Analogue of the RSA-cryptosystem in quadratic unique factorization domains
In the article, the analogue of a RSA-cryptosystem in general quadratic unique factorization domains is obtained. A scheme of digital signature on the basis of the generalized RSA-cryptosystem is suggested. The analogue of Wiener's theorem on low private key is obtained. We prove the equivalence of the problems of generalized RSA-modulus factorization and private key search when the domain of all algebraic integer elements of the quadratic field is Euclidean. A method to secure the generalized RSA-cryptosystem of the iterated encryption cracking is proposed.