The authors of this article focus on the analysis of safety weaks of digital signature schemes used within e-Government service in condition of Slovak republic. Main part is orientated on the possibility of attacks on eID card with using RSA digital signature scheme what was in the last months very frequently medialized in Slovakia. In the practical part on the base of mathematically description is analysed possible weaks of RSA digital signature schemes especially complexity of factorization problems dependence of length of key is describe and compare with more effectiveness ECDSA scheme. On the base of studies the authors mentioned the recommendations for parameters selection of very often used digital signature schemes focus on access to safety-critical applications supported during process of digitalization of e-Government in Slovak republic.
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