# CRYPTOGRAPHIC PROTOCOLS BASED ON SOLVING OF CUBIC EQUATIONS

There are considered protocols for public and deniable encryption with generating ciphertext in form of the set of the coefficients of cubic congruence modulo an integer that is difficult for factoring. It is proposed a general approach to constructing analogous protocols using modulo computations over binary polynomials. There are discussed peculiarities of solving cubic equations in finite binary fields. A general approach of the construction of an algorithm for solving cubic equations in finite binary fields is shown, which greatly simplifies the procedure of solving equations. It is proposed a novel digital signature protocol with cubic verification equation of general type, which is based on simultaneous encryption of both secret and fictitious messages. It is proposed to calculate the stability estimates of the developed algorithm of the electronic digital signature and algorithms based on calculations over binary polynomials.

**Authors:** N. A. Moldovyan, D. S. Budchan

**Direction:** Informatics and Computer Technologies

**Keywords:** Cryptography, encryption, deniable encryption, digital signature, cubic equation, binary finite field

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