Authors:
George Stergiopoulos
;
Miltiadis Kandias
and
Dimitris Gritzalis
Affiliation:
Athens University of Economics & Business, Greece
Keyword(s):
Cryptosystem, Complex Number, Complex Logarithm, Security.
Related
Ontology
Subjects/Areas/Topics:
Applied Cryptography
;
Cryptographic Techniques and Key Management
;
Data and Application Security and Privacy
;
Data Engineering
;
Data Protection
;
Databases and Data Security
;
Formal Methods for Security
;
Information and Systems Security
Abstract:
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 cryptosystem,
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 Fei
stel 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.
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