GRS Code-Based Digital Signature System Over GF(q)

Most current public key schemes are theoretically vulnerable to potential attacks on quantum computer operations.Post-quantum public key cryptosystems provide defenses against these attacks.One of the most intensively researched cryptographic algorithms against quantum computing attacks is code-based public key cryptography.The main issue today is determining how to select parameters that strike a balance between effectiveness and security.In practice,no cryptographic scheme has yet been developed that perfectly balances these two aspects.The main reason for this is that the public key size is far too large to be widely used.However,the algorithm’s security,encryption,and decryption performance are superior to other types of public key cryptosystems.Code-based digital signature schemes are widely used in global intelligent infrastructure services that are integrated into the Internet of Things(Io T),primarily for the creation of special signatures or authentication schemes.Vehicle Ad Hoc Network(VANET)is a classic Io T application that has been at the forefront of technological advancement in recent years,and VANET services include numerous special signature schemes.However,it continues to face security and privacy concerns.As a result,preparations for privacy-preserving services based on post-quantum cryptographic primitives should begin immediately,and some privacy-preserving services that are resistant to potential future threats should be designed.To begin,this paper will investigate and select generalized Reed-Solomon(GRS)codes over the q-ary Galois Field(GF(q)),Build a code-based classic public key cryptographic signature algorithm(CFS algorithm)and investigate its feasibility and related performance optimization,as well as provide a complete security proof and analysis.Constructing a cryptographic algorithm based on the GF(q)code class can effectively reduce the public key size while maintaining security,which is advantageous for the application of related algorithms.To create the digital signature,we will use an iterative search method to find the error vector corresponding to one of the GRS code syndromes.Using the GRS code on GF(q)can provide more parameter flexibility.This scheme has higher security and a smaller public key size when compared to other code-based digital signature schemes.The public key size is only 4.1 percent of the original CFS scheme in the case of slightly improved security.Second,given the scarcity of computing and storage resources in VANETs,as well as the high demand for privacy protection,this paper proposes a traceable code-based VANET ring signature scheme to guard against quantum computing attacks.Quick verification that is appropriate for VANET application scenarios.Our scheme allows users to include tracking information in their signatures,which is a user-friendly feature.A trusted third party can only implement the tracking function if the user enters the correct information.As a result,the scheme described in this paper can track users in special cases while maintaining the anonymity of ring signatures.Finally,the proposed scheme is subjected to a performance and security analysis in this paper.By calculating the three indicators of signature complexity,security,and public key size,this paper demonstrates that the proposed scheme is feasible,security,and efficient.Feasible imply that using GRS codes on GF(q)to build a code-based digital signature scheme can produce valid signatures.Security means that this scheme has a smaller public key size,and it is semantically and computationally security.Efficient means that under the premise of ensuring security,the proposed scheme has a smaller number of public keys.A code-based signature scheme’s security is determined not only by its semantic security,but also by the security of the difficult problems associated with the scheme.This paper first performs a provable security analysis on the scheme,demonstrating that it can be reduced to corresponding difficult problems.And,as a result of the different code classes chosen,the difficulty of solving the related difficult problems varies.The paper then goes on to analyze the most efficient attack method for solving the difficult problem,as well as fully proving the security of the proposed scheme.