Prime Order. – In: Proc. of International Workshop on Cryptographic Hardware and Embedded Systems, 14 May 2001. Berlin, Heidelberg, Springer, pp. 142-158.10.1007/3-540-44709-1_13
]Search in Google Scholar
[
17. Schoof, R. Elliptic Curves over Finite Fields and the Computation of Square Roots mod p. – Mathematics of Computation, Vol. 44, 1985, No 170, pp. 483-494.10.1090/S0025-5718-1985-0777280-6
]Search in Google Scholar
[
18. I. F. Blake, G. Seroussi, N. P. Smart, Eds. Advances in Elliptic Curve Cryptography. – Cambridge University Press, Vol. 317, 25 April 2005.10.1017/CBO9780511546570
]Search in Google Scholar
[
19. Menezes, A. J., T. Okamoto, S. A. Vanstone. Reducing Elliptic Curve Logarithms to Logarithms in a Finite Field. – IEEE Transactions on Information Theory, Vol. 39, September 1993, No 5, pp. 1639-1646.10.1109/18.259647
]Search in Google Scholar
[
20. Shor, P. W. Algorithms for Quantum Computation: Discrete Logarithms and Factoring. – In: Proc. of 35th Annual Symposium on Foundations of Computer Science, IEEE, 20 November 1994, pp. 124-134.
]Search in Google Scholar
[
21. Balasubramanian, R., N. Koblitz. The Improbability that an Elliptic Curve has Subexponential Discrete Log Problem under the Menezes-Okamoto-Vanstone Algorithm. – Journal of Cryptology, Vol. 11, 1 March 1998, No 2, pp. 141-145.10.1007/s001459900040
]Search in Google Scholar
[
22. Gaudry, P., F. Hess, N. P. Smart. Constructive and Destructive Facets of Weil Descent on Elliptic Curves. – Journal of Cryptology, Vol. 15, March 2002, No 1, pp. 19-46.10.1007/s00145-001-0011-x
]Search in Google Scholar
[
23. PUB, F. Digital Signature Standard (DSS). – FIPS PUB. 27 January 2000, pp. 186-192.
]Search in Google Scholar
[
24. SEC, S. 2: Recommended Elliptic Curve Domain Parameters. Standards for Efficient Cryptography Group, Certicom Corp., September 2000.
]Search in Google Scholar
[
25. Brainpool, E. C. ECC Brainpool Standard Curves and Curve Generation. October, 2005. http://www.ecc-brainpool.org.
]Search in Google Scholar
[
26. Lochter, M., J. Mekle. RFC 5639: ECC Brainpool Standard Curves & Curve Generation. Internet Engineering Task Force, March 2010.
]Search in Google Scholar
[
27. Bernstein, D. J., Tanja Lange. SafeCurves: Choosing Safe Curves for Elliptic Curve Cryptography. 2015. Citations in this document. September 2014. https://safecurves.cr.yp.to10.1112/S1461157014000394
]Search in Google Scholar
[
28. Liu, Z., H. Seo. IoT-NUMS: Evaluating NUMS Elliptic Curve Cryptography for IoT Platforms. – IEEE Transactions on Information Forensics and Security, Vol. 14, 13 July 2018, No 3, pp. 720-729.10.1109/TIFS.2018.2856123
]Search in Google Scholar
[
29. Chen, L., et. al. Report on Post-Quantum Cryptography. US Department of Commerce, National Institute of Standards and Technology, 28 April 2016.
]Search in Google Scholar
[
30. Roetteler, M., M. Naehrig, K. M. Svore, K. Lauter. Quantum Resource Estimates for Computing Elliptic Curve Discrete Logarithms. – In: Proc. of International Conference on the Theory and Application of Cryptology and Information Security, 3 December 2017, Cham, Springer, pp. 241-270.10.1007/978-3-319-70697-9_9
]Search in Google Scholar
[
31. Pohlig, S., M. Hellman. An Improved Algorithm for Computing Logarithms over GF(p) and Its Cryptographic Significance (Corresp.). – IEEE Transactions on Information Theory, Vol. 24, January 1978, No 1, pp. 106-110.10.1109/TIT.1978.1055817
]Search in Google Scholar
[
32. Van Oorschot, P. C., M. J. Wiener. Parallel Collision Search with Cryptanalytic Applications. – Journal of Cryptology, Vol. 12, January 1999, No 1, pp. 1-28.10.1007/PL00003816
]Search in Google Scholar
[
33. Bos, J. W., C. Costello, P. Longa, M. Naehrig. Selecting Elliptic Curves for Cryptography: An Efficiency and Security Analysis. – Journal of Cryptographic Engineering, Vol. 6, November 2016, No 4, pp. 259-286.10.1007/s13389-015-0097-y
