Multivariate Cryptography-Based Anonymous Certificate Scheme

A quantum-safe anonymous certificate design for privacy-sensitive applications

Abel C. H. Chen· 2026· DOI 10.48550/arXiv.2607.13554

The core problem

As quantum computing technology continues to mature, the US National Institute of Standards and Technology (NIST) has outlined a migration timeline for Post-Quantum Cryptography (PQC), recommending the deprecation of certain elliptic curve cryptography (ECC) by 2030. Privacy-sensitive application scenarios, such as vehicular communications, require the use of anonymous certificates. However, existing anonymous certificate schemes are still largely based on ECC, which will become vulnerable to quantum attacks. Therefore, this study proposes a multivariate cryptography-based anonymous certificate scheme, aiming to design quantum-safe anonymous certificates suitable for privacy-sensitive application services. The proposed scheme is supported by rigorous mathematical proofs and illustrated with computational cases.

The study presents computational cases that validate the proposed scheme. The results show that the multivariate cryptography-based anonymous certificate scheme can efficiently generate and verify anonymous certificates. The computational overhead is comparable to existing ECC-based schemes, while providing quantum resistance. The mathematical proofs confirm the security properties, including anonymity, unforgeability, and resistance to quantum adversaries. The scheme is particularly suitable for vehicular communications, where privacy and security are paramount. The computational cases include key generation, certificate issuance, and anonymous authentication, demonstrating the practical applicability of the scheme.

As quantum computing technology continues to mature, the US National Institute of Standards and Technology (NIST) has outlined a migration timeline for Post-Quantum Cryptography (PQC), recommending the deprecation of certain elliptic curve cryptography (ECC) by 2030. Privacy-sensitive application scenarios, such as vehicular communications, require the use of anonymous certificates. However, existing anonymous certificate schemes are still largely based on ECC, which will become vulnerable to quantum attacks. Therefore, this study proposes a multivariate cryptography-based anonymous certificate scheme, aiming to design quantum-safe anonymous certificates suitable for privacy-sensitive application services. The proposed scheme is supported by rigorous mathematical proofs and illustrated with computational cases.

The proposed scheme leverages multivariate cryptography, which is based on the difficulty of solving systems of multivariate polynomial equations over finite fields. The core mathematical problem can be expressed as:

The proposed scheme addresses the imminent threat of quantum computing to existing anonymous certificate schemes. By leveraging multivariate cryptography, it provides a quantum-safe alternative that maintains the privacy requirements of applications like vehicular communications. The rigorous mathematical proofs and computational cases support its security and efficiency. However, the scheme's performance in large-scale deployments and its resistance to side-channel attacks require further investigation. Future work includes optimizing the polynomial system for faster computations and integrating the scheme into existing PQC standards. The architecture of the scheme can be visualized as follows: This diagram illustrates the flow of certificate generation, issuance, and anonymous authentication.

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