Author(s)

Dandan Su

Corresponding Author

Dandan Su

ABSTRACT

In modern cryptography, the periodic property of polynomial is very important to the security of cryptosystems. RSAI, one of the most famous public key cryptosystems, has been extended to algebraic integer rings and integer matrix rings. In this paper, the factorization of polynomials over finite fields is discussed, and the number of irreducible polynomials and primitive polynomials over finite fields, the judgment of primitive polynomials, and the method of constructing high-order irreducible polynomials by using lower-order irreducible polynomials are given. The simulated RSA public key cryptosystem is improved, and the problem of ciphertext expansion is solved by properly selecting parameters. The security of the improved system is discussed, and a new simulation of RSA is given, which has no ciphertext expansion and is closer to the standard RSA concept.

KEYWORDS

Rsa, Security, Finite field