In IEEE 1609.2 and IEEE 1609.2.1 standards for Vehicle-to-everything (V2X) secure communication, various security algorithms based on Elliptic Curve Cryptography (ECC) have been adopted and designed. To enhance the efficiency of the Security Credential Management System (SCMS), this study evaluates the computational time for key generation, key expansion, signature generation, and signature verification under different security strengths. This study discusses relevant techniques based on Elliptic Curve Qu-Vanstone (ECQV) implicit certificates, analyzes the length of uncompressed elliptic curve points, compressed elliptic curve points, explicit certificates, and implicit certificates. Furthermore, this study proposes mathematical models to demonstrate the probability of ECQV cracking and provides suggestions for mitigating ECQV cracking risks.

翻译：在针对车联网（V2X）安全通信的IEEE 1609.2及IEEE 1609.2.1标准中，已采纳并设计了多种基于椭圆曲线密码学（ECC）的安全算法。为提升安全凭证管理系统（SCMS）的运行效率，本研究评估了不同安全强度下密钥生成、密钥扩展、签名生成及签名验证的计算耗时。本研究探讨了基于椭圆曲线Qu-Vanstone（ECQV）隐式证书的相关技术，分析了非压缩椭圆曲线点、压缩椭圆曲线点、显式证书及隐式证书的长度。此外，本研究提出了用于展示ECQV破解概率的数学模型，并为降低ECQV破解风险提供了建议。