Analysis of secret-key algorithm vulnerability in RSA-cryptosystems

This work describes results of analysis of public - and private-key generation algorithms in asymmetric RSA-cryptosystems. We demonstrated that RSA-cryptosystem can be compromised not only by large number factorization. Under Euler function value is multiple to 10, there is a probability of occurrence of two same public keys, when formed open exponents end in 1 or 9. 8 lemmas are described and proven with theoretical justification of same public keys occurrence. It is recommended to produce a complete test on full match of public- and private-key during key generation to improve vulnerability protection of cryptosystem.