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Regular version of the site

Working paper

Research on OpenSSL Elliptic Curves for Compliance with the Russian National Digital Signature Standard

Cryptology ePrint Archive. 2020/097. International Association for Cryptologic Research, 2020. No. 097.
Malakhov S.
The survey deals with elliptic curves which are implemented in the OpenSSL 1.1.1d software library. The objective of this work is to highlight the elliptic curves which comply with the Russian national digital signature standard, namely the GOST R 34.10--2012. For this reason the paper focuses on the OpenSSL elliptic curves over a finite field of a prime order and provides the results of testing those curves for compliance with the GOST R 34.10--2012 requirements. Two cases are observed. The first case covers a complete set of restrictions imposed on elliptic curves parameters, whereas the second one differs in that a restriction on a bit length of a number of points on the curve is omitted. For both cases the paper presents tables which list the curves tested along with corresponding match marks. In order to conduct tests the Wolfram Mathematica computing system was employed, and the Wolfram language source code is given in the appendices. Note, that the paper does not address to a rationale of the requirements of the standard nor does it focus on the parameters generation issues.