Public Key Identification Scheme Based on Quaternion Properties

Abstract

Public key cryptosystems are based on the difficulty of solving complicated problems in mathematics. As examples there are Integer Factorization Problem (IFP), Discrete Logarithm Problem (DLP) in finite multiplicative group and Elliptic Curved Discrete Logarithm Problem (ECDLP). More recently, different algorithms have been introduced in order to solve eth problems. These algorithms are exponential and sub-exponential with regard to their complexities. But according to the new research, in the near future, new hardwares and new methods will come to decrease the complexity of solving the problems. Therefore, new difficult problems and their application in public key cryptosystems are being investigated. Identification protocols are one of the much applicable protocols in cryptography. The identification protocol controls the users entering a system. In this paper, using quaternion numbers, a difficult problem and based on it a new identification scheme will be introduced.

Keywords : Quaternion, Rotation Matrix, Norm, Identification.

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