]Search in Google Scholar
[
34. Hamburg, M. Ed448-Goldilocks, a New Elliptic Curve. IACR Cryptol. ePrint Arch. Jun 2015, 2015/625.
]Search in Google Scholar
[
35. Crandall, R. E. Method and Apparatus for Public Key Exchange in a Cryptographic System. October 1992. US Patent. (5,159,632).
]Search in Google Scholar
[
36. Dąbrowski, P., R. Gliwa, J. Szmidt, R. Wicik. Generation and Implementation of Cryptographically Strong Elliptic Curves. – In: Proc. of International Conference on Number-Theoretic Methods in Cryptology, 11 September 2017. Cham, Springer, pp. 25-36.10.1007/978-3-319-76620-1_2
]Search in Google Scholar
[
37. Morain, F. Building Cyclic Elliptic Curves Modulo Large Primes. – In: Proc. of Workshop on the Theory and Application of of Cryptographic Techniques, 8 April 1991. Berlin, Heidelberg, Springer, pp. 328-336.10.1007/3-540-46416-6_28
]Search in Google Scholar
[
38. Cohen, H. A Course in Computational Algebraic Number Theory. Berlin, Springer-Verlag, August 1993.10.1007/978-3-662-02945-9
]Search in Google Scholar
[
39. Bernstein, D. J., et.al. How to Manipulate Curve Standards: A White Paper for the Black Hat. – In: Proc. of International Conference on Research in Security Standardisation, 15 December 2015, Cham, Springer, pp. 109-139. http://bada55.cr.yp.to10.1007/978-3-319-27152-1_6
]Search in Google Scholar
[
40. San, C. V. A Survey of Elliptic Curve Cryptosystems. Part I. Introductory. Technical Report, NAS Technical Report-NAS-03-012, 2003.
]Search in Google Scholar
[
41. https://www.schneier.com/blog/archives/2013/09/the_nsa_is_brea.html
]Search in Google Scholar
[
42. Costello, C., P. Longa, M. Naehrig. A Brief Discussion on Selecting New Elliptic Curves. Microsoft Research. Microsoft, 8 June 2015.
]Search in Google Scholar
[
43. https://www.nist.gov/system/files/documents/2017/05/09/2014-VCAT-Annual-Report_final.pdf
]Search in Google Scholar
[
44. https://cryptosith.org/michael/data/talks/2015-04-28-UWNumberTheorySeminar.pdf
]Search in Google Scholar
[
45. Scott, M. Re: NIST Announces Set of Elliptic Curves. Posting to the sci.crypt Mailing List, 1999.
]Search in Google Scholar
[
46. Savaş, E., T. A. Schmidt, C. K. Koç. Generating Elliptic Curves of Prime Order. – In: Proc. of InInternational Workshop on Cryptographic Hardware and Embedded Systems, 14 May 2001. Berlin, Heidelberg, Springer, pp. 142-158.10.1007/3-540-44709-1_13
]Search in Google Scholar
[
47. Alekseev, E. K., V. D. Nikolaev, S. V. Smyshlyaev. On the Security Properties of Russian Standardized Elliptic Curves. Vol. 9, 2018, No 3, pp. 5-32.10.4213/mvk260
]Search in Google Scholar
[
48. Petitcolas, F. La cryptographie Militaire. 1883.
]Search in Google Scholar
[
49. Yin, E. Curve Selection in Elliptic Curve Cryptography. San Jose State University, Project, Spring, 2005.
]Search in Google Scholar
[
50. Abhishek, K., E. G. Raj. Computation of Trusted Short Weierstrass Elliptic Curves for Cryptography. – Cybernetics and Information Technologies, Vol. 21, 2021, No 2, pp. 70-88.10.2478/cait-2021-0020
]Search in Google Scholar