Some Public-key Cryptosystems Over Finite Fields

Abstract

In this paper, we present two public-key cry ptosystems over finite fields. First of them is based on polynomials. The presented system also considers a digital signature algorithm. Its security is based on the difficulty of finding discrete logarithms over GF(qd+1) with sufficiently large q and d. Is is also examined along with comparison with other polynomial based public-key systems. The other public-key cryptosystem is based on linear codes. McEliece studied the first code-based public-key cryptosystem. We are inspired by McEliece system in the construction of the new system. We examine its security using linear algebra and compare it with the other code-based cryptosystems. Our new cryptosystems are too reliable in terms of security.