An augmented approach for pseudo-free groups in smart cyber-physical system

The contemporary advancement in smart technology has led to a greater business prospective. Smart system like cyber-physical system (CPS) has become prevalent in many area of applications. Challenges in integration of CPS with group of network has physical components to sense the state of changes in the real world is paving way towards the introduction of enhanced security mechanism. In this paper, we propose a security framework for group of network is a pseudo-free to communicate with the cyber physical system to assure high security. Pseudo-freeness is a very strong assumption of security used in cryptography. Group is said to be pseudo-free group, if an adversary who is allowed to see group description, is unable to solve non-trivial equations. Non-trivial equations are the equations that have no solution in a free group. The notion of pseudo-freeness was introduced with few open problems whether such groups exists in cryptosystem or not. The conjecture that the RSA group is pseudo-free has been settled for case of static adversary who is given only the group description and its goal is to come up with an equation and solution. Later on the notion of pseudo-freeness has been extended to adaptive adversary for case of univariate equations. In case of adaptive pseudo-free groups, the adversary learns solutions of some non-trivial equations before producing a new equation. Here we make extension to the notion of pseudo-free groups from univariate to multivariate equations and system of equations in face of adaptive adversary. We define and prove the security of adaptive pseudo-free groups for case of multivariate equations and system of equations. According to the results, this framework can be used as a system design for a group to have strong security with cyber physical system.