On the security properties of Russian standardized elliptic curves

In the last two decades elliptic curves have become a necessary part of numerous cryptographic primitives and protocols. Hence it is extremely important to use the elliptic curves that do not weaken the security of such protocols. We investigate the elliptic curves used with GOST R 34.10-2001, GOST R 34.10-2012 and the accompanying algorithms, their security properties and generation process.