We are excited to share our latest work, Anonymous PGC, which has been accepted by EUROCRYPT 2026.
Paper (ePrint): https://eprint.iacr.org/2025/884
Context & Motivation
In 2019, our team proposed PGC (ESORICS 2020), introducing Twisted ElGamal to achieve confidential transfers. This work was concurrent with Zether and its core design was later adopted by Solana for their ZK-token extension.
However, existing account-based privacy solutions like Anonymous Zether (IEEE S&P 2021) still face critical hurdles:
Weak Security Model: Vulnerability to rogue-key attacks due to randomness reuse.
Limited Anonymity: Restrictive parity constraints on participant indices.
Lack of Multi-receiver Support: Difficulty in supporting t \geq 2t≥2 receivers efficiently.
Anonymous PGC resolves these challenges by introducing a new framework and novel ZK primitives.
Key Contributions
Solving the GK Generalization Open Problem: We generalized the Groth-Kohlweiss (GK) 11-out-of-nn proof (EUROCRYPT 2015) to the kk-out-of-nn case.
- Range-Proof Friendly (RPF): It seamlessly “solders” with off-the-shelf range proofs (e.g., Bulletproofs), addressing a critical gap in prior work.
Efficient Heterogeneous kk-out-of-nn Proof: We extended the Attema-Cramer-Fehr (ACF) proof (CRYPTO 2021) to support Distinct Group Homomorphisms (DGH).
This allows proving statements across different public keys without ad-hoc PoKs.
We reduced complexities from O(n(n-k))O(n(n−k)) to O(n)O(n) while maintaining logarithmic proof size.
Performance Improvements: Compared to Anonymous Zether (for n=64n=64 and t=8t=8):
2.4x faster in transaction generation.
5.7x faster in verification.
2.2x reduction in transaction size.
Integration with Ethereum
As the community explores Privacy Pools and Stealth Addresses, the efficiency of kk-out-of-nn proofs is paramount. Anonymous PGC offers a “sweet spot” by being account-native and significantly more efficient than circuit-based or FHE-based alternatives.
We are currently refining the implementation and are looking for research grants or advisory roles to assist with the engineering integration into the Ethereum ecosystem.
Any feedback will be highly apprecitaed!
