Encryption based on Walks in Algebraic GRAphs (EWAGRA) is used for protection of authors’ rights, access to electronic books or documents located at certain knowledge base (Information Quality Assurance Support Systems of a university, digital library supporting distance education, various digital archivas and etc). The method allows to generate nonlinear stream ciphers, which have some similarity with a one-time pad: different keys produce distinct ciphertexts from the same plaintext. In contrast to the case of a one-time pad the length of the key is flexible and the encryption map is a nonlinear polynomial map, which order is growing with the growth of the dimension n of the plainspace. The encryption has good resistance to attacks of the adversary when he has no access to plaintext space or has rather small number intercepted plaintext–ciphertext pairs. It is known that encryption and decryption maps are cubical maps. So, interception of n³ + o(n) plaintext–ciphertext pairs allows to conduct a plain linearisation attack for finding the inverse map. We consider the idea of modification of this encryption algorithm after sending each message without use key exchange protocols. So the new algorithm is resistant to plain linearisation attacks. Additionally, we observe some new multivariate El Gamal type cryptosystems and cryptosystems based on highly nonlinear modifications of graph bases cubical maps