An Energy Efficient Authentication Scheme using Chebyshev Chaotic Map for Smart Grid Environment

As one of the important applications of Smart grid, charging between electric vehicles has attracted much attention. However, authentication between vehicle users and an aggregator may be vulnerable to various attacks due to the usage of wireless communications. In order to reduce the computational costs yet preserve required security, the Chebyshev chaotic map based authentication schemes are proposed. However, the security requirements of Chebyshev polynomials bring a new challenge to the design of authentication schemes based on Chebyshev chaotic maps. To solve this issue, we propose a practical Chebyshev polynomial algorithm by using a binary exponentiation algorithm based on square matrix to achieve secure and efficient Chebyshev polynomial computation. We further apply the proposed algorithm to construct an energy-efficient authentication and key agreement scheme for smart grid environments. Compared with state-of-the-art schemes, the proposed authentication scheme effectively reduces the computational costs and communication costs by adopting the proposed Chebyshev polynomial algorithm. Furthermore, the ProVerif tool is employed to analyze the security of the proposed authentication scheme. Our experimental results justified that our proposed authentication scheme can outperform state-of-the-art schemes in terms of the computational overhead while achieving privacy protection.