Computer Science Department King Abdulla II School for Information Technology The University of Jordan, Amman, Jordan

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Abstract—The confidentiality of information is an important aspect of security. One way to achieve the confidentiality is through restricting access to information to the authorized users only. Access control can be enforced by using encryption. In this case, all the information is encrypted and keys are assigned to users such that each key reveals the authorized part of the information. Key assignment can be classified as key-based or object-based schemes based on the focus of the scheme. Sabri and Khedri [1] present algebraic structures to specify algebraically cryptosystems by capturing the common properties of ciphers, secrets and keys. Also, these structures are used for the analysis of security properties in objectbased key assignment schemes. However, these structures are abstract, and no linkage has been proposed to the existing cryptosystems. In this paper, we extend their work by giving concrete models for their algebraic structures. We give concrete models to Vigen`ere, transposition ciphers, DES and RSA cryptosystems. Also, we investigate the effects of extra algebraic properties that some cryptosystems may have on the security analysis of object-based schemes.

Index Terms—Object-based key assignment schemes, verification, cryptography, algebraic structures.

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Cite: Khair Eddin Sabri, "Algebraic Analysis of Object-Based Key Assignment Schemes," Journal of Software vol. 9, no. 8, pp. 2033-2042, 2014.