  In recent years, the elliptic curve Qu-Vanstone (ECQV) implicit certificate
scheme has found application in security credential management systems (SCMS)
and secure vehicle-to-everything (V2X) communication to issue pseudonymous
certificates. However, the vulnerability of elliptic-curve cryptography (ECC)
to polynomial-time attacks posed by quantum computing raises concerns. In order
to enhance resistance against quantum computing threats, various post-quantum
cryptography methods have been adopted as standard (e.g. Dilithium) or
candidate standard methods (e.g. McEliece cryptography), but state of the art
has proven to be challenging to implement implicit certificates using
lattice-based cryptography methods. Therefore, this study proposes a
post-quantum cryptography McEliece-Chen (PQCMC) based on an efficient random
invertible matrix generation method to issue pseudonymous certificates with
less computation time. The study provides mathematical models to validate the
key expansion process for implicit certificates. Furthermore, comprehensive
security evaluations and discussions are conducted to demonstrate that distinct
implicit certificates can be linked to the same end entity. In experiments, a
comparison is conducted between the certificate length and computation time to
evaluate the performance of the proposed PQCMC. This study demonstrates the
viability of the implicit certificate scheme based on PQC as a means of
countering quantum computing threats.
