Quantum-Resistant Updatable Public Keys: Enhancing the Quisquis Protocol with LWE-Based Security

The advent of quantum computing presents significant challenges to current cryptographic systems, particularly those based on the Discrete Logarithm Problem (DLP), which underpins the security of many cryptocurrencies. In response, we propose a quantum-resistant adaptation of the Updatable Public Key (UPK) primitive in the Quisquis cryptocurrency protocol. This adaptation transitions from a DLP-based security model to one grounded in the Learning With Errors (LWE) assumption, which is believed to be secure against quantum attacks. Our LWE-based UPK scheme preserves the key advantages of Quisquis, including the ability to update public keys in a publicly verifiable manner while maintaining their indistinguishability from freshly generated keys. We discuss the challenges introduced by this transition, particularly the accumulation of noise during key updates, and outline future work to address these issues. Our work ensures that Quisquis remains a robust and efficient solution for privacy-preserving transactions in a post-quantum world.