The security of the RSA cryptosystem and electronic signature

Electronic document has a significant use in practice. It should fulfil requirements similar to those of paper document. An essential element of electronic document security is the electronic signature. This article presents the discussion on the security of cryptographic protocol - electronic signature - taking into account the possibilities of an accompanying attack on an asymmetric cryptosystem with an application of factorization and Euler's function. The discussion about potential vulnerabilities in verification of the electronic signature from the point of view of weak and strong RSA keys will be presented as well. This article is taking into account the problem of key length and the quality of the components for the public key. The considerations will be presented from the point of view of an attack on the electronic signature using standalone computer and a group of computers in network. The computation of Euler's function in an algorithm using parallel mode will be presented. In this article we show a relation between investment in security infrastructure and the value of protected information.