(untitled) (Al-Mansour Journal, 2023)
After the 1973, there are several Public Key Cryptosystems are developments, all systems based on hard mathematical problems such as Discrete Logarithm, Integer Factorization, Subset, or Elliptic Curve Discrete Logarithm Problem. Which problems are defined over Finite Abelian Group. In this paper we proposes new concept in the public key system that is depend on complex numbers field. The complex numbers can be define over Finite Field to construct an Abelian Group under addition and multiplication operations, we call it Complex Finite Field. There are a hard mathematical problem is proposed in the constructed group we call it Complex Discrete Logarithm Problem. After that we design public key cryptosystems based on the suggested problem. Also it appears to offer equal security for a far smaller bit size, with problem harder than DLP.