Generating cubic equations as a method for public encryption

The paper introduces a new method for public encryption in which the enciphering process is performed as generating coefficients of some cubic equation over finite ring and the deciphering process is solving the equation. Security of the method is based on difficulty of factoring problem, namely, difficulty of factoring a composite number $n$ that serves as public key. The private key is the pair of primes $p$ and $q$ such that $n=pq$. The deciphering process is performed as solving cubic congruence modulo $n$. Finding roots of cubic equations in the fields $GF(p)$ and $GF(q)$ is the first step of the decryption. We have described a method for solving cubic equations defined over ground finite fields. The proposed public encryption algorithm has been applied to design bi-deniable encryption protocol.