Cryptography and canonical number systems in quadratic fields

This paper proposes an encryption method based on representation of messages in the canonical number systems (CNS) in quadratic fields. The essence of the encryption method is conversion of the representation of integers from the conventional number system to their representation in the CNS in a certain quadratic field. A sufficiently wide range of CNS with a given number of digits ensures resistance of the method to "accidental guessing" of the secret keys. Nonlinear nature of the conversion ensures its resistance to frequency analysis.