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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2015, Number 3, Pages 60–71
(Mi basm397)
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This article is cited in 2 scientific papers (total in 2 papers)
Research articles
Generating cubic equations as a method for public encryption
N. A. Moldovyana, A. A. Moldovyanb, V. A. Shcherbacovc a St. Petersburg Institute for Informatics and Automation of Russian Academy of Sciences, 14 Liniya, 39, St. Petersburg 199178, Russia
b ITMO University, Kronverksky pr., 10, St. Petersburg, 197101, Russia
c Institute of Mathematics and Computer Science Academy of Sciences of Moldova, Academiei str. 5, MD-2028, Chişinău, Moldova
Abstract:
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.
Keywords and phrases:
cryptography, ciphering, public encryption, deniable encryption, public key, cubic equation, Galois field, factoring problem.
Received: 02.10.2015
Citation:
N. A. Moldovyan, A. A. Moldovyan, V. A. Shcherbacov, “Generating cubic equations as a method for public encryption”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2015, no. 3, 60–71
Linking options:
https://www.mathnet.ru/eng/basm397 https://www.mathnet.ru/eng/basm/y2015/i3/p60
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Abstract page: | 328 | Full-text PDF : | 55 | References: | 37 |
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