Affine Ciphers Based on Quadratic and Cubic Functions

Currently, affine ciphers, despite their vulnerabilities, are an effective means of cryptographic protection of information in cases where the critical parameter is the time of encryption and data transmission. Our work is devoted to the problem of development of nonlinear affine ciphers based on quadratic and cubic functions, as well as the elimination of ambiguities that arise during decryption. The study demonstrates that the use of nonlinear functions in cryptographic transformations allows for an increase in the number of key variants and, accordingly, the cryptographic strength of the proposed algorithm. Conditions that the coefficients of the nonlinear equations and the modulus values must satisfy are defined. A method for unambiguous decryption of quadratic affine ciphers is developed that is based on double numbering of the alphabet symbols. This doubles the modulus value but allows for the selection of a range of numerical codes, on which quadratic residues can be uniquely determined. Examples of quadratic and cubic affine ciphers are provided.