IMCS/Publications/BASM/Issues/BASM n.3 (79), 2015/

Generating Cubic Equations as a Method for Public Encryption

Authors: N. A. Moldovyan, A. A. Moldovyan, Şcerbacov Victor


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.

N. A. Moldovyan
St. Petersburg Institute for Informatics
and Automation of Russian Academy of Sciences
14 Liniya, 39, St.Petersburg 199178

A. A. Moldovyan
ITMO University
Kronverksky pr., 10, St.Petersburg, 197101

V. A. Shcherbacov
Institute of Mathematics and Computer Science
Academy of Sciences of Moldova
Academiei str. 5, MD−2028 Chisinau


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