Approaching encryption through complex number logarithms

In this paper, we approach encryption through the properties of complex logarithm and the complex plane. We introduce a mathematical concept to be used in cryptography. As an example, we propose a new crypto-system, by mixing known robust techniques such as chain-block encryption and AES-like structures together with complex exponentiation to provide robust encryption of plaintext messages. The proposed method implements encryption by transforming complex numbers into position vectors in a two-dimensional Cartesian coordinate system called the complex plane and utilizes the properties of the complex logarithm together with well-defined techniques from global standards (such as AES), in order to ensure robustness against cryptanalysis. This is made possible without implementing any computational costly algorithm. This has two important consequences: First, it may open up viable solutions to known limitations in cryptography such as relatively complex key schedules (i.e. in Feistel ciphers) and the need for relatively large keys used in encryption methods (bit-wise). Second, it proposes a new mathematical concept that can be used in future cryptosystems. An example of this is the preliminary cryptosystem found in this paper. We present its algorithm and show that it can be implemented using fast mechanisms for encryption and decryption.