ABSTRACT
RSA is one of the most common and widespread asymmetric cryptosystems. A lot of cryptographic protocols that deal with encryption, digital signature, and distribution of key information are based on RSA scheme. A research by a group of scientists led by Arjen Lenstra confirms the problem of RSA implementation, namely generation of parameters that will ensure the system’s security in practice. From among 11.5 million of RSA key certificates under research there has been found more than 26000 vulnerable keys with size of 1024 bits and 10 keys with size of 2048 bits. Factorization cost estimate is explained first of all, by the lack of flexibility of cloud computing services order, and, secondly, by the direct use of existing implementations of the algorithm general number field sieve for cloud technologies. The interest of assessing RSA security in practice is the highlighted issue of size or rather the nature of size growth of the set of secure crypto parameters.
