The first step is to sort out the current status and issues of Ethereum and formulate an appropriate approach. The current PQC discussion is summarized here. Furthermore, as of 2022, already discussed NIST Post-Quantum-Cryptography Standardization Process and What it means for Ethereum.
The challenge is that ECDLP can be solved by Shore’s algorithm, which requires a change in Ethereum’s signature scheme. Falcon, a lattice-based signature scheme, has emerged as a strong candidate due to its efficiency and compact size.
The problem is how to deploy it in the current Ethereum, and the following methods have been proposed.
- The Account Abstraction
- Hard fork
- Hybrid
The advantages and disadvantages of integrating Falcon into Ethereum are here.