Methods for solving equations with errors based on the HHL algorithm

To solve polynomial systems,Harrow,Hassidim,and Lloyd(HHL)proposed a quantum algorithm called HHL algorithm.Based on the HHL algorithm,Chen et al.presented an algorithm,the solving the Boolean solutions of polynomial systems(PoSSoB)algorithm.Furthermore,Ding et al.introduced the Boolean Macaulay matrix and analyzed the lower bound on the condition number.Inspired by Ding et al.’s research,several related algorithms are proposed in this paper.First,the improved PoSSoB algorithm using the Boolean Macaulay matrix is proved to have lower complexity.Second,for solving equations with errors,a quantum algorithm for the max-polynomial system solving(Max-PoSSo)problem is proposed based on the improved PoSSoB algorithm.Besides,the Max-PoSSo algorithm is extended to the learning with errors(LWE)problem and its special case,the learning parity with noise(LPN)problem,providing a quantitative criterion,the condition number,for the security of these basic problems.

Physical layer authentication for automotive cyber physical systems based on modified HB protocol

Automotive cyber physical systems(CPSs)are ever more utilizing wireless technology for V2X communication as a potential way out for challenges regarding collision detection,wire strap up troubles and collision avoidance.However,security is constrained as a result of the energy and performance limitations of modem wireless systems.Accordingly,the need for efficient secret key generation and management mechanism for secured communication among computationally weak wireless devices has motivated the introduction of new authentication protocols.Recently,there has been a great interest in physical layer based secret key generation schemes by utilizing channel reciprocity.Consequently,it is observed that the sequence generated by two communicating parties contain mismatched bits which need to be reconciled by exchanging information over a public channel.This can be an immense security threat as it may let an adversary attain and recover segments of the key in known channel conditions.We proposed Hopper-Blum based physical layer(HB-PL)authentication scheme in which an enhanced physical layer key generation method integrates the Hopper-Blum(HB)authentication protocol.The information collected from the shared channel is used as secret keys for the HB protocol and the mismatched bits are used as the induced noise for learning parity with noise(LPN)problem.The proposed scheme aims to provide a way out for bit reconciliation process without leakage of information over a public channel.Moreover,HB protocol is computationally efficient and simple which helps to reduce the number of exchange messages during the authentication process.We have performed several experiments which show that our proposed design can generate secret keys with improved security strength and high performance in comparison to the current authentication techniques.Our scheme requires less than 55 exchange messages to achieve more than 95%of correct authentication.