Algebraic models of asymmetric cryptographic systems - Яремчук, Юрій Євгенович (Ukrainian Information Security Research Journal, 2014)
Modeling cryptographic methods on the level of algebraic structures enables a deeper understanding of the principles of their construction, operation features, and exploring their properties. The existing algebraic models of asymmetric cryptographic systems do not provide the full possibilities of their use. We consider an algebraic model of public distribution of secret keys, as well as an algebraic model of asymmetric encryption, authentication of interaction parties and digital signing as polybasic universal algebras. Based on the presented algebras, we considered existing cryptosystem models, as well as proposed models of distribution of secret keys and asymmetric encryption, using mathematical tools of recurrent U -and V sequences. We proposed a different version of the authentication model of interaction parties and of digital signing, using mathematical tools of recurrent V sequences, which in different occasions provide a simplification of computation, and enhance cryptographic reliability compared with the known analogs.