Code-Based Butterfly Key Expansion for Pseudonymous Certificates

As quantum computing technology continues to advance, Shor's quantum algorithm poses a significant threat to mainstream cryptographic methods, including RSA and elliptic curve cryptography. Consequently, post-quantum cryptography (PQC) has emerged as an inevitable trend for the future. Among PQC approaches, lattice-based cryptography and hash-based cryptography have already been standardized, while code-based cryptography remains a candidate for standardization. In light of these developments, this study proposes a Code-based Butterfly Key Expansion (CBKE) mechanism, built on code-based cryptography principles. The proposed method enables a registration authority (RA) to expand an original code-based caterpillar public key into a code-based cocoon public key, achieving anonymity for entities other than the RA. Subsequently, a certificate authority further expands the code-based cocoon public key into a code-based butterfly public key, which is then embedded in a pseudonymous certificate as the public key for the end entity. This approach ensures anonymity for both the RA and other entities. To enhance computational efficiency, the study proposes a random invertible matrix generation algorithm with a time complexity of O(n). This algorithm achieves high efficiency and anonymity without increasing the key length, thereby addressing the computational demands of the proposed method effectively